Journal articles on the topic 'Early Exercise Boundary'

American call options are financial derivatives that give the holder the right but not the obligation to buy an underlying security at a pre-determined price. They differ from European options in that they may be exercised at any time prior to their expiration, rather than only at expiration. Their value is described by the Black-Scholes PDE together with a constraint that arises from the possibility of early exercise. This leads to a free boundary problem for the optimal exercise boundary, which determines whether or not it is beneficial for the holder to exercise the option prior to expiration. However, an exact solution cannot be found, and therefore by using asymptotic techniques employed in the study of boundary layers in fluid mechanics, we find an asymptotic expression for the location of the optimal exercise boundary and the value of the option near to expiration.

In many democratic parliamentary systems, election timing is an important decision availed to governments according to sovereign political systems. Prudent governments can take advantage of this constitutional option in order to maximize their expected remaining life in power. The problem of establishing the optimal time to call an election based on observed poll data has been well studied with several solution methods and various degrees of modeling complexity. The derivation of the optimal exercise boundary holds strong similarities with the American option valuation problem from mathematical finance. A seminal technique refined by Longstaff and Schwartz in 2001 provided a method to estimate the exercise boundary of the American options using a Monte Carlo method and a least squares objective. In this paper, we modify the basic technique to establish the optimal exercise boundary for calling a political election. Several innovative adaptations are required to make the method work with the additional complexity in the electoral problem. The transfer of Monte Carlo methods from finance to determine the optimal exercise of real-options appears to be a new approach.

This paper proposes an innovative algorithm that significantly improves on the approximation of the optimal early exercise boundary obtained with simulation based methods for American option pricing. The method works by exploiting and leveraging the information in multiple cross-sectional regressions to the fullest by averaging the individually obtained estimates at each early exercise step, starting from just before maturity, in the backwards induction algorithm. With this method, less errors are accumulated, and as a result of this, the price estimate is essentially unbiased even for long maturity options. Numerical results demonstrate the improvements from our method and show that these are robust to the choice of simulation setup, the characteristics of the option, and the dimensionality of the problem. Finally, because our method naturally disassociates the estimation of the optimal early exercise boundary from the pricing of the option, significant efficiency gains can be obtained by using less simulated paths and repetitions to estimate the optimal early exercise boundary than with the regular method.

AbstractWe present qualitative and quantitative comparisons of various analytical and numerical approximation methods for calculating a position of the early exercise boundary of American put options paying zero dividends. We analyse the asymptotic behaviour of these methods close to expiration, and introduce a new numerical scheme for computing the early exercise boundary. Our local iterative numerical scheme is based on a solution to a nonlinear integral equation. We compare numerical results obtained by the new method to those of the projected successive over-relaxation method and the analytical approximation formula recently derived by Zhu [‘A new analytical approximation formula for the optimal exercise boundary of American put options’, Int. J. Theor. Appl. Finance9 (2006) 1141–1177].

A new stopping problem and the critical exercise price of American fractional lookback option are developed in the case where the stock price follows a special mixed jump diffusion fractional Brownian motion. By using Itô formula and Wick-Itô-Skorohod integral a new market pricing model is built, and the fundamental solutions of stochastic parabolic partial differential equations are deduced under the condition of Merton assumptions. With an optimal stopping problem and the exercise boundary, the explicit integral representation of early exercise premium and the critical exercise price are also derived. Numerical simulation illustrates the asymptotic behavior of this critical boundary.

We consider the American put with finite time horizon T, assuming that, under an EMM chosen by the market, the stock returns follow a regular Lévy process of exponential type. We formulate the free boundary value problem for the price of the American put, and develop the non-Gaussian analog of the method of lines and Carr's randomization method used in the Gaussian option pricing theory. The result is the (discretized) early exercise boundary and prices of the American put for all strikes and maturities from 0 to T. In the case of exponential jump-diffusion processes, a simple efficient pricing scheme is constructed. We show that for many classes of Lévy processes, the early exercise boundary is separated from the strike price by a non-vanishing margin on the interval [0, T), and that as the riskless rate vanishes, the optimal exercise price goes to zero uniformly over the interval [0, T), which is in the stark contrast with the Gaussian case.

In this paper we develop a Laplace transform method and a finite difference method for solving American option pricing problem when the change of the option price with time is considered as a fractal transmission system. In this scenario, the option price is governed by a time-fractional partial differential equation (PDE) with free boundary. The Laplace transform method is applied to the time-fractional PDE. It then leads to a nonlinear equation for the free boundary (i.e., optimal early exercise boundary) function in Laplace space. After numerically finding the solution of the nonlinear equation, the Laplace inversion is used to transform the approximate early exercise boundary into the time space. Finally the approximate price of the American option is obtained. A boundary-searching finite difference method is also proposed to solve the free-boundary time-fractional PDEs for pricing the American options. Numerical examples are carried out to compare the Laplace approach with the finite difference method and it is confirmed that the former approach is much faster than the latter one.

Using a fast numerical technique, we investigate a large database of investors’ suboptimal nonexercise of short-maturity American call options on dividend-paying stocks listed on the Dow Jones. The correct modeling of the discrete dividend is essential for a correct calculation of the early exercise boundary, as confirmed by theoretical insights. Pricing with stochastic volatility and jumps instead of the Black–Scholes–Merton benchmark cuts the amount lost by investors through suboptimal exercise by one-quarter. The remaining three-quarters are largely unexplained by transaction fees and may be interpreted as an opportunity cost for the investors to monitor optimal exercise.

We consider an optimal stopping problem arising in connection with the exercise of an executive stock option by an agent with inside information. The agent is assumed to have noisy information on the terminal value of the stock, does not trade the stock or outside securities, and maximises the expected discounted payoff over all stopping times with regard to an enlarged filtration which includes the inside information. This leads to a stopping problem governed by a time-inhomogeneous diffusion and a call-type reward. We establish conditions under which the option value exhibits time decay, and derive the smooth fit condition for the solution to the free boundary problem governing the maximum expected reward, and derive the early exercise decomposition of the value function. The resulting integral equation for the unknown exercise boundary is solved numerically and this shows that the insider may exercise the option before maturity, in situations when an agent without the privileged information may not. Hence we show that early exercise may arise due to the agent having inside information on the future stock price.

This paper deals with a new numerical method for the approximation of the early exercise boundary in the American option pricing problem. In more detail, using the mean-value theorem for integrals, we provide a flexible algorithm that allows for reaching a more accurate numerical solution with fewer calculations rather than other previously described methods.

Accurately as well as efficiently calculating the early exercise boundary is the key to the highly nonlinear problem of pricing American options. Many analytical approximations have been proposed in the past, aiming at improving the computational efficiency and the easiness of using the formula, while maintaining a reasonable numerical accuracy at the same time. In this paper, we shall present an approximation formula based on Bunch and Johnson's work [6]. After clearly pointing out some errors in Bunch and Johnson's paper [6], we will propose an improved approximation formula that can significantly enhance the computational accuracy, particularly for options of long lifetime.

British put options are financial derivatives with an early exercise feature whereby on payoff, the holder receives the best prediction of the European put payoff under the hypothesis that the true drift of the stock price is equal to a contract drift. In this paper, we derive simple analytic approximations for the optimal exercise boundary and the option valuation, valid for short expiry times – which is a common feature of most options traded in the market. Empirical results show that the approximations provide accurate results for expiries of at least up to two months.

Following the economic rationale introduced by Peskir & Samee (2011, 2013) we present a new class of barrier options within the British payoff mechanism where the holder enjoys the early exercise feature of American type options whereupon his payoff (deliverable immediately) is the best prediction of the European payoff under the hypothesis that the true drift of the stock price equals a contract drift. Should the option holder believe the true drift of the stock price to be unfavorable (based upon the observed price movements) he can substitute the true drift with the contract drift and minimize his losses. In this paper, we focus on the knock-out put option with an up barrier. We derive a closed form expression for the arbitrage-free price in terms of the rational exercise boundary and show that the rational exercise boundary itself can be characterized as the unique solution to a nonlinear integral equation. Using these results, we perform a financial analysis of the British knock-out put option. We spot some of the trends previously seen in Peskir & Samee (2011) but observe some behavior unique to the knock-out case. Finally, we derive the British put-call and up-down symmetry relations which express the arbitrage-free price and the rational exercise boundary of the British down-and-out call option in terms of the arbitrage-free price and the rational exercise boundary of the British up-and-out put option.

This study presents an efficient method for pricing the American fractional lookback option in the case where the stock price follows a mixed jump diffusion fraction Brownian motion. By using It ô formula and Wick–It ô–Skorohod integral, a new market pricing model is built. The fundamental solutions of stochastic parabolic partial differential equations are estimated under the condition of Merton assumptions. The explicit integral representation of early exercise premium and the critical exercise price are also given. Numerical simulation illustrates some notable features of American fractional lookback options.

A new framework for pricing the American fractional lookback option is developed in the case where the stock price follows a mixed jump-diffusion fraction Brownian motion. By using Itô formula and Wick-Itô-Skorohod integral a new market pricing model is built. The fundamental solutions of stochastic parabolic partial differential equations are estimated under the condition of Merton assumptions. The explicit integral representation of early exercise premium and the critical exercise price are also given. Numerical simulation illustrates some notable features of American fractional lookback options.

AbstractThis paper proposes an alternative characterization of the early exercise premium that is valid for any Markovian and diffusion underlying price process as well as for any parameterization of the exercise boundary. This new representation is shown to provide the best pricing alternative available in the literature for medium- and long-term American option contracts, under the constant elasticity of variance model. Moreover, the proposed pricing methodology is also extended easily to the valuation of American options on defaultable equity and possesses appropriate asymptotic properties.

We study the pricing of the American options with fractal transmission system under two-state regime switching models. This pricing problem can be formulated as a free boundary problem of time-fractional partial differential equation (FPDE) system. Firstly, applying Laplace transform to the governing FPDEs with respect to the time variable results in second-order ordinary differential equations (ODEs) with two free boundaries. Then, the solutions of ODEs are expressed in an explicit form. Consequently the early exercise boundaries and the values for the American option are recovered using the Gaver-Stehfest formula. Numerical comparisons of the methods with the finite difference methods are carried out to verify the efficiency of the methods.

Following the economic rationale of Peskir & Samee [The British put option, Applied Mathematical Finance 18 (6), 537–563 (2011); The British call option, Quantitative Finance 13 (1), 95–109 (2013)], we present a new class of asset-or-nothing put option where the holder enjoys the early exercise feature of American asset-or-nothing put option whereupon his payoff is the ‘best prediction’ of the European asset-or-nothing put option payoff under the hypothesis that the true drift equals a contract drift. Based on the observed price movements, the option holder finds that if the true drift of the stock price is unfavorable, then he can substitute it with the contract drift and minimize his losses. The key to the British asset-or-nothing put option is the protection feature as not only can the option holder exercise at or above the strike price to a substantial reimbursement of the original option price (covering the ability to sell in a liquid option market completely endogenously) but also when the stock price movements are favorable he will generally receive high returns. We derive a closed form expression for the arbitrage-free price in terms of the rational exercise boundary and show that the rational exercise boundary itself can be characterized as the unique solution to a nonlinear integral equation. We also analyze the financial meaning of the British asset-or-nothing put option using the results above and show that with the contract drift properly selected, the British asset-or-nothing put option becomes a very attractive alternative to the classic European/American asset-or-nothing put option.

As the American early exercise results in a free boundary problem, in this article we add a penalty term to obtain a partial differential equation, and we also focus on an improved definition of the penalty term for American options. We replace the constant penalty parameter with a time-dependent function. The novelty and advantage of our approach consists in introducing a bounded, time-dependent penalty function, enabling us to construct an efficient, stable, and adaptive numerical approximation scheme, while in contrast, the existing standard approach to the penalisation of the American put option-free boundary problem involves a constant penalty parameter. To gain insight into the accuracy of our proposed extension, we compare the solution of the extension to standard reference solutions from the literature. This illustrates the improvement of using a penalty function instead of a penalising constant.

AbstractThis article analyzes the exercise of state authority in Kurdish areas in the early Turkish Republic and discusses the state's ineffectiveness in dominating these areas. It argues that the mere existence of a highly ambitious social-engineering project, increased state presence in the region, and military power does not mean high levels of state capacity. Based on primary documents, this article discusses the problems of autonomy, coherence, and implementation that the Turkish state encountered in its nation-building project. It shows how the state's ideological rigidities and its shortage of resources and dedicated personnel undermined its capacity to control and shape the Kurdish areas. While the state attempted to regulate citizens’ private lives in Kurdish areas, the local society also tried to mold state employees in accordance with its own interests. A blurred boundary between the state and society was one of the unintended consequences of increased state presence in everyday life.

In this paper, we present an implicit finite difference method for the numerical solution of the Black–Scholes model of American put options without dividend payments. We combine the proposed numerical method by using a front-fixing approach where the option price and the early exercise boundary are computed simultaneously. We study the consistency and prove the stability of the implicit method by fixing the values of the free boundary and of its first derivative. We improve the accuracy of the computed solution via a mesh refinement based on Richardson’s extrapolation. Comparisons with some proposed methods for the American options problem are carried out to validate the obtained numerical results and to show the efficiency of the proposed numerical method. Finally, by using an a posteriori error estimator, we find a suitable computational grid requiring that the computed solution verifies a prefixed error tolerance.

This article focuses on Indian women who were integral to defining mission in the early history of the Christian Medical College and Hospital in Vellore. It is an exercise in (re)reading the biography of Ida Scudder in order to “tease out” of the text the presence and contribution of Indian women. It identifies at least three layers of Indian women who negotiate the complexities of inter-cultural relationships, encourage the tenacity and boundary breaking possibilities of mission, and use the mission theory “Woman's Work for Woman” in their own ways. Woven throughout these layers are actions that broaden the scope of mission, engaging in ministries of healing.

This paper develops a unified formulation and a new computational methodology for the entire class of the multi-factor Markovian interest rate models. The early exercise premium representation for general American options is derived for all Markovian models. The option cash flow functions are decomposed into fast and slowly varying components. The fast varying components have the same expression for all options within a model. They are calculated analytically. Only the slowly varying components are option specific. Their backward induction for a finite time interval is carried out from Taylor expansion expressions. The small coefficient of the expansion is the product of the variance and the width of the time interval. The option price is calculated by dividing its time horizon into smaller intervals and numerically iterating the Taylor expansion expressions of one time interval. Other new results include: (i) The derivation of a new "almost" Markovian LIBOR market model and its related Markovian short-rate model; (ii) the universal form of the critical boundary near the maturity for the American options in the one-factor Markovian models; and (iii) approximate analytic expressions for the entire critical boundary of the American put stock option. The put price calculated from the boundary has relative precision better than 10-5.

High-intensity interval training (HIIT) has been proposed to exert vasculoprotective effects. This study aimed to evaluate whether HIIT affects the microvasculature, including the endothelial glycocalyx barrier, and to identify associated microRNAs (miRNAs). Fifty healthy participants (23.1 ± 3.0 yr) performed a 4-wk 4 × 30-s all-out running HIIT. Sidestream dark-field imaging was performed at baseline and follow-up to detect changes of the sublingual microvasculature including the endothelial glycocalyx. Exercise parameters were determined by continuous running field test and documentation of high-intensity runs. miRNAs potentially associated with glycocalyx thickness were selected by structured literature search and blood samples for miRNA, and lactate measurements were drawn at baseline and follow-up HIIT. At baseline, a correlation between maximal exercise performance capacity and glycocalyx thickness (determined by perfused boundary region) was detected ( P = 0.045, r = 0.303). Increased exercise performance at follow-up also correlated with glycocalyx thickness ( P = 0.031, r = 0.416), and increased high-intensity sprinting speed was associated with an increased number of perfused vessels ( P = 0.0129, r = 0.449). Literature search identified miR-143, -96-5p, and -24, which were upregulated by HIIT already at baseline and showed an association with peak blood lactate levels after sprints (all P < 0.05). Moreover, increased baseline miR-143 levels predicted increased glycocalyx thickness at follow-up (AUCmiR-143 = 0.92, 95% confidence interval, 0.81–1.0, P = 0.0008). Elevated resting miR-126 levels after the intervention were associated with cell-free versican mRNA levels. We conclude that HIIT induces changes in the endothelial glycocalyx of the microvasculature. Associated miRNAs such as miR-143 may represent a tool for monitoring early vasculoprotective adaptations to physical activity. NEW & NOTEWORTHY High-intensity interval training is known to improve health-related fitness in general and in lifestyle-induced chronic diseases. To visualize microvasculature structure and to detect exercise-induced changes, sublingual sidestream dark-field imaging microscopy was used, and circulating miRNAs were measured. This study shows that exercise-induced changes correlate with associated circulating miRNA, which might be useful for monitoring vasculoprotective effects. Furthermore, sidestream dark-field imaging may represent a sensitive tool for the early detection of exercise-induced systemic vascular changes.

The general character of Canada-U.S. relations would have been sharply different in the past 65-70 years had there not been established the International Joint Commission under the Boundary Waters Treaty of 1909. That Treaty anticipated in a remarkably prophetic way the lively and sometimes dangerous disputes that arise over shared water resources, boundary and trans-boundary. By providing a mechanism for the settlement of disputes over boundary and trans-boundary water courses, lakes, rivers, etc. and by providing also an investigative mechanism for all other disputes that' may take place along the boundary, the framers of the Boundary Waters Treaty created perhaps better than they knew. For the International Joint Commission has proven to be an instrument of flexibility and high utility. For almost 70 years it has issued Orders of Approval in over 50 cases involving the construction of works affecting the levels and flows of boundary waters as well as causing trans-boundary waters to rise at the boundary and therefore, requiring the approval of the Commission. The whole question of water use/water allocation between neighbouring states sharing common river basins or having rivers and lakes as boundaries is involved in this exercise. It could not have been foreseen, however, that the pioneer language of the pollution provisions of the Boundary Waters Treaty should have moved the Commission with ease into the environmental era. While the Commission was investigating pollution of water questions as early as 1912, and while it recommended a Canada-U.S. Great Lakes Pollution Treaty as early as 1920, it was a great achievement of both countries in signing the Great Lakes Water Quality Agreement in 1972 and again in 1978, which created the massive environmental role as monitor, co-ordinator and advisor that the Commission now plays in relation to both governments in the Great Lakes basin, and also, in the other watersheds along the 5 500 mile frontier of both countries. With the rise in the knowledge of air pollution, and the interfacing between air, water and land use, there is now a whole complex that is ecologically at the basis of the concerns of Canada and the United States and is of prime interest to the Commission, and has become a fundamental aspect of its work. The future of the Commission is vital to the future of both countries as its successful past has been in maintaining reasonably friendly relations despite the tensions which disputes over water resources can cause. It is the thrust of this paper to describe and demonstrate the processes in dispute avoidance and dispute settlement, in shared resource-planning, for which the Boundary Waters Treaty, the Great Lakes Quality Agreement and the work of the Commission now stand.

This paper is concerned with regime-switching American option pricing. We develop new numerical schemes by extending the penalty method approach and by employing the θ-method. With regime-switching, American option prices satisfy a system of m free boundary value problems, where m is the number of regimes considered for the market. An (optimal) early exercise boundary is associated with each regime. Straightforward implementation of the θ-method would result in a system of nonlinear equations requiring a time-consuming iterative procedure at each time step. To avoid such complications, we implement an implicit approach by explicitly treating the nonlinear terms and/or the linear terms from other regimes, resulting in computationally efficient algorithms. We establish an upper bound condition for the time step size and prove that under the condition the implicit schemes satisfy a discrete version of the positivity constraint for American option values. We compare the implicit schemes with a tree model that generalizes the Cox-Ross-Rubinstein (CRR) binomial tree model, and with an analytical approximation solution for two-regime case due to Buffington and Elliott. Numerical examples demonstrate the accuracy and stability of the new implicit schemes.

Afghanistan assumed its modern cartographic form in piecemeal fashion between the late 1860s and early 1890s in the context of British imperial boundary-making projects in South Asia and the Middle East. The bordering of Afghanistan was contextualized by the global British empire and multiple boundary conflicts and frontier anxieties involving the British and the French, German, Russian, and other imperial powers as well as local rulers. The fundamental point here is that the map of Afghanistan is a product of imperial and interimperial concerns, and it has not benefited the Afghan people. The map of Afghanistan may or may not have served the imperial purposes for which it was created, but more importantly, by uncritically accepting it and its imperial heritage, we Afghans have become victims of an imperial map of ourselves. Afghans and non-Afghans will benefit from directly confronting the coercive impact of imperial mapping agendas on the largely invisible people “on the map” of Afghanistan. This essay historicizes the production of maps of modern Afghanistan, exposing imperial and crypto-colonial influences upon our national cartography. In so doing, it critically reimagines our spatial politics and reconfigures our intellectual infrastructure. It is an exercise in historical recentering designed to instill Afghan humanity and agency onto the map of Afghanistan.

This paper deals with randomization methods for valuing American options written on dividend-paying assets, which are based on the idea of treating the maturity date as a random variable. In the randomization method introduced by Carr in 1998, he used the Erlangian distributed random variable to develop a recursive algorithm starting from the so-called Canadian option with an exponentially distributed random maturity. The purposes of this paper are (i) to provide much simpler pricing formulas for the Canadian option; (ii) to interpret the Gaver–Stehfest method developed for inverting Laplace transforms as an alternative randomization method in the context of valuing American options; and (iii) to evaluate the performance of the Gaver–Stehfest method in details with theoretical and numerical views. Numerical experiments indicate that the Gaver–Stehfest method works well to generate accurate approximations for the early exercise boundary as well as the option value.

The American chooser option is a relatively new compound option that has the characteristic of offering exceptional risk reduction for highly volatile assets. This has become particularly significant since the start of the global financial crisis. In this paper, we derive mathematical properties of American chooser options. We show that the two optimal stopping boundaries for American chooser options with finite horizon can be characterized as the unique solution pair to a system formed by two nonlinear integral equations, arising from the early exercise premium (EEP) representation. The proof of EEP representation is based on the method of change-of-variable formula with local time on curves. The key mathematical properties of American chooser options are proved, specifically smooth-fit, continuity of value function and continuity of free-boundary among others. We compare the performance of the American chooser option against the American strangle option. We also conduct numerical experiments to illustrate our results.

<abstract><p>In this paper, the pricing of stock loans when the underlying follows a L$ \acute{e} $vy-$ \alpha $-stable process with jumps is considered. Under this complicated model, the stock loan value satisfies a fractional-partial-integro-differential equation (FPIDE) with a free boundary. The difficulties in solving the resulting FPIDE system are caused by the non-localness of the fractional-integro differential operator, together with the nonlinearity resulting from the early exercise opportunity of stock loans. Despite so many difficulties, we have managed to propose a preconditioned conjugate gradient normal residual (PCGNR) method to price efficiently the stock loan under such a complicated model. In the proposed approach, the moving pricing domain is successfully dealt with by introducing a penalty term, however, the semi-globalness of the fractional-integro operator is elegantly handled by the PCGNR method together with the fast Fourier transform (FFT) technique. Remarkably, we show both theoretically and numerically that the solution determined from the fixed domain problem by the current method is always above the intrinsic value of the corresponding option. Numerical experiments suggest the accuracy and advantage of the current approach over other methods that can be compared. Based on the numerical results, a quantitative discussion on the impacts of key parameters is also provided.</p></abstract>

AbstractWe report a teenage boy presented with dilated cardiomyopathy (DCM) with no initial skeletal involvement and initial normal creatine kinases. One year after the heart transplantation, he had exercise-induced transient muscle weakness with elevated creatine kinases (CKs). Muscle biopsy showed normal structures and normal dystrophin immunohistochemical labeling, but utrophin, which is an autosomal homologue of dystrophin, was overexpressed at sarcolemma. Sanger sequencing confirmed a heterozygous c.31 + 1G > A, 5′ splice site point mutation at the first intron of dystrophin gene. A review of previous reports of patients with different point mutations in the same region, the first exon–intron boundary that involved the muscle promotor to exon 1, confirmed a high correlation of cardiospecific phenotype sparing the muscles with this specific site of mutations. The confirmation of upregulation of brain and Purkinje isoforms of dystrophin protein in the skeletal muscles but not in the heart in past studies help to explain the skeletal sparing presentation. X-linked DCM (XLDCM) is an important cause of isolated cardiomyopathy. Routine immunohistochemical staining study including dystrophin in cardiac muscle biopsy, and dystrophin and utrophin labelling on skeletal muscle biopsy for patients with subsequent muscle symptoms or raised creatine kinases, help in the early diagnosis of the XLDCM. Future experimental study to determine the aberrant pre-mRNA splicing of this specific splice site mutation involving exon 1 and intron 1 will help to understand better the underlying complex mechanism of the splicing regulation.

The author analyzes the post-Cold War international arena thoroughly, be delineating one by one Us different systemic, geopolitical, hegemonic, and strategic metamorphoses. The emergence of a fragmented transnational subsystem — the social component of the international System — has made this era fertile ground for third-wave conflicts, i.e. cultural conflicts or shocks between civilizations. The lack of any recognized leadership and the collective exercise of the system's governability may lead one to observe that armed violence is being waged by means other than those of major inter-state wars. In such a context, one may deduce that emphasis on the concept of collective security is working to the detriment of defence-minded thinking and to the benefit of strategies for active and very early conflict prevention. The entire realm of strategy is thus open to a wide-ranging, Worldwide arena. The main consequences have been an end to the old custodial arrangements of geopolitics, thereby transforming NATO in Europe, and a renewed activism in Asia, where the trend is towards creation of a specific security subsystem. These transformations of the international System have brought about metamorphoses in the notions of enemy, boundary, conflict, and power. Such changes also highlight the « rationality deficit » now affecting the System and the proliferation of the notion of « meaning », which is everywhere lacking in consistency. The shifting of the security dilemma to the subnational, internal level has accordingly resulted from the breakup of nations and the decolonization of empires. The author concludes that it may prove useful, even valuable, to try and identify the normative elements of the post-Cold War international System and to outline, however imperfectly, the new distribution of international power. The reader will also find afresh look at the doctrinal debate about international System theory and about the epistemology of the discipline that deals with it.

Abstract Modeling the geographical distribution of the phase and amplitude of the diurnal change is a challenging problem. This paper addresses the issues of modeling the diurnal mode of precipitation over the Tropics. Largely an early morning precipitation maximum over the oceans and an afternoon rainfall maximum over land areas describe the first-order diurnal variability. However, large variability in phase and amplitude prevails even within the land and oceanic areas. This paper addresses the importance of a multimodel superensemble for much improved prediction of the diurnal mode as compared to what is possible from individual models. To begin this exercise, the skills of the member models, the ensemble mean of the member models, a unified cloud model, and the superensemble for the prediction of total rain as well as its day versus night distribution were examined. Here it is shown that the distributions of total rain over the earth (tropical belt) and over certain geographical regions are predicted reasonably well (RMSE less than 18%) from the construction of a multimodel superensemble. This dataset is well suited for addressing the diurnal change. The large errors in phase of the diurnal modes in individual models usually stem from numerous physical processes such as the cloud radiation, shallow and deep cumulus convection, and the physics of the planetary boundary layer. The multimodel superensemble is designed to reduce such systematic errors and provide meaningful forecasts. That application for the diurnal mode appears very promising. This paper examines some of the regions such as the Tibetan Plateau, the eastern foothills of the Himalayas, and the Amazon region of South America that are traditionally difficult for modeling the diurnal change. In nearly all of these regions, errors in phase and amplitude of the diurnal mode of precipitation increase with the increased length of forecasts. Model forecast errors on the order of 6–12 h for phase and 50% for the amplitude are often seen from the member models. The multimodel superensemble reduces these errors and provides a close match (RMSE &lt; 6 h) to the observed phase. The percent of daily rain and their phases obtained from the multimodel superensemble at 3-hourly intervals for different regions of the Tropics showed a closer match (pattern correlation about 0.4) with the satellite estimates. This is another area where the individual member models conveyed a much lower skill.

This study investigates valuation of guaranteed minimum maturity benefits (GMMB) in variable annuity contract in the case where the guarantees can be surrendered at any time prior to the maturity. In the event of the option being exercised early, early surrender charges will be applied. We model the underlying mutual fund dynamics under regime-switching volatility. The valuation problem can be reduced to an American option pricing problem, which is essentially an optimal stopping problem. Then, we obtain the pricing partial differential equation by a standard Markovian argument. A detailed discussion shows that the solution of the problem involves an optimal surrender boundary. The properties of the optimal surrender boundary are given. The regime-switching Volterra-type integral equation of the optimal surrender boundary is derived by probabilistic methods. Furthermore, a sensitivity analysis is performed for the optimal surrender decision. In the end, we adopt the trinomial tree method to determine the optimal strategy.

Mapping Iron Age field systemsAn assessment of the applicability of aerial photographyThere is little doubt that agriculture constituted the fundamental activity in prehistoric Denmark following its introduction 6000 years ago. Traces of cultivation are, however, almost solely preserved in the form of ard marks on surfaces sealed beneath barrows or layers of aeolian sand. Only one period in prehistory shows coherent traces revealing how field systems were formed and how they fitted into the landscape. During the course of the Late Bronze Age (1000-500 BC), a system of cultivation was introduced over large parts of NW Europe in which the individual fields or plots were separated from one another by low earthen banks and terrace edges or lynchets. These field systems could extend over several hundred hectares.These cultivation systems appear primarily to have been in use between 500 BC and AD 200. Research into prehistoric field systems has a long tradition extending all the way back to the 1920s in England, The Netherlands and Denmark, whereas in NW Germany and on Gotland work took place during the 1970s, with the Baltic Countries being involved in the 1990s. Early research was directed in particular towards mapping the field systems which, at that time, lay untouched in agriculturally marginal areas such as heath and woodland.In Denmark, Gudmund Hatt was a pioneer in this field. During the course of several campaigns, especially during the 1930s, he recorded 120 occurrences of field systems, primarily on the heaths of Northern and Western Jutland. These were published in 1949 in his major work Oldtidsagre (i.e. Prehistoric Fields). His work was continued by Viggo Nielsen who recorded 200 field systems in the forests of Zealand and Bornholm, largely between 1953 and 1963. In the former Aarhus county, the record has subsequently been augmented by a systematic reconnaissance of the forests which took place between 1988 and 1992. Subsequently, this led to the extensive investigations of field systems at Alstrup Krat near Mariager. As early as the 1920s, English researchers were aware of the fact that both ploughed-down and preserved field systems were visible on aerial photographs. However, the method was first applied in Denmark, The Netherlands and NW Germany in the 1970s, leading to a several-fold increase in the number known localities. In Denmark, P.H. Sørensen recorded 447 field systems in the former Viborg and North Jutland counties alone. P. H. Sørensen has published a series of articles dealing with various aspects of aerial photography in relation to ancient field systems. For example, the colour and origin of the various soil marks, the shape and size of the plots, different types of field systems and the relationship with soil type. He has also published several surveys of individual field systems. A significant problem with P.H. Sørensen’s work relates to the very few published plans showing the field systems and to the fact that these are based exclusively on a single series of aerial photographs.The main aim of this article is to demonstrate the potential for mapping field systems on the basis of not one but several series of aerial photographs. This is done through the detailed survey and mapping of three individual field systems and access to a series of data sources with respect to the interpretation of information contained in the aerial photographs. These comprise an interpretation of the origin of soil marks of banks and lynchets and an evaluation of the degree to which this interpretation is influenced by subjectivity. It is beyond the scope of this investigation to locate the field systems within a settlement and landscape context.Sources and study areaIn order to explore the problems and questions outlined above, three field systems were chosen in the central part of Himmerland: Skørbæk Hede, Gundersted and Store Binderup (fig. 1). This selection took place on the basis of an examination and assessment of almost all recorded field systems in Himmerland evident on several series of aerial photographs. These three field systems chosen are among those best preserved and also the most cohesive. Furthermore, all three have been mapped previously: Skørbæk Hede by Hatt on the basis of field survey, and the two others by P.H. Sørensen on the basis of aerial photographs. This provides the opportunity to evaluate any possible subjectivity in the procedure employed. Hatt makes a distinction between field boundary banks and lynchets. This opens up the possibility of evaluating how the two forms of boundary appear on aerial photographs. At Gundersted Hatt cut two sections through boundary banks. These, together with sections from other of Hatt’s excavations and more recent examples from the investigations at Alsing Krat, form the basis for an investigation of how soil marks arise and develop over time. In this investigation, use has also been made of historical maps in order to reveal the influence of historical cultivation on the presence/absence of soil marks. The earliest maps are from c. 1780. The primary source remains, however, series of vertical aerial photographs. Access to the latter has become considerably easier in recent years. A large proportion is now accessible via various web portals, and recently an overview became available of the contents of private and public archives. For the purposes of this investigation, use has been made of scanned contact copies of aerial photograph series from 1954, 1961 and 1967. From digital archives, use has been made of aerial photographs from 1979 and 1981 and the orthophoto maps from 2007 and 2008, respectively.Digitalisation and rectification of aerial photographsPreviously, mapping on the basis of aerial photographs was a laborious process involving tracing paper and the transfer of features to topographic maps. The introduction of GIS has, however, eased the process considerably and has also made it easy to compare various map themes such as soil-type, land-use, and digital finds databases. Before mapping can commence, the aerial photograph must be scanned, rectified and geo-referenced. rectification was carried out using the programme Airphoto, while geo-referencing and drawing in of the features were done in MapInfo. An example is shown in figure 2.Soil marks – how do they originate?In order to understand how the boundary banks and lynchets between plots appear as soil marks on the aerial photographs, it is necessary to examine how these boundaries were built up and also the influences to which they have been exposed from their creation and up until the time when they are visible on aerial photographs. Figures 3 and 4 show sections through two boundary banks at Gundersted These were carried out by Hatt at the beginning of the 1930s, just prior to the area coming under cultivation again and 20-25 years before the first aerial photographs revealed pale traces of boundary banks. As the area had not been cultivated since the Iron Age, the stratigraphy is the result of natural soil-formation processes: a podsol has been formed, comprising a heath mor layer uppermost, beneath this a bleached sand layer and an iron pan, and at the base the old cultivation layer and the topsoil core of the boundary bank, consisting of brown and grey sand. Ploughing of the boundary banks will, initially, not result in significant soil marks as the three uppermost layers are of equal thickness along the whole length of the section. A pale soil mark will, however, appear when the boundary bank has been levelled out and the plough begins to turn up material from the light topsoil core. This soil transport can in some instances continue for more than 70 years, but the soil marks will as a consequence also become wide and fragmented. This account of the processes leading to the appearance of the pale soil marks is completely different from the only other theory proposed in this respect, i.e. that of P.H. Sørensen. He describes a development involving three phases, beginning with the ploughing up of the bleached sand horizon which generates a pale soil-colour trace. Later in the development there is a shift to a dark trace, when the material in the topsoil core becomes ploughed up. In the final phase, the trace shifts again to a pale colour, when the plough begins to bring up the subsoil. However, these two sections show neither a bleached sand horizon nor a darker topsoil core. Furthermore, no colour changes have been observed at any of the localities. The fact that the boundary banks are apparent as pale soil marks is not due to ploughing up of the bleached sand layer but of the topsoil bank core. Ploughing down of the other boundary form, the terrace edge or lynchet, as shown in figure 5, will similarly result in the formation of a pale soil-colour trace through material being brought up from the pale topsoil core. P.H. Sørensen was also fully aware of this situation, and it can be confirmed by comparing Hatt’s map of the Skørbæk Hede site, where a distinction is made between boundary banks and lynchets, with the soil marks apparent on the aerial photograph series Basic Cover 1954 (fig. 6).Dark vegetation marks and pale erosion marksAlmost all the soil marks that form a basis for the mapping of the three field systems appear pale in relation to the surroundings. There are, however, occasional exceptions to this rule in the form of dark marks in areas of heather heathland and newly-ploughed heath. On the aerial photograph of Skørbæk Hede from 1954, a few dark marks can be seen directly south of Trenddalen (fig. 6) which correspond with the results of Hatt’s survey. These lie in an area which was cultivated between 1937 and 1954. In 1961, the area was taken out of cultivation and became covered with small trees. A corresponding phenomenon can be observed to the west of the settlement where the heather heathland was cultivated between 1954 and 1961 (fig. 7). These marks probably arise from the vegetation as a consequence of better growing conditions over the topsoil cores of the boundary banks. The fact that lynchets and boundary banks offer different growing conditions has been documented at Alstrup Krat where it could be seen that in several places anemones grew on the lynchets. Differences in the vegetation on the field surfaces and the boundary banks have also been observed on aerial photographs showing the scheduled examples of field systems at Lundby Hede and Øster Lem Hede.The final type of soil-colour trace to be dealt with here comprises the very pale patches that occur on both sides of Trenddalen at Skørbæk Hede and on the western margins of the field system at Gundersted. These could possibly be interpreted as ploughed-up deposits of aeolian sand, but this is not the case. By comparison with the topography and through stereoscopic viewing of the aerial photographs it becomes clear that these features are located on steeply sloping terrain and that they are due to ploughing up of the sandy subsoil. They become both larger and more pronounced with time as more and more subsoil sand is progressively eroded out due to ploughing (figs. 6, 7, 8 and 9).The influence of historic cultivation on soil marksThe fact that Hatt could still see boundary banks and lynchets in the landscape during his investigations in the 1930s was of course due to these areas not having been ploughed since they were abandoned at some time during the Iron Age. The Royal Danish Academy of Sciences and Letters’ conceptual map from the end of the 18th century shows that 30% of Himmerland was covered by heath, 42% was cultivated, 21% lay as meadow and bog and only 4% was covered by woodland (fig. 1). By comparing the identified field systems with the heath areas on the maps, an idea can be gained of the duration of cultivation and how it has influenced the soil marks. Correspondingly, by comparing plans showing soil marks with the cultivated area shown on the conceptual map, it is possible to investigate whether cultivation, presumably continuous here since the 12th century, has erased traces of field systems dating from the Early Iron Age. Plates I-III show combined plans of soil marks from boundary banks, lynchets and recorded barrows at the three localities. The ordnance maps from the 1880s have been chosen as a background, showing contour lines, land use and wetland areas, and the cultivated areas have been added from the conceptual map. At both Gundersted and Skørbæk Hede, there are clearly no soil marks in the areas marked as cultivated on the conceptual map. Conversely, the immediately adjacent heath areas show many coherent traces. On this basis, it must be assumed that the field systems from the Early Iron Age also once extended into areas shown as cultivated on the conceptual map but that the long-term cultivation has apparently erased any trace of them. It should, however, be mentioned that Lis Helles Olesen’s investigations in NW Jutland only reveal a slight preponderance of field systems located on the old heath areas, so there may well be regional differences.The original total extent of the field systems is of course difficult to assess, but the field system at Store Binderup provides an idea of the order of magnitude. This field system is apparent as a well-defined topographic unit surrounded by wetland areas; the latter are shown on the conceptual map to be completely covered by heath. The field system extends over c. 75% of the cultivable area. In order to examine the influence of modern cultivation on the clarity of the soil marks, plans showing traces of the boundary banks have been compared with a series of historical maps. In general, the soil marks at all three localities appear most clear in areas which were cultivated latest. Former heath areas completely lacking in soil marks have probably never been cultivated. The last 50 years of cultivation with large agricultural machinery has had a dramatic effect on the soil marks. On figures 7, 8 and 9, clear evidence of ploughing out can be seen, whereby the soil marks in several places increase from 5 to 9 m in width. The negative effect of long-term cultivation on soil marks documented here only applies to pale soil marks on sandy soils. A number of field systems are apparent as dark soil marks, the visibility of which does not appear to be affected to the same extent by long-term cultivation. These make up only 3% of those recorded by P.H. Sørensen, and no sections through boundary banks are available from any of these field systems.Comparison of maps produced by field survey and from aerial photographsEvery map expresses an interpretation of what has been observed. This also applies of course to both Hatt’s mapping of the field systems on the ground in the 1930s and the subsequent mapping conducted on the basis of aerial photographs. Quality and credibility are, however, increased considerably, if the features observed can be confirmed by several sources or several researchers, reducing the subjective aspect to a minimum.On figures 10 and 11, the author’s plan of Skørbæk Hede based on aerial photographs is compared with the results of Hatt’s field survey. There is no doubt whatsoever that the aerial photographs are better able to show the overall extent of the field system. Conversely, the resulting plan is less detailed than Hatt’s map. In a few cases, however, sub-divisions of the fields are seen on the aerial photographs which Hatt did not record in his survey (figs. 8-9). In order to investigate subjectivity in the interpretation of the aerial photographs, a comparison has been made between the author’s and P.H. Sørensen’s plans of the field systems at Gundersted and Store Binderup (figs. 12, 13 and 14). Good agreement can be seen in the interpretation of the soil marks apparent on the aerial photographs of both localities. This suggests that the subjective aspect of the interpretational process is not a major problem.Evaluation of the method’s range with respect to studies of the agrarian landscapeAerial photographs encompass a great research potential relative to studies of the arable landscape during the Late Bronze Age and Early Iron Age. They are the only source available with respect to mapping the morphology and extent of the field systems, with the exception of the few remains tangible which still exist in woodland and on heaths. Field systems are particularly important in a cultural-historical context because they constitute the sole example from prehistory of the appearance of a total integrated cultivation system and how it was adapted to the landscape.The information contained on the aerial photographs, particularly in the form of pale soil marks resulting from the exposure or ploughing-up of the topsoil core of the boundary banks and lynchets, is a credible source relative to the mapping of the morphology and extent of field systems. Comparison between the maps and plans produced by several researchers mapping does not give cause to perceive the interpretation of the information as the aerial photographs as being particularly subjective. On the contrary, very good agreement can be seen between these interpretations.In a mapping exercise, use should be made of a number of different series of vertical aerial photographs as this provides the most detailed picture of the morphology of the field systems.A very significant source of error has been identified which must be taken into account when mapping the extent of the field systems, i.e. cultivation during historical times. In areas that were cultivated prior to the enclosure movement, i.e. in the very great majority of cases presumably since the 12th century, it cannot be expected to find pale soil marks. Long-term cultivation and the consequent mixing of the upper soil layers have erased most traces of boundary banks and lynchets. Renewed cultivation within the last 100-150 years appears, conversely, only seems to have had a marginal effect on the occurrence of soil marks. As mentioned above there can, however, be marked regional differences on the influence of historical cultivation on the clarity and degree of preservation of the soil marks. This is an aspect it will be interesting to study in more detail in the future.Michael VinterMoesgård Museum

BackgroundAlongside midwifery units (AMUs) were identified as a novel hybrid organisational form in the Birthplace in England Research Programme, to which this is a follow-on study. The number of such units (also known as hospital birth centres) has increased greatly in the UK since 2007. They provide midwife-led care to low-risk women adjacent to maternity units run by obstetricians, aiming to provide a homely environment to support normal childbirth. Women are transferred to the obstetric unit (OU) if they want an epidural or if complications occur.AimsThis study aimed to investigate the ways that AMUs in England are organised, staffed and managed. It also aimed to look at the experiences of women receiving maternity care in an AMU and the views and experiences of maternity staff, including both those who work in an AMU and those in the adjacent OU.MethodsAn organisational ethnography approach was used, incorporating case studies of four AMUs, selected for maximum variation on the basis of geographical context, length of establishment of an AMU, size of unit, management, leadership and physical design. Interviews were conducted between December 2011 and October 2012 with service managers and key stakeholders (n = 35), with professionals working within and in relation to AMUs (n = 54) and with postnatal women and birth partners (n = 47). Observations were conducted of key decision-making points in the service (n = 20) and relevant service documents and guidelines were collected and reviewed.FindingsWomen and their families valued AMU care highly for its relaxed and comfortable environment, in which they felt cared for and valued, and for its support for normal birth. However, key points of transition for women could pose threats to equity of access and quality of their care, such as information and preparation for AMU care, and gaining admission in labour and transfer out of the unit. Midwives working in AMUs highly valued the environment, approach and the opportunity to exercise greater professional autonomy, but relations between units could also be experienced as problematic and as threats to professional autonomy as well as to quality and safety of care. We identified key themes that pose potential challenges for the quality, safety and sustainability of AMU care: boundary work and management, professional issues, staffing models and relationships, skills and confidence, and information and access for women.ConclusionsAMUs have a role to play in contributing to service quality and safety. They provide care that is satisfying for women, their partners and families and for health professionals, and they facilitate appropriate care pathways and professional roles and skills. There is a potential for AMUs to provide equitable access to midwife-led care when midwifery unit care is the default option (opt-out) for all healthy women. The Birthplace in England study indicated that AMUs provide safe and cost-effective care. However, the opportunity to plan to birth in an AMU is not yet available to all eligible women, and is often an opt-in service, which may limit access. The alignment of physical, philosophical and professional boundaries is inherent in the rationale for AMU provision, but poses challenges for managing the service to ensure key safety features of quality and safety are maintained. We discuss some key issues that may be relevant to managers in seeking to respond to such challenges, including professional education, inter- and intraprofessional communication, relationships and teamwork, integrated models of midwifery and women’s care pathways. Further work is recommended to examine approaches to scaling up of midwifery unit provision, including staffing and support models. Research is also recommended on how to support women effectively in early labour and on provision of evidence-based and supportive information for women.FundingThe National Institute for Health Research Health Services and Delivery Research programme.

The empirical research shows that the log-return of stock price in finance market rejects the normal distribution and admits a subclass of the asymmetric distribution. Hence, the pricing problem of stock loan is investigated under the assumption that the log-return of stock price follows the CGMY process in this work. Under this framework, the pricing model of stock loan can be described by a free boundary condition problem of space-fractional partial differential equation (FPDE). First of all, in order to change the original model defined in a fixed domain, a penalty term is introduced, and then a first order fully implicit difference schemes is developed. Secondly, based on the numerical scheme, we prove the stock loan value generated by our method does not fall below the value obtained when the contract of stock loan is exercised early. Finally, the numerical experiments are implemented and the impacts of key parameters in the CGMY model on the value and optimal redemption price of stock loan are analyzed, and some reasonable explanation should be given.

The Disaster Medicine Centre “Zaschita” is a coordinating center with the general goal of management and medical relief delivery in response to major emergencies. The Russian Disaster Medicine Service has accumulated a national and international experiences of emergency responses to earthquakes (Columbia 1999, Neftegorsk 1995, Turkey 1999, Iran 2003, Afghanistan 2002, China 2008, etc.). The Health Ministries of the Russian Federation and of Peoples Republic of China have concluded a treaty of collaborative activities in the field of in public health services and disaster medicine. The promotion of cooperation in health sector is based on the key elements of collaboration, which is an a method coping with emergencies. All activities have been discussed during annual meetings, and are planned for participants on the basis of practical field experience and of emergency medical care technologies. These include: (1) mechanisms of trans-boundary field collaboration in management during major disasters; (2) sharing of field experiences for coping with natural disasters; (3) early warning networks and information technologies; (4) staff preparedness programs and postgraduate education; (5) new psycho-physiological technologies for staff selection, training, and conformity of medical teams; (6) coordination and management of international-scale exercises; (7) technology of medical relief provided for injured in major disasters; and (8) lessons learned from technological emergencies. The details of the consequences and issues associated with mutual management will be discussed.