Dissertations / Theses on the topic 'Price paths'

This thesis explores the question of model-free trading and hedging in markets where traded asset prices are continuous and where one may trade continuously in time with no transaction costs. In particular, we make no assumptions on the volatility of traded asset prices. The contributions of the thesis are as follows. First, we propose a framework of model-independent replication of financial derivatives based on solutions to systems of PDEs evaluated at market-observed inputs. This provides a model-independent extension of the paradigm of dynamic hedging to general markets with continuous prices. We then relate these replication strategies to local martingales of a certain closed form and characterise the latter for several specifications of markets. The markets we consider are: (1) a market with no traded claims, (2) a market with an underlying asset and a convex claim, (3) a market with an underlying asset and a set of co-maturing call options. The auxiliary results for the latter two markets may be of interest outside of the local martingale characterisation results. Thirdly, we propose a definition of integration with continuous paths that justifies a probability-free version of the hedging results outlined earlier. Finally, we present a number of smaller contributions related to model-free hedging and to probability-free integration with continuous paths.

>Magister Scientiae - MSc<br>This paper focuses on the newly revived interest to model free approach in finance. Instead of postulating some probability measure it emerges in a form of an outer-measure. We review the behavior of a market stock price and the stochastic assumptions imposed to the stock price when deriving the Black-Scholes formula in the classical case. Without any stochastic assumptions we derive the Black-Scholes formula using a model free approach. We do this by means of protocols that describe the market/game. We prove a statement that prices a European option in continuous time.

Dans un graphe non orienté, le problème du sous-graphe k-sommet connexe consiste à déterminer un sous-graphe de poids minimum tel que entre chaque paires de sommets, il existe k chemins sommet-disjoints. Ce modèle a été étudié dans la littérature en termes d'arête connexité. Cependant, le cas de la sommet connexité n'a pas été traité jusqu'à présent. Nous décrivons de nouvelles inégalités valides et nous présentons un algorithme de Coupes et Branchements ainsi qu'une large étude expérimentale qui montrent l'efficacité des contraintes utilisées. Nous proposons ensuite une formulation étendue pour le même problème pour une connexité k=2, suivi d'un algorithme de Génération de Colonnes et Branchements pour résoudre cette formulation.Nous étudions ensuite la version avec chemins bornés du problème. Le problème consiste à trouver un sous-graphe de poids minimum, tel que entre chaque paire d'origine-destination, il existe k chemins sommet-disjoints de longueur au plus L. Nous proposons une formulation linéaire en nombres entiers pour L=2,3. Nous présentons de nouvelles inégalités valides et nous proposons des algorithmes de séparation pour ces contraintes. Nous présentons ensuite un algorithme de Coupes et Branchements qu'on a testé sur des instances de la TSPLIB<br>Given a weighted undirected graph and an integer k, the k-node-connected subgraph problem is to find a minimum weight subgraph which contains k-node-disjoint paths between every pair of nodes. We introduce new classes of valid inequalities and discuss their facial aspect. We also devise separation routines, investigate the structural properties of the linear relaxation and discuss some reduction operations that can be used in a preprocessing phase for the separation. Using these results, we devise a Branch-and-Cut algorithm and present some computational results. Then we present a new extended formulation for the the k-node-connected subgraph problem, along with a Branch-and-Cut-and-Price algorithm for solving the problem.Next, we investigate the hop-constrained version of the problem. The k node-disjoint hop-constrained network design problem is to find a minimum weight subgraph such that between every origin and destination there exist at least k node-disjoint paths of length at most L. We propose an integer linear programming formulation for L=2,3 and investigate the associated polytope. We introduce valid inequalities and devise separation algorithms. Then, we propose a B\&amp;C algorithm for solving the problem along with some computational results

Cette thèse étudie des systèmes locaux de gestion de transfert de pétrole ayant une architecture de réseau de canalisation. Pour leur représentativité, deux systèmes localisés au Venezuela et appartenant à l'entreprise PDVSA (Pétroles du Venezuela) ont été retenus pour illustrer les méthodes proposées et les valider : le Terminal Maritime de Pétrole de Guaraguao et le Centre de Stockage de Punta de Palmas. Dans ces réseaux des connexions, appelées " alignements ", sont établies en ouvrant/fermant des vannes à travers d'un système SCADA (Supervisory Control and Data Acquisition). Le choix d'un alignement doit tenir compte de critères d'optimisation. La minimisation des interférences avec d'autres alignements, liée à la notion de capacité opérative, a été identifiée comme le critère de choix le plus important. Les contributions de cette thèse reposent sur une modélisation sous forme de graphes, et sur des algorithmes appartenant au domaine de la recherche opérationnelle. Elles contribuent à fournir aux opérateurs de supervision des outils d'analyse permettant d'optimiser le choix des alignements. Des indicateurs permettant de quantifier l'impact des opérations d'alignement ou des défaillances, sur la capacité opérative du système, sont proposés. La minimisation de l'impact sur la capacité opérative, va correspondre à la minimisation des interférences avec des alignements potentiels. Un algorithme de calcul de ces indicateurs, est présenté, ainsi que des algorithmes de recherche de chemin, de détermination d'éléments critiques, et de recherche d'alignements utilisant des pompes. Ces algorithmes sont basés sur des algorithmes classiques s'adressant au problème du plus court chemin, du flot maximum et du nombre maximum de chemins disjoints. Cependant, ils utilisent des méthodes innovantes, comme l'ajout de contraintes considérant l'existence de sous-types d'alignements, le calcul dynamique des coûts des chemins à partir de son impact sur la capacité opérative, et la recherche de chemins via un point intermédiaire obligatoire. Les contributions sont potentiellement applicables dans des domaines autres que le transport de pétrole. Les algorithmes ont été mis en œuvre en utilisant le langage Python et ont été testés en utilisant les données réelles des réseaux étudiés. L'objectif à moyen terme de ces travaux est le développement d'un logiciel d'assistance à la prise de décision.

In this thesis, we study robust combinatorial problems with interval data. We introduce several new measures of robustness in response to the drawbacks of existing measures of robustness. The idea of these new measures is to ensure that the solutions are satisfactory for the decision maker in all scenarios, including the worst case scenario. Therefore, we have introduced a threshold over the worst case costs, in which above this threshold, solutions are no longer satisfactory for the decision maker. It is, however, important to consider other criteria than just the worst case.<p>Therefore, in each of these new measures, a second criteria is used to evaluate the performance of the solution in other scenarios such as the best case one. <p><p>We also study the robust deviation p-elements problem. In fact, we study when this solution is equal to the optimal solution in the scenario where the cost of each element is the midpoint of its corresponding interval. <p><p>Then, we finally formulate the robust combinatorial problem with interval data as a bicriteria problem. We also integrate the decision maker's preferences over certain types of solutions into the model. We propose a method that uses these preferences to find the set of solutions that are never preferred by any other solution. We call this set the final set. <p><p>We study the properties of the final sets from a coherence point of view and from a robust point of view. From a coherence point of view, we study necessary and sufficient conditions for the final set to be monotonic, for the corresponding preferences to be without cycles, and for the set to be stable.<p>Those that do not satisfy these properties are eliminated since we believe these properties to be essential. We also study other properties such as the transitivity of the preference and indifference relations and more. We note that many of our final sets are included in one another and some are even intersections of other final sets. From a robust point of view, we compare our final sets with different measures of robustness and with the first- and second-degree stochastic dominance. We show which sets contain all of these solutions and which only contain these types of solutions. Therefore, when the decision maker chooses his preferences to find the final set, he knows what types of solutions may or may not be in the set.<p><p>Lastly, we implement this method and apply it to the Robust Shortest Path Problem. We look at how this method performs using different types of randomly generated instances. <p><br>Doctorat en sciences, Orientation recherche opérationnelle<br>info:eu-repo/semantics/nonPublished

L’état de santé des personnes âgées se dégrade, les niveaux de dépendance s’accroissent, induisant de profondes conséquences sur l’organisation sanitaire en France. Les fractures du col du fémur illustrent ce défi au regard de leur fort impact sur la qualité de vie et sur la morbi-mortalité des patients. Notre étude quantitative et qualitative, (Jan. 2012 - Jan. 2013) au sein du principal service de chirurgie orthopédique d’Alsace, a permis de retracer le parcours de soin de 107 patients âgés de 75 ans et plus. Notre principale conclusion est que le patient n’a que très peu de place dans le processus décisionnel de son parcours de soin. Cela est d’autant plus dommageable que cette fracture revêt une double signification: physique (besoin d’assistance accrue) et symbolique (dépendance anticipée). Notre étude interactionniste permet de dégager des pistes d’actions opérationnelles dans les domaines sanitaires, politiques et éthiques afin de limiter les effets délétères de cette pathologie<br>In a context of depressed health-conditions for elderly people, the levels of dependency are rising. It induces deep consequences for the entire health care organisation. For instance, the fractures of the femoral neck (FFN) represent a healthcare challenge regarding their strong impact on patients’ quality of life and on their morbity-mortality. We conducted a qualitative and quantitative study (Jan. 2012- Jan. 2013) within the main department of orthopedic surgery in Alsace in order to track the healthcare paths of 107 patients of 75 years-old or more. Our main conclusion is that patients are poorly involved in the decisions for their care. This is all the more harmful because the FFN is in fact dual. It is both a physical (higher assistance needed) and a symbolic (earlier dependency) breakage. Our interactionist study identifies areas for pragmatic actions in health-care, public policies and ethic that could contribute to absorb / reduce the pernicious effects of this pathology

Many problems in applied mathematics and physics are formulated most naturally in terms of matrices, and can be solved by computing functions of these matrices. For example, in quantum mechanics, the coherent dynamics of physical systems is described by the matrix exponential of their Hamiltonian. In state of the art experiments, one can now observe such unitary evolution of many-body systems, which is of fundamental interest in the study of many-body quantum phenomena. On the other hand the theoretical simulation of such non-equilibrium many-body dynamics is very challenging. In this thesis, we develop a symbolic approach to matrix functions and quantum dynamics based on a novel algebraic structure we identify for sets of walks on graphs. We begin by establishing the graph theoretic equivalent to the fundamental theorem of arithmetic: all the walks on any finite digraph uniquely factorise into products of prime elements. These are the simple paths and simple cycles, walks forbidden from visiting any vertex more than once. We give an algorithm that efficiently factorises individual walks and obtain a recursive formula to factorise sets of walks. This yields a universal continued fraction representation for the formal series of all walks on digraphs. It only involves simple paths and simple cycles and is thus called a path-sum. In the second part, we recast matrix functions into path-sums. We present explicit results for a matrix raised to a complex power, the matrix exponential, matrix inverse, and matrix logarithm. We introduce generalised matrix powers which extend desirable properties of the Drazin inverse to all powers of a matrix. In the third part, we derive an intermediary form of path-sum, called walk-sum, relying solely on physical considerations. Walk-sum describes the dynamics of a quantum system as resulting from the coherent superposition of its histories, a discrete analogue to the Feynman path-integrals. Using walk-sum we simulate the dynamics of quantum random walks and of Rydberg-excited Mott insulators. Using path-sum, we demonstrate many-body Anderson localisation in an interacting disordered spin system. We give two observable signatures of this phenomenon: localisation of the system magnetisation and of the linear magnetic response function. Lastly we return to the study of sets of walks. We show that one can construct as many representations of series of walks as there are ways to define a walk product such that the factorisation of a walk always exist and is unique. Illustrating this result we briefly present three further methods to evaluate functions of matrices. Regardless of the method used, we show that graphs are uniquely characterised, up to an isomorphism, by the prime walks they sustain.

La prise de décision est une partie intégrante de notre vie quotidienne où le décideur est confronté à des problèmes composés de plusieurs objectifs habituellement contradictoires. Dans ce travail, nous traitons des problèmes d'optimisation multiobjectif dans des espaces de recherche continus ou discrets. Nous avons développé plusieurs nouveaux algorithmes basés sur les métaheuristiques hybrides évolutionnaires, en particulier sur l'algorithme MOEA/D. Nous avons proposé l'algorithme HEMH qui utilise l'algorithme DM-GRASP pour construire une population initiale de solutions de bonne qualité dispersées le long de l'ensemble des solutions Pareto optimales. Les résultats expérimentaux montrent la supériorité de toutes les variantes hybrides proposées sur les algorithmes originaux MOEA/D et SPEA2. Malgré ces bons résultats, notre approche possède quelques limitations, levées dans une version améliorée de HEMH : HEMH2 et deux autres variantes HEMHde et HEMHpr. Le Adaptive Binary DE inclus dans les HEMH2 et HEMHde a de meilleures capacités d'exploration qui pallient aux capacités de recherche locale contenues dans la HEMH, HEMH2 et HEMHde. Motivés par ces résultats, nous avons proposé un nouvel algorithme baptisé HESSA pour explorer un espace continu de recherche où le processus de recherche est réalisé par différentes stratégies de recherche. Les résultats expérimentaux montrent la supériorité de HESSA à la fois sur MOEA/D et dMOPSO. Tous les algorithmes proposés ont été vérifiés, testé et comparés à certaines méthodes MOEAs. Les résultats expérimentaux montrent que toutes les propositions sont très compétitives et peuvent être considérés comme une alternative fiable<br>Many real-world decision making problems consist of several conflicting objectives, the solutions of which is called the Pareto-optimal set. Hybrid metaheuristics proved their efficiency in solving these problems. They tend to enhance search capabilities by incorporating different metaheuristics. Thus, we are concerned with developing new hybrid schemes by incorporating different strategies with exploiting the pros and avoiding the drawback of the original ones. First, HEMH is proposed in which the search process includes two phases DMGRASP obtains an initial set of efficient solutions in the 1st phase. Then, greedy randomized path-relinking with local search or reproduction operators explore the non-visited regions. The efficient solutions explored over the search are collected. Second, a comparative study is developed to study the hybridization of different metaheuristics with MOEA/D. The 1st proposal combines adaptive discrete differential Evolution with MOEA/D. The 2nd combines greedy path-relinking with MOEA/D. The 3rd and the 4th proposals combine both of them in MOEA/D. Third, an improved version of HEMH is presented. HEMH2 uses inverse greedy to build its initial population. Then, differential evolution and path-relink improves these solutions by investigating the non-visited regions in the search space. Also, Pareto adaptive epsilon concept controls the archiving process. Motivated by the obtained results, HESSA is proposed to solve continuous problems. It adopts a pool of search strategies, each of which has a specified success ratio. A new offspring is generated using a randomly selected one. Then, the success ratios are adapted according to the success of the generated offspring. The efficient solutions are collected to act as global guides. The proposed algorithms are verified against the state of the art MOEAs using a set of instances from literature. Results indicate that all proposals are competitive and represent viable alternatives

Thesis (Ph.D. (Applied Mathematics)) -- University of Limpopo, 2021<br>Vovk and Shafer, [41], introduced game-theoretic framework for probability in mathematical finance. This is a new trend in financial mathematics in which no probabilistic assumptions on the space of price paths are made. The only assumption considered is the no-arbitrage opportunity widely accepted by the financial mathematics community. This approach rests on game theory rather than measure theory. We deal with various properties and constructions of quadratic variation for model-free càdlàg price paths and integrals driven by such paths. Quadratic variation plays an important role in the analysis of price paths of financial securities which are modelled by Brownian motion and it is sometimes used as the measure of volatility (i.e. risk). This work considers mainly càdlàg price paths rather than just continuous paths. It turns out that this is a natural settings for processes with jumps. We prove the existence of partition independent quadratic variation. In addition, following assumptions as in Revuz and Yor’s book, the existence and uniqueness of the solutions of SDEs with Lipschitz coefficients, driven by model-free price paths is proven.<br>National Research Foundation (NRF)

碩士<br>國立臺北大學<br>不動產與城鄉環境學系<br>101<br>The Cost Approach is one of the three major approaches to value. Although the Sales Comparison Approach is applied in principle in sales transaction frequently market, the Cost Approach is still necessary for value check. Besides, we must rely on the Cost Approach when there is no sale or rental transaction. The accrued depreciation is vital in the process of cost value appraisal. The depreciation, the main factor affecting the value loss of property, involves lots of complicated proceeding. However, due to the difficulty to uncouple the land and building value, the problem that land should not have physical deterioration and functional obsolescence is inevitably ignored and might lead to miscalculation of depreciation. Using 876 transaction data of improved property, this paper extracts the land value applying appraisal methods; followed by multiple regressions with dependent variable on the value of building. Considering spatial autocorrelation might occur in real estate prices according to past literatures; hence, we use Spatial Autoregression Model to solve this problem. The empirical outcome shows the depreciation path is convex, similar to Fixed-Percentage method and The Sum of Years Digits method. In addition, the depreciation rate for building is higher(2.10%>1.04%) compare to depreciation of improved property. Spatial Error Model(SEM) is better than Ordinary Least Squares Estimator(OLS)。

碩士<br>國立中山大學<br>資訊工程學系研究所<br>92<br>In ad hoc network, one needs other nodes to relay data packets. But resources in each node are limited. Therefore, these nodes may not relay other’s data packet without getting any benefit. In this paper, a routing path selecting algorithm based on price mechanism is proposed. It helps nodes to get some benefits by relaying others’ data packets. Moreover, the algorithm we proposed selects a routing path with less payment and more resources. Simulation results show that the drop rate, block rate and the cost of routing paths are reduced compared to the competing algorithms.

Unmanned Vehicles (UVs) have been significantly utilized in military and civil applications over the last decade. Path-planning of UVs plays an important role in effectively using the available resources such as the UVs and sensors as efficiently as possible. The main purpose of this thesis is to address two path planning problems involving a single UV. The two problems we consider are the quota problem and the budget problem. In the quota problem, the vehicle has to visit a sufficient number of targets to satisfy the quota requirement on the total prize collected in the tour. In the budget problem, the vehicle has to comply with a constraint of the distance traveled by the UV. We solve both these problems using a practical heuristic called the prize-multiplier approach. This approach first uses a primal-dual algorithm to first assign the targets to the UV. The Lin – Kernighan Heuristic (LKH) is then applied to generate a tour of the assigned targets for the UV. We tested this approach on two different vehicle models. One model is a simple vehicle which can move in any direction without a constraint on its turning radius. The other model is a Reeds-Shepp vehicle. We also modeled both problems in C++ using the multi-commodity flow formulations, and solved them to optimality by using the Concert Technology of CPLEX. We used the results generated by CPLEX to determine the quality of the solutions produced by the heuristics. By comparing the objective values of the obtained solutions and the running times of the heuristics and CPLEX, one can conclude that the proposed heuristics produce solutions with good quality to our problems within our desired time limits.

碩士<br>國立臺灣大學<br>電機工程學研究所<br>99<br>Prize competition is an open approach of soliciting expertise and creativity from the public to increase business success or solving problems. A collective solution is a problem-solving method generated by a group after the problem is posed to the group. Although prize competitions for seeking collective solutions have been adopted and have successfully stimulated collective innovations in many cases, there are yet needs for methodology to design an effective prize competition for seeking collective solutions. The challenges include characterization of solution providers’ submission strategy for reasonable winning prize setting and mechanism design to connect the collective solutions from all solution providers and weave them into a better solution. In this thesis, we consider a problem of shortest path seeking in a transportation network, where there are one path solution seeker (PSS) and many path solution providers (PSPs) with asymmetric information. The PSS would like to solicit a shortest path solution between two nodes of the transportation network from PSPs. Individual PSPs have different and only partial network information. The PSS and PSPs have common statistical information about PSPs. The PSS divides the network into two sections and holds a prize competition in each section to solicit shortest path solutions from PSPs among specified pair of cities in the section. To protect PSPs’ intellectual right, PSPs first submit the distance of paths only. The PSP, whose submitted distance is the shortest for a pair of nodes, then submits the solution path of the pair and wins a prize. After procuring shortest paths in each section, the PSS can further connect them into a shortest path between the PSS’ desired pair of cities. A remaining design issue is that under such a prize competition mechanism, how the prize value should be designed so that the PSS can maximize the value of the shortest path with minimum cost of prizes. To design the optimal prize value, specific challenges are as follows: (1) How to formulate the PSPs&apos;&apos; path provisioning response to the prize? (2) How to set the optimal prizes to each section as budget of the prize competition? The problem of PSS’ prize setting in consideration of individual PSPs’ strategy of submitting path solution is formulated as a single-leader and multiple-follower Stackelberg game with incomplete information. The factors affecting individual PSPs’ submission behavior include the prize, path computation cost, transportation network information, and crucially, one PSP model about competition with other PSPs. From individual PSPs’ viewpoint, one will win the prize competition when the distance of submission is shorter than the shortest path submitted by other PSPs. Therefore, individual PSPs’ winning probability can be modeled by uncertainty of other PSPs’ provision submission behavior. This model can be a foundation to design a mechanism for the PSS to set optimal prize. For PSS’ prize setting problem, in addition to value of path and cost of the winning prize, probability distribution of information about PSPs’ path computation cost, total number of nodes in a network and path distance obtained by data collection and experience are formulated. Individual PSPs’ competitive behavior response under the prize competition model is analyzed by considering different distributions of shortest path submitted by other competitive PSPs. Requirement to submit shorter distance (better solution) is deducted to the best response to prize competition. The analysis results show that the distance of submission path is shorter as mean of probability distribution of other PSPs’ distance of submission shortest path decreases but is shorter first and then becomes longer as variance of other PSPs’ probability distribution of submission distance of shortest path decreases. Finally, numerical study is performed and results are as follows： (1) For individual PSPs, the prize is the key factor to submit the shortest path (the best solution), not other PSPs’ submission behaviors； (2) When the prize is setting higher, the shorter distance (better solution) the PSS may procure； (3) Decreasing tendency of expected distance of shortest path the PSS procures becomes inconspicuous when prize is setting higher； (4) The section with fewer PSPs needs higher prize to induce competition than the other section ； (5) Expected profit is higher when more PSPs are expected to participate in the prize competition.

Thesis (Ph. D.)--Florida State University, 2004.<br>Advisor: Dr. Richard M. Morton, Florida State University, College of Business, Dept. of Accounting. Title and description from dissertation home page (viewed Sept. 23, 2004). Includes bibliographical references.

It is well established that stock market volatility has a memory of the past, moreover it is found that volatility correlations are long ranged. As a consequence, volatility cannot be characterized by a single correlation time in general. Recent empirical work suggests that the volatility correlation functions of various assets actually decay as a power law. Moreover it is well established that the distribution functions for the returns do not obey a Gaussian distribution, but follow more the type of distributions that incorporate what are commonly known as fat–tailed distributions. As a result, if one is to model the evolution of the stock price, stock market or any financial derivative, then standard Brownian motion models are inaccurate. One must take into account the results obtained from empirical studies and work with models that include realistic features observed on the market. In this thesis we show that it is possible to derive the path integral for a non-Gaussian option pricing model that can capture fat–tails. However we find that the path integral technique can only be used on a very small set of problems, as a number of situations of interest are shown to be intractable.<br>http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1378473<br>Thesis (Ph.D.) -- University of Adelaide, School of Electrical and Electronic Engineering, 2010

碩士<br>大葉大學<br>資訊管理學系碩士班<br>96<br>In this modern society, people can purchase what they want by internet. But the things are variey in the internet, the price will be different for the same product in dif-ferent website. So, people who are careful calculation and strict budgeting may surf every website and find the most suitable and reasonable for themselves. But this is not efficient and people increase more time in surfing internet. Therefore, this research only offers users to find the price comments of records, and users can purchase the re-cord after competing the price through this electric business website. It can reduse us-ers’ time in surfing the internet. In this study is based om ontology,it will present the popular types of records to show the way ontology. And TOVE ontology engineering approach through the estab-lishment of record ontology, TOVE ontology engineering approach through the defini-tion of modern music in every category, it can be clear standardized, and the definition of categories, the link is between property and inference rules. Through ontology semantic search conducted in the knowledge base of information than the right, price assessment of search services, coupled with shopping search path, allowing users more convenient to buy. In this study music as an example the establishment of ontology, produce a price assessment of the search system. By Protégé ontology editor establish categories and attributes hidden between the association and the use interface. Users can search through the use of the system, in the knowledge database to find relevant information and make it more suitable for users of the results, and reached through this system of services and knowledge-sharing knowledge re-use.

The mining industry in South Africa has long been a crucial contributor to the Gross Domestic Product (GDP) starting in the 18th century. In 2010, the direct contribution towards the GDP from the mining industry was 10% and 19.8% indirect. During the last decade global financial uncertainty resulted in commodity prices hitting record numbers when Gold soared to a high at $1900/ounce in September 2011, and thereafter the dismal decline to a low of $1200/ounce in July 2013. Executives in these markets have reacted strongly to reduce operational costs and focussing on better production efficiencies. One such a cost for mining within South Africa is the Operational Expenditure (OPEX) associated with electrical energy that has steadily grown on the back of higher than inflation rate escalations. Companies from the Energy Intensive User Group (EIUG) witnessed energy unit prices (c/kWh) and their percentage of OPEX grow to 20% from 7% in 2008. The requirement therefore is for more accurate energy budget forecasting models to predict what energy unit price escalations (c/kWh) occur along with the required units (kWh) at mines or new projects and their impact on OPEX. Research on statistical models for energy forecasting within the mining industry indicated that the historical low unit price and its notable insignificant impact on OPEX never required accurate forecasting to be done and thus a lack of available information occurred. AngloGold Ashanti (AGA) however approached Deloittes in 2011 to conclude a study for such a statistical model to forecast energy loads on one of its operations. The model selected for the project was the Monte Carlo analysis and the rationale made sense as research indicated that it had common uses in energy forecasting at process utility level within other industries. For the purpose of evaluation a second regression model was selected as it is well-known within the statistical fraternity and should be able to provide high level comparison to the Monte Carlo model. Finally these were compared to an internal model used within AGA. Investigations into the variables that influence the energy requirement of a typical deep level mine indicated that via a process of statistical elimination tonnes broken and year are the best variables applicable in a mine energy model for conventional mining methods. Mines plan on a tonnage profile over the Life of Mine (LOM) so the variables were known for the given evaluation and were therefore used in both the Monte Carlo Analysis that worked on tonnes and Regression Analysis that worked on years. The models were executed to 2040 and then compared to the mine energy departments’ model in future evaluations along with current actuals as measured on a monthly basis. The best comparison against current actuals came from the mine energy departments’ model with the lowest error percentage at 6% with the Regression model at 11% and the Monte Carlo at 20% for the past 21 months. This, when calculated along with the unit price path studies from the EIUG for different unit cost scenarios gave the Net Present Value (NPV) reduction that each model has due to energy. A financial analysis with the Capital Asset Pricing Model (CAPM) and the Security Market Line (SML) indicated that the required rate of return that investors of AGA shares have is 11.92%. Using this value the NPV analysis showed that the mine energy model has the best or lowest NPV impact and that the regression model was totally out of line with expectations. Investors that provide funding for large capital projects require a higher return as the associated risk with their money increases. The models discussed in this research all work on an extrapolation principle and if investors are satisfied with 6% error for the historical 2 years and not to mention the outlook deviations, then there is significance and a contribution from the work done. This statement is made as no clear evidence of any similar or applicable statistical model could be found in research that pertains to deep level mining. Mining has been taking place since the 18th century, shallow ore resources are depleted and most mining companies would therefore look towards deeper deposits. The research indicates that to some extent there exist the opportunity and some rationale in predicting energy requirements for deep level mining applications. Especially when considering the legislative and operational cost implications for the mining houses within the South African economy and with the requirements from government to ensure sustainable work and job creation from industry in alignment with the National Growth Path (NGP). For this, these models should provide an energy outlook guideline but not exact values, and must be considered along with the impact on financial figures.<br>MBA, North-West University, Potchefstroom Campus, 2014

碩士<br>東海大學<br>經濟系<br>102<br>This paper constructs a neutral intervention operation dual exchange rate open economy model is characterized by the Gardner (1984), Lai (1994) and Liaw (2000). We use the “implicit function technique” of first generation regime collapsing, which is offered by Chang and Lai (1990) to analyze if the monetary authority tend to curb the rising price level through the tight monetary policy which the economy is facing a beneficial shock on the demand side of the commodity market. Under the former economic circumstances, what will be the dynamic effect of the relevant macroeconomic variables if the monetary authority executes the policy？ The major findings are (1) not only the price ceiling threshold level is the key factor of price regime collapsing, but also is the important determinant of the price regime collapsing whether or not？(2) if the price ceiling threshold level is between the initial price level and the new long run equilibrium price level, then the relative amplitude of “capital mobility degree”and the price ceiling threshold level are the two key factors to decide the dynamic path and pattern of the relevant macroeconomic variables.

碩士<br>東海大學<br>經濟系<br>102<br>This paper constructs a open economy general equilibrium macroeconomic model is characterized by the Dornbusch (1976) exchange rate dynamic adjustment model and Eaton and Turnovsky (1982‚1984)‚Lai (2006) open economy forward foreign exchange market model. We use the “implicit function technique” of first generation regime collapsing‚ which is offered by Chang and Lai (1990) to analyze if the monetary authority tend to curb the rising price level through the tight monetary policy which the economy is facing a beneficial shock on the demand side of the commodity market. Under the former economic circumstances‚ what will be the dynamic effect of the relevant macroeconomic variables if the monetary authority executes the policy? The major findings are (i) not only the price ceiling threshold level is the key factor of price regime collapsing‚ but also is the important determinant of the price regime collapsing whether or not? (ii) if the price ceiling threshold level is between the initial price level and the new long run equilibrium price level‚ then (a) the relative amplitude of “real exchange rate of trade balance reaction coefficient” and “the tight money effect”(b) the relative amplitude of“ the speculation degree of speculator” are the two key factors to decide the dynamic path of the forward exchange rate.