Journal articles: 'Interest rate models – Mathematical models'

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Zhu, You-Lan. "Three-factor interest rate models." Communications in Mathematical Sciences 1, no. 3 (2003): 557–73. http://dx.doi.org/10.4310/cms.2003.v1.n3.a8.

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Di Persio, Luca, Gregorio Pellegrini, and Michele Bonollo. "Polynomial Chaos Expansion Approach to Interest Rate Models." Journal of Probability and Statistics 2015 (2015): 1–24. http://dx.doi.org/10.1155/2015/369053.

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The Polynomial Chaos Expansion (PCE) technique allows us to recover a finite second-order random variable exploiting suitable linear combinations of orthogonal polynomials which are functions of a given stochastic quantityξ, hence acting as a kind of random basis. The PCE methodology has been developed as a mathematically rigorous Uncertainty Quantification (UQ) method which aims at providing reliable numerical estimates for some uncertain physical quantities defining the dynamic of certain engineering models and their related simulations. In the present paper, we use the PCE approach in order to analyze some equity and interest rate models. In particular, we take into consideration those models which are based on, for example, the Geometric Brownian Motion, the Vasicek model, and the CIR model. We present theoretical as well as related concrete numerical approximation results considering, without loss of generality, the one-dimensional case. We also provide both an efficiency study and an accuracy study of our approach by comparing its outputs with the ones obtained adopting the Monte Carlo approach, both in its standard and its enhanced version.

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Yanishevskyi, V. S., and L. S. Nodzhak. "The path integral method in interest rate models." Mathematical Modeling and Computing 8, no. 1 (2020): 125–36. http://dx.doi.org/10.23939/mmc2021.01.125.

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An application of path integral method to Merton and Vasicek stochastic models of interest rate is considered. Two approaches to a path integral construction are shown. The first approach consists in using Wieners measure with the following substitution of solutions of stochastic equations into the models. The second approach is realised by using transformation from Wieners measure to the integral measure related to the stochastic variables of Merton and Vasicek equations. The introduction of boundary conditions is considered in the second approach in order to remove incorrect time asymptotes from the classic Merton and Vasicek models of interest rates. By the example of Merton model with zero drift, a Dirichlet boundary condition is considered. A path integral representation of term structure of interest rate is obtained. The estimate of the obtained path integrals is performed, where it is shown that the time asymptote is limited.

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CHEN, XINFU, and JIN LIANG. "A double obstacle model for pricing bi-leg defaultable interest rate swaps." European Journal of Applied Mathematics 31, no. 3 (September 4, 2019): 511–43. http://dx.doi.org/10.1017/s0956792519000184.

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Two mathematical models under so-called intensity and structure frameworks to pricing a double defaultable interest rate swap are established. The default could happen or jump to a high probability in both fixed and floating parties on the predetermined boundaries. The models lead to a new and interesting mathematical problem. As the intensity approaches infinity in designated regions, the solutions of the intensity models converge to a solution of a structure-type model which is an initial value problem of a partial differential equation coupled with two obstacles problem in their restricted regions. According to the value of the fixed rate, three cases are discussed. The free boundary that determines the swap rate and the free boundaries that determine the earlier termination of the contract (due to counterparty’s default) are analysed.

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Rainer, Martin. "Calibration of stochastic models for interest rate derivatives." Optimization 58, no. 3 (April 2009): 373–88. http://dx.doi.org/10.1080/02331930902741796.

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Jamshidian, F. "A simple class of square-root interest-rate models." Applied Mathematical Finance 2, no. 1 (March 1995): 61–72. http://dx.doi.org/10.1080/13504869500000004.

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Rebonato, Riccardo. "Review Paper. Interest–rate term–structure pricing models: a review." Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 460, no. 2043 (March 8, 2004): 667–728. http://dx.doi.org/10.1098/rspa.2003.1255.

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Slinko, Irina. "ON FINITE DIMENSIONAL REALIZATIONS OF TWO-COUNTRY INTEREST RATE MODELS." Mathematical Finance 20, no. 1 (January 2010): 117–43. http://dx.doi.org/10.1111/j.1467-9965.2009.00392.x.

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Mancini, Cecilia, and Roberto Renò. "Threshold estimation of Markov models with jumps and interest rate modeling." Journal of Econometrics 160, no. 1 (January 2011): 77–92. http://dx.doi.org/10.1016/j.jeconom.2010.03.019.

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Ferreiro, Ana M., José A. García-Rodríguez, José G. López-Salas, and Carlos Vázquez. "SABR/LIBOR market models: Pricing and calibration for some interest rate derivatives." Applied Mathematics and Computation 242 (September 2014): 65–89. http://dx.doi.org/10.1016/j.amc.2014.05.017.

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Gómez-Valle, L., and J. Martínez-Rodríguez. "The risk-neutral stochastic volatility in interest rate models with jump–diffusion processes." Journal of Computational and Applied Mathematics 347 (February 2019): 49–61. http://dx.doi.org/10.1016/j.cam.2018.07.048.

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Gómez-Valle, L., and J. Martínez-Rodríguez. "Estimation of risk-neutral processes in single-factor jump-diffusion interest rate models." Journal of Computational and Applied Mathematics 291 (January 2016): 48–57. http://dx.doi.org/10.1016/j.cam.2015.02.031.

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Gáll, József, Gyula Pap, and Willem Peeters. "Random field forward interest rate models, market price of risk and their statistics." ANNALI DELL'UNIVERSITA' DI FERRARA 53, no. 2 (October 3, 2007): 233–42. http://dx.doi.org/10.1007/s11565-007-0011-3.

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Discacciati, Andrea, and Matteo Bottai. "Instantaneous Geometric Rates via Generalized Linear Models." Stata Journal: Promoting communications on statistics and Stata 17, no. 2 (June 2017): 358–71. http://dx.doi.org/10.1177/1536867x1701700207.

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The instantaneous geometric rate represents the instantaneous probability of an event of interest per unit of time. In this article, we propose a method to model the effect of covariates on the instantaneous geometric rate with two models: the proportional instantaneous geometric rate model and the proportional instantaneous geometric odds model. We show that these models can be fit within the generalized linear model framework by using two nonstandard link functions that we implement in the user-defined link programs log_igr and logit_igr. We illustrate how to fit these models and how to interpret the results with an example from a randomized clinical trial on survival in patients with metastatic renal carcinoma.

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Wissel, Johannes. "Some results on strong solutions of SDEs with applications to interest rate models." Stochastic Processes and their Applications 117, no. 6 (June 2007): 720–41. http://dx.doi.org/10.1016/j.spa.2006.09.011.

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Lo, C. F. "Lie-Algebraic Approach for Pricing Zero-Coupon Bonds in Single-Factor Interest Rate Models." Journal of Applied Mathematics 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/276238.

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The Lie-algebraic approach has been applied to solve the bond pricing problem in single-factor interest rate models. Four of the popular single-factor models, namely, the Vasicek model, Cox-Ingersoll-Ross model, double square-root model, and Ahn-Gao model, are investigated. By exploiting the dynamical symmetry of their bond pricing equations, analytical closed-form pricing formulae can be derived in a straightfoward manner. Time-varying model parameters could also be incorporated into the derivation of the bond price formulae, and this has the added advantage of allowing yield curves to be fitted. Furthermore, the Lie-algebraic approach can be easily extended to formulate new analytically tractable single-factor interest rate models.

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Monsalve-Cobis, Abelardo, Wenceslao González-Manteiga, and Manuel Febrero-Bande. "Goodness-of-fit test for interest rate models: An approach based on empirical processes." Computational Statistics & Data Analysis 55, no. 12 (December 2011): 3073–92. http://dx.doi.org/10.1016/j.csda.2011.06.004.

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Lyuu, Yuh-Dauh, and Chuan-Ju Wang. "On the construction and complexity of the bivariate lattice with stochastic interest rate models." Computers & Mathematics with Applications 61, no. 4 (February 2011): 1107–21. http://dx.doi.org/10.1016/j.camwa.2010.12.061.

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19

Zalai, Ernő. "The von Neumann Model and the Early Models of General Equilibrium." Acta Oeconomica 54, no. 1 (May 1, 2004): 3–38. http://dx.doi.org/10.1556/aoecon.54.2004.1.2.

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The paper reconstructs the von Neumann model, comments on its salient features and critically reviews some of its generalisations. The issues related to thetreatment of consumption, decomposability and uniqueness of the rate of growth and interest will be especially scrutinised. The most prominent models of general equilibrium that appeared before or roughly at the same time as von Neumann's model will be also reviewed in the paper and compared with it. It will be demonstrated that none of them had any noticeable influence on von Neumann's model, which is genuinely distinct, ideologically free and methodologically fresh and forward-looking. It will be argued that the model can be viewed as a brilliant mathematical metaphor of some deep-rooted old vision, pertaining to the core issues of commodity production.

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Peixinho, N., and A. Pinho. "Study of Viscoplasticity Models for the Impact Behavior of High-Strength Steels." Journal of Computational and Nonlinear Dynamics 2, no. 2 (November 17, 2006): 114–23. http://dx.doi.org/10.1115/1.2447129.

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This study reports on modeling the mechanical behavior of high-strength steels subjected to impact loading. The materials studied were steel grades of interest for crashworthiness applications: dual-phase and transformation induced plasticity (TRIP) steels. The challenges associated with the numerical simulation of impact events involving these materials include the modeling of extensive plastic deformation, particularly the change of material properties with strain rate. Tensile testing was performed at different strain rates on the materials studied. The test results were used to compare and validate constitutive equations that provide a mathematical description of strain-rate dependence of the material properties. The Cowper–Symonds equation and modified variants were examined. The crashworthiness performance of thin-walled sections made of dual-phase and TRIP steels was also investigated. Axial crushing tests were performed at different speeds on top-hat and hexagonal tubes. The experimental results were compared with numerical simulations obtained using an explicit finite element program (LS-DYNA) and the original and modified Cowper–Symonds equations.

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Karaś, Marek, and Anna Serwatka. "Discrete-time market models from the small investor point of view and the first fundamental-type theorem." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 16, no. 1 (December 1, 2017): 17–40. http://dx.doi.org/10.1515/aupcsm-2017-0002.

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Abstract In this paper, we discuss the no-arbitrage condition in a discrete financial market model which does not hold the same interest rate assumptions. Our research was based on, essentially, one of the most important results in mathematical finance, called the Fundamental Theorem of Asset Pricing. For the standard approach a risk-free bank account process is used as numeraire. In those models it is assumed that the interest rates for borrowing and saving money are the same. In our paper we consider the model of a market (with d risky assets), which does not hold the same interest rate assumptions. We introduce two predictable processes for modelling deposits and loans. We propose a new concept of a martingale pair for the market and prove that if there exists a martingale pair for the considered market, then there is no arbitrage opportunity. We also consider special cases in which the existence of a martingale pair is necessary and the sufficient conditions for these markets to be arbitrage free.

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Yao, Ding Jun, and Rong Ming Wang. "Exponential bounds for ruin probability in two moving average risk models with constant interest rate." Acta Mathematica Sinica, English Series 24, no. 2 (February 2008): 319–28. http://dx.doi.org/10.1007/s10114-007-1004-y.

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Chiarella, Carl, Sara Pasquali, and Wolfgang J. Runggaldier. "On filtering in Markovian term structure models: an approximation approach." Advances in Applied Probability 33, no. 04 (December 2001): 794–809. http://dx.doi.org/10.1017/s0001867800011204.

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We consider a parametrization of the Heath-Jarrow-Morton (HJM) family of term structure of interest rate models that allows a finite-dimensional Markovian representation of the stochastic dynamics. This parametrization results from letting the volatility function depend on time to maturity and on two factors: the instantaneous spot rate and one fixed-maturity forward rate. Our main purpose is an estimation methodology for which we have to model the observations under the historical probability measure. This leads us to consider as an additional third factor the market price of interest rate risk, that connects the historical and the HJM martingale measures. Assuming that the information comes from noisy observations of the fixed-maturity forward rate, the purpose is to estimate recursively, on the basis of this information, the three Markovian factors as well as the parameters in the model, in particular those in the volatility function. This leads to a nonlinear filtering problem, for the solution of which we describe an approximation methodology, based on time discretization and quantization. We prove the convergence of the approximate filters for each of the observed trajectories.

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Brody, Dorje C., Lane P. Hughston, and Ewan Mackie. "General theory of geometric Lévy models for dynamic asset pricing." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2142 (February 29, 2012): 1778–98. http://dx.doi.org/10.1098/rspa.2011.0670.

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The geometric Lévy model (GLM) is a natural generalization of the geometric Brownian motion (GBM) model used in the derivation of the Black–Scholes formula. The theory of such models simplifies considerably if one takes a pricing kernel approach. In one dimension, once the underlying Lévy process has been specified, the GLM has four parameters: the initial price, the interest rate, the volatility and the risk aversion. The pricing kernel is the product of a discount factor and a risk aversion martingale. For GBM, the risk aversion parameter is the market price of risk. For a GLM, this interpretation is not valid: the excess rate of return is a nonlinear function of the volatility and the risk aversion. It is shown that for positive volatility and risk aversion, the excess rate of return above the interest rate is positive, and is increasing with respect to these variables. In the case of foreign exchange, Siegel's paradox implies that one can construct foreign exchange models for which the excess rate of return is positive for both the exchange rate and the inverse exchange rate. This condition is shown to hold for any geometric Lévy model for foreign exchange in which volatility exceeds risk aversion.

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Zhang, Xili. "Modeling the Dynamics of Shanghai Interbank Offered Rate Based on Single-Factor Short Rate Processes." Mathematical Problems in Engineering 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/540803.

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Using the Shanghai Interbank Offered Rate data of overnight, 1 week, 2 week and 1 month, this paper provides a comparative analysis of some popular one-factor short rate models, including the Merton model, the geometric Brownian model, the Vasicek model, the Cox-Ingersoll-Ross model, and the mean-reversion jump-diffusion model. The parameter estimation and the model selection of these single-factor short interest rate models are investigated. We document that the most successful model in capturing the Shanghai Interbank Offered Rate is the mean-reversion jump-diffusion model.

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WANG, ZHIFENG, FANGYING WEI, and YUZHOU FANG. "PASS-THROUGH RATE STUDY FOR HONG KONG BANKING INDUSTRY AND ITS APPLICATION TO NONMATURITY DEPOSITS INTEREST RATE RISK MANAGEMENT." Annals of Financial Economics 14, no. 02 (April 21, 2019): 1950009. http://dx.doi.org/10.1142/s201049521950009x.

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Basel Committee on Banking Supervision published Standards on Interest Rate Risk in Banking Book in April 2016. Apart from others, it proposed a standardized framework under which banks should identify core and noncore deposits within their stable nonmaturity deposits (NMD) and determine appropriate cash flow slotting for the NMD. This paper proposed a unique solution to slot Core NMD into repricing time buckets to address Basel requirements on NMD. The proposed solution was based on pass-through rate model under ECM (error correction model) framework. The solution itself showed interesting mathematical property to form a generalized Fibonacci sequence with converged partial sum. What is more, this paper proposed a model-neutral back testing scheme to make objective comparison of performance across different NMD repricing behavior models. The contents of this paper are expected to be useful for practitioners due to lack of quantitative modeling and model validation methodologies on this topic in the industry while, at the same time, to motivate academic discussion on the best practice and further enhancement of the modeling approach for the industry.

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Wang, Anjiao. "The Pricing of Total Return Swap Under Default Contagion Models with Jump-Diffusion Interest Rate Risk." Indian Journal of Pure and Applied Mathematics 51, no. 1 (March 2020): 361–73. http://dx.doi.org/10.1007/s13226-020-0405-9.

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Zeng, Yunhui, Xiuli Wang, and Lu Lin. "Remodeling and Estimation for Sparse Partially Linear Regression Models." Abstract and Applied Analysis 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/687151.

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When the dimension of covariates in the regression model is high, one usually uses a submodel as a working model that contains significant variables. But it may be highly biased and the resulting estimator of the parameter of interest may be very poor when the coefficients of removed variables are not exactly zero. In this paper, based on the selected submodel, we introduce a two-stage remodeling method to get the consistent estimator for the parameter of interest. More precisely, in the first stage, by a multistep adjustment, we reconstruct an unbiased model based on the correlation information between the covariates; in the second stage, we further reduce the adjusted model by a semiparametric variable selection method and get a new estimator of the parameter of interest simultaneously. Its convergence rate and asymptotic normality are also obtained. The simulation results further illustrate that the new estimator outperforms those obtained by the submodel and the full model in the sense of mean square errors of point estimation and mean square prediction errors of model prediction.

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FRY, H. M., and F. T. SMITH. "Rate effects on the growth of centres." European Journal of Applied Mathematics 28, no. 2 (July 7, 2016): 221–42. http://dx.doi.org/10.1017/s0956792516000231.

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Entropy maximising spatial interaction models have been widely exploited in a range of disciplines and applications: from trade and migration flows to the spread of riots and the understanding of spatial patterns in archaeological sites of interest. When embedded into a dynamic system and framed in the context of a retail model, the dynamics of centre growth poses an interesting mathematical problem, with bifurcations and phase changes, which may be addressed analytically. In this paper, we present some analysis of the continuous retail model and the corresponding discrete version, which yields insights into the effect of space on the evolving system, and an understanding of why certain retail centres are more successful than others. The slowly developing growths and the fast explosive growths that are of particular concern are explained in detail.

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Kaibe, Bosiu C., and John G. O’Hara. "Symmetry Analysis of an Interest Rate Derivatives PDE Model in Financial Mathematics." Symmetry 11, no. 8 (August 16, 2019): 1056. http://dx.doi.org/10.3390/sym11081056.

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We perform Lie symmetry analysis to a zero-coupon bond pricing equation whose price evolution is described in terms of a partial differential equation (PDE). As a result, using the computer software package SYM, run in conjunction with Mathematica, a new family of Lie symmetry group and generators of the aforementioned pricing equation are derived. We furthermore compute the exact invariant solutions which constitute the pricing models for the bond by making use of the derived infinitesimal generators and the associated similarity reduction equations. Using known solutions, we again compute more solutions via group point transformations.

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Shea, G. S. "Uncertainty and implied variance bounds in long-memory models of the interest rate term structure." Empirical Economics 16, no. 3 (September 1991): 287–312. http://dx.doi.org/10.1007/bf01206277.

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Goard, Joanna, and Noel Hansen. "Comparison of the performance of a time‐dependent short‐interest rate model with time‐independent models." Applied Mathematical Finance 11, no. 2 (June 2004): 147–64. http://dx.doi.org/10.1080/13504860410001686034.

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Shao, S. "Asymptotic solutions of diffusion models for risk reserves." International Journal of Mathematics and Mathematical Sciences 2003, no. 35 (2003): 2221–39. http://dx.doi.org/10.1155/s0161171203208231.

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We study a family of diffusion models for risk reserves which account for the investment income earned and for the inflation experienced on claim amounts. After we defined the process of the conditional probability of ruin over finite time and imposed the appropriate boundary conditions, classical results from the theory of diffusion processes turn the stochastic differential equation to a special class of initial and boundary value problems defined by a linear diffusion equation. Armed with asymptotic analysis and perturbation theory, we obtain the asymptotic solutions of the diffusion models (possibly degenerate) governing the conditional probability of ruin over a finite time in terms of interest rate.

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Metta, Nirupaplava, Michael Ghijs, Elisabeth Schäfer, Ashish Kumar, Philippe Cappuyns, Ivo Van Assche, Ravendra Singh, et al. "Dynamic Flowsheet Model Development and Sensitivity Analysis of a Continuous Pharmaceutical Tablet Manufacturing Process Using the Wet Granulation Route." Processes 7, no. 4 (April 24, 2019): 234. http://dx.doi.org/10.3390/pr7040234.

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In view of growing interest and investment in continuous manufacturing, the development and utilization of mathematical model(s) of the manufacturing line is of prime importance. These models are essential for understanding the complex interplay between process-wide critical process parameters (CPPs) and critical quality attributes (CQAs) beyond the individual process operations. In this work, a flowsheet model that is an approximate representation of the ConsiGma TM -25 line for continuous tablet manufacturing, including wet granulation, is developed. The manufacturing line involves various unit operations, i.e., feeders, blenders, a twin-screw wet granulator, a fluidized bed dryer, a mill, and a tablet press. The unit operations are simulated using various modeling approaches such as data-driven models, semi-empirical models, population balance models, and mechanistic models. Intermediate feeders, blenders, and transfer lines between the units are also simulated. The continuous process is simulated using the flowsheet model thus developed and case studies are provided to demonstrate its application for dynamic simulation. Finally, the flowsheet model is used to systematically identify critical process parameters (CPPs) that affect process responses of interest using global sensitivity analysis methods. Liquid feed rate to the granulator, and air temperature and drying time in the dryer are identified as CPPs affecting the tablet properties.

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Tian, Tianhai, Yanli Zhou, Yonghong Wu, and Xiangyu Ge. "Estimation of Parameters in Mean-Reverting Stochastic Systems." Mathematical Problems in Engineering 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/317059.

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Stochastic differential equation (SDE) is a very important mathematical tool to describe complex systems in which noise plays an important role. SDE models have been widely used to study the dynamic properties of various nonlinear systems in biology, engineering, finance, and economics, as well as physical sciences. Since a SDE can generate unlimited numbers of trajectories, it is difficult to estimate model parameters based on experimental observations which may represent only one trajectory of the stochastic model. Although substantial research efforts have been made to develop effective methods, it is still a challenge to infer unknown parameters in SDE models from observations that may have large variations. Using an interest rate model as a test problem, in this work we use the Bayesian inference and Markov Chain Monte Carlo method to estimate unknown parameters in SDE models.

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Kuz’min, A. Yu. "An Accounting Procedure for Bonds with a Double Currency Denomination in Accordance with the IFRS." Accounting. Analysis. Auditing 7, no. 6 (December 19, 2020): 55–63. http://dx.doi.org/10.26794/2408-9303-2020-7-6-55-63.

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The study is devoted to the development of accounting procedure and recording the financial results of bonds with a double currency denomination in accordance with International Financial Reporting standards (IFRS). The methodological base of the research includes system and dynamic-situational analysis, evaluation models of financial mathematics, accounting procedures of the theory of financial accounting. Based on the assumptions made at the formal mathematical level, this procedure is fully algorithmized, despite the ambiguity or impossibility of direct assessment of such basic accounting indicators as the initial estimate, the internal effective interest rate, and the amortized cost of a financial instrument. Considerable attention is paid to the issues of mathematical evaluation and reflection of financial results when preparing financial statements in accordance with the concept of amortized cost and effective interest rate, taking into account the impact of changes in the currency component in dynamics. The originality and uniqueness of the developed procedure is that it is applicable to the situations where coupon payments are paid several times a year. The theoretical and practical significance of the research is determined by the development of scientific and applied tools that include accounting and process models, evaluation algorithms and procedures that can be used by accounting and audit departments in practical work when solving problems of reporting in accordance with IFRS.

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TANG, G. H., Y. L. HE, and W. Q. TAO. "COMPARISON OF GAS SLIP MODELS WITH SOLUTIONS OF LINEARIZED BOLTZMANN EQUATION AND DIRECT SIMULATION OF MONTE CARLO METHOD." International Journal of Modern Physics C 18, no. 02 (February 2007): 203–16. http://dx.doi.org/10.1142/s0129183107010383.

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Analytical solutions of the Navier–Stokes equation based on a locally fully-developed flow assumption with various gas slip models are presented and comparisons for velocity profile, flow rate, friction factor, and pressure distribution are performed. The effect of the second-order coefficient in the slip boundary condition becomes significant as the Knudsen number increases. Most slip models are limited to slip regime or marginally transition regime and break down around Kn = 0.1 while Sreekanth's model, followed by Mitsuya's model, gives a good agreement with the linearized Boltzmann solutions from slip regime up to Kn = 2 for flow rate and friction factor predictions. These two models should be of great use for slip flow analysis in micro-electro-mechanical systems (MEMS) and, in particular, in situations where the flow rate and flow resistance are of interest.

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Chaudhury, Rahul, and Sahidul Islam. "A Multi-Objective Risk Return Trade off Models for Banks: Fuzzy Programming Approach." Mathematical Modelling of Engineering Problems 8, no. 2 (April 28, 2021): 179–88. http://dx.doi.org/10.18280/mmep.080203.

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The main focus of banking sector is on the risk management. Asset liability management (ALM) is one of the key processes to manage the risks. The objective of this paper is to develop a multi-objective asset liability optimization model for banks with the maximization of market value of equity and minimization of duration gap as the objective function. Several liquidity ratios, concept of duration and convexity are considered to manage the risk properly. Interest rate risk and liquidity risk are two major considerations in both the regulation and management of a bank. As we know that, with the fluctuation of the market interest rate, the market value of assets and liabilities of a bank changes and that affects a change in owner’s equity. In order to overcome such type of situation here we will use the concept of duration and convexity to manage the interest rate risk. In case of liquidity risk the shortage of liquidity may also put that bank in risk and simultaneously it is very crucial to manage the cash flow properly. So here we will use some major liquidity ratios to manage the liquidity risk. We will take the help of fuzzy programming technique to solve our model properly. A numerical example is given to illustrate our model by considering a hypothetical bank balance sheet. Also we will compare the result obtained by fuzzy technique with result obtained by a non fuzzy based technique.

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Brusov, Peter, Tatiana Filatova, She-I. Chang, and George Lin. "Innovative Investment Models with Frequent Payments of Tax on Income and of Interest on Debt." Mathematics 9, no. 13 (June 25, 2021): 1491. http://dx.doi.org/10.3390/math9131491.

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New modern investment models are created to be as close as possible to real investment conditions. We consider long-term as well as arbitrary duration models with payments of interest on debt and of tax on income a few times per year (semi-annually, quarterly and monthly), which could be applied in real economic practice. Their verification will lead to the creation of a comprehensive system of adequate and correct assessment of the effectiveness of the company’s investment program and its investment strategy. One of the most important elements of calculating the effectiveness of investment projects is the assessment of the discount rate, the calculation methods of which are generalized for the real conditions of the implementation of investment projects. We consider the effectiveness of the investment project from two points of view: the equity owners and the owners of equity and debt. NPV for each of these cases is calculated by two different methods: with the separation of credit and investment flows (and thus discounting the flows using two different rates) and without such separation (with discounting of both flows using the same rate, and WACC can be chosen as the rate). Numerical calculations, conducted for four investment models (without flow separation) show that: (1) in the case of considering the effectiveness of an investment project for owners of equity capital, the increase in the number of payments of tax on income and of interest on debt p leads to a decrease in NPV: this means that the effectiveness of an investment project decreases with p; (2) in the case of considering the effectiveness of an investment project for owners of equity and debt capital, the increase in the number of payments of tax on income and of interest on debt p leads to an increase in NPV: this means that the effectiveness of an investment project increases with p. In the former case, companies should pay tax on profit and interest on debt once per year, while in the latter case, more frequent payments are profitable for the effectiveness of investment. Eight innovative investment models created in this paper can assist decision-makers in the optimal design, planning and control of company investments and the development of a company’s investment strategy.

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Huang, Wen Lai, Lin Zhang, Kaiguo Chen, and Guo Lu. "Mesoscale Mechanisms in Viscoplastic Deformation of Metals and Their Applications to Constitutive Models." Materials 14, no. 16 (August 19, 2021): 4667. http://dx.doi.org/10.3390/ma14164667.

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Deformation of metals has attracted great interest for a long time. However, the constitutive models for viscoplastic deformation at high strain rates are still under intensive development, and more physical mechanisms are expected to be involved. In this work, we employ the newly-proposed methodology of mesoscience to identify the mechanisms governing the mesoscale complexity of collective dislocations, and then apply them to improving constitutive models. Through analyzing the competing effects of various processes on the mesoscale behavior, we have recognized two competing mechanisms governing the mesoscale complex behavior of dislocations, i.e., maximization of the rate of plastic work, and minimization of the elastic energy. Relevant understandings have also been discussed. Extremal expressions have been proposed for these two mesoscale mechanisms, respectively, and a stability condition for mesoscale structures has been established through a recently-proposed mathematical technique, considering the compromise between the two competing mechanisms. Such a stability condition, as an additional constraint, has been employed subsequently to close a two-phase model mimicking the practical dislocation cells, and thus to take into account the heterogeneous distributions of dislocations. This scheme has been exemplified in three increasingly complicated constitutive models, and improves the agreements of their results with experimental ones.

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Tappe, Stefan. "An alternative approach on the existence of affine realizations for HJM term structure models." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, no. 2122 (April 21, 2010): 3033–60. http://dx.doi.org/10.1098/rspa.2009.0493.

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We propose an alternative approach on the existence of affine realizations for Heath, Jarrow and Morton interest rate models. It is applicable to a wide class of models, and simultaneously it is conceptually rather comprehensible. We also supplement some known existence results for particular volatility structures and provide further insights into the geometry of term structure models.

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Shen, Haosheng, Chuan Zhang, Jundong Zhang, Baicheng Yang, and Baozhu Jia. "Applicable and Comparative Research of Compressor Mass Flow Rate and Isentropic Efficiency Empirical Models to Marine Large-Scale Compressor." Energies 13, no. 1 (December 20, 2019): 47. http://dx.doi.org/10.3390/en13010047.

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A compressor is an indispensable component of marine large two-stroke diesel engines. For this type of engine, the compressor mass flow rate and isentropic efficiency empirical models are preferred for both the working cycle dynamic simulation research and the design and testing of control and diagnostics algorithms due to their compact and simple structures, and satisfactory prediction accuracy. Due to absence of comprehensive applicable and comparative research on compressor mass flow rate and isentropic efficiency empirical models for large-scale marine compressors in the literature, two marine compressors with different size, flow rate range, and speed range were selected as research objects in this paper, and a relevant study was conducted to compare and analyze the prediction ability of several classical models, and some recently proposed compressor mass flow rate and isentropic efficiency empirical models. The range of this comparative study includes the prediction accuracy in the design operating area and the extrapolation ability in off-design operating areas. Based on the obtained research results, several guidelines are summarized, which can be followed when developing compressor mathematical models, especially for marine applications. In addition, several research interests are discussed and presented, which can be further studied in the future.

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Evans, Matthew R. "Modelling ecological systems in a changing world." Philosophical Transactions of the Royal Society B: Biological Sciences 367, no. 1586 (January 19, 2012): 181–90. http://dx.doi.org/10.1098/rstb.2011.0172.

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The world is changing at an unprecedented rate. In such a situation, we need to understand the nature of the change and to make predictions about the way in which it might affect systems of interest; often we may also wish to understand what might be done to mitigate the predicted effects. In ecology, we usually make such predictions (or forecasts) by making use of mathematical models that describe the system and projecting them into the future, under changed conditions. Approaches emphasizing the desirability of simple models with analytical tractability and those that use assumed causal relationships derived statistically from data currently dominate ecological modelling. Although such models are excellent at describing the way in which a system has behaved, they are poor at predicting its future state, especially in novel conditions. In order to address questions about the impact of environmental change, and to understand what, if any, action might be taken to ameliorate it, ecologists need to develop the ability to project models into novel, future conditions. This will require the development of models based on understanding the processes that result in a system behaving the way it does, rather than relying on a description of the system, as a whole, remaining valid indefinitely.

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Joyce, C. J., and A. B. Williams. "Kinetics of absorption atelectasis during anesthesia: a mathematical model." Journal of Applied Physiology 86, no. 4 (April 1, 1999): 1116–25. http://dx.doi.org/10.1152/jappl.1999.86.4.1116.

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Recent computed tomography studies show that inspired gas composition affects the development of anesthesia-related atelectasis. This suggests that gas absorption plays an important role in the genesis of the atelectasis. A mathematical model was developed that combined models of gas exchange from an ideal lung compartment, peripheral gas exchange, and gas uptake from a closed collapsible cavity. It was assumed that, initially, the lung functioned as an ideal lung compartment but that, with induction of anesthesia, the airways to dependent areas of lung closed and these areas of lung behaved as a closed collapsible cavity. The main parameter of interest was the time the unventilated area of lung took to collapse; the effects of preoxygenation and of different inspired gas mixtures during anesthesia were examined. Preoxygenation increased the rate of gas uptake from the unventilated area of lung and was the most important determinant of the time to collapse. Increasing the inspired O2 fraction during anesthesia reduced the time to collapse. Which inert gas (N2 or N2O) was breathed during anesthesia had minimal effect on the time to collapse.

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Park, Sang-Hyeon, Min-Ku Lee, and Jeong-Hoon Kim. "The Term Structure of Interest Rates Under Heath–Jarrow–Morton Models with Fast Mean-Reverting Stochastic Volatility." Fluctuation and Noise Letters 15, no. 02 (June 2016): 1650014. http://dx.doi.org/10.1142/s0219477516500140.

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This paper is a study of the term structure of interest rates based on the Heath–Jarrow–Morton (HJM) models with Hull–White volatility function. Under fast mean-reverting stochastic volatility, we obtain an analytic formula for an approximate bond price with estimated error using a Markovian transform method combined with a singular perturbation method. The stochastic volatility correction effect against time-to-maturity is revealed so that it can capture more of the complexities of the interest rate term structure.

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Giet, Ludovic, and Michel Lubrano. "A minimum Hellinger distance estimator for stochastic differential equations: An application to statistical inference for continuous time interest rate models." Computational Statistics & Data Analysis 52, no. 6 (February 2008): 2945–65. http://dx.doi.org/10.1016/j.csda.2007.10.004.

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Gáll, József, Gyula Pap, and Martien C. A. van Zuijlen. "Maximum likelihood estimator of the volatility of forward rates driven by geometric spatial AR sheet." Journal of Applied Mathematics 2004, no. 4 (2004): 293–309. http://dx.doi.org/10.1155/s1110757x04306133.

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Discrete-time forward interest rate curve models are studied, where the curves are driven by a random field. Under the assumption of no-arbitrage, the maximum likelihood estimator of the volatility parameter is given and its asymptotic behaviour is studied. First, the so-called martingale models are examined, but we will also deal with the general case, where we include the market price of risk in the discount factor.

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de la Cruz, Rolando, Oslando Padilla, Mauricio A. Valle, and Gonzalo A. Ruz. "Modeling Recidivism through Bayesian Regression Models and Deep Neural Networks." Mathematics 9, no. 6 (March 17, 2021): 639. http://dx.doi.org/10.3390/math9060639.

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This study aims to analyze and explore criminal recidivism with different modeling strategies: one based on an explanation of the phenomenon and another based on a prediction task. We compared three common statistical approaches for modeling recidivism: the logistic regression model, the Cox regression model, and the cure rate model. The parameters of these models were estimated from a Bayesian point of view. Additionally, for prediction purposes, we compared the Cox proportional model, a random survival forest, and a deep neural network. To conduct this study, we used a real dataset that corresponds to a cohort of individuals which consisted of men convicted of sexual crimes against women in 1973 in England and Wales. The results show that the logistic regression model tends to give more precise estimations of the probabilities of recidivism both globally and with the subgroups considered, but at the expense of running a model for each moment of the time that is of interest. The cure rate model with a relatively simple distribution, such as Weibull, provides acceptable estimations, and these tend to be better with longer follow-up periods. The Cox regression model can provide the most biased estimations with certain subgroups. The prediction results show the deep neural network’s superiority compared to the Cox proportional model and the random survival forest.

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Burlov, Viacheslav, Andrey Andreev, and Fedor Gomazov. "Development of a model for the management of environmental safety of the region, taking into account of the GIS capacity." MATEC Web of Conferences 193 (2018): 02038. http://dx.doi.org/10.1051/matecconf/201819302038.

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The system of space monitoring (SM) is of great importance, as a means of ensuring environmental safety. This system is based on remote sensing. The structure of SM is a distributed system. This system comprises independent data storage, system control, system of dynamic ratings, capacity and forecasting, control system, information system (IS) processing of monitoring data. As IS it is necessary to choose a geographic information system (GIS). IS monitoring refers to the problem-oriented system. These information systems include specialized databases models. All monitoring systems use sets of models, which allow building complex enterprise models. The peculiarity of the SM is the need to coordinate support of this monitoring and rate of the GIS capacity. Production Manager's decision is the impact on the object of monitoring. Results management and environmental data are received at the monitoring subsystem. Integration of SM and GIS monitoring has led to the creation of geoinformation space monitor (GISM). The operation of the system GISM is designed to provide a guaranteed result taking into account the capacity. Basis – the decision of the decision makers (DM). Therefore, an independent scientific and practical interest is the adequate mathematical model of DM.

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Li, Jinzhi, and Shixia Ma. "Pricing Options with Credit Risk in Markovian Regime-Switching Markets." Journal of Applied Mathematics 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/621371.

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This paper investigates the valuation of European option with credit risk in a reduced form model when the stock price is driven by the so-called Markov-modulated jump-diffusion process, in which the arrival rate of rare events and the volatility rate of stock are controlled by a continuous-time Markov chain. We also assume that the interest rate and the default intensity follow the Vasicek models whose parameters are governed by the same Markov chain. We study the pricing of European option and present numerical illustrations.

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Journal articles on the topic 'Interest rate models – Mathematical models'

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