[PDF] Extremes Of Multidimensional Stationary Diffusion Processes And Applications In Finance eBook

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Page : pages
File Size : 37,40 MB
Release : 2007
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This thesis deals with the extreme behavior of multidimensional reversible diffusion processes. The partial maxima of the process, measured in a suitable norm, are considered up to the time horizon T>0. The fine tail asymptotics of the maxima is evaluated for fixed T>0 as well as the long time behavior in the sense of classical extreme value theory. The problem can be reduced to the analysis of spectral asymptotics for the generator of the process subject to Dirichlet boundary conditions on bounded domains which extend to the whole state space. The results are applied to multidimensional diffusion processes in financial mathematics. Multivariate short-rate models are presented and their extreme behavior is explicitly analyzed. In addition, goodness-of-fit tests are developed taking into account the extremes in the data.

Author : Jan Baldeaux
Publisher : Springer Science & Business Media
Page : 432 pages
File Size : 32,44 MB
Release : 2013-08-13
Category : Mathematics
ISBN : 3319007475

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This research monograph provides an introduction to tractable multidimensional diffusion models, where transition densities, Laplace transforms, Fourier transforms, fundamental solutions or functionals can be obtained in explicit form. The book also provides an introduction to the use of Lie symmetry group methods for diffusions, which allows to compute a wide range of functionals. Besides the well-known methodology on affine diffusions it presents a novel approach to affine processes with applications in finance. Numerical methods, including Monte Carlo and quadrature methods, are discussed together with supporting material on stochastic processes. Applications in finance, for instance, on credit risk and credit valuation adjustment are included in the book. The functionals of multidimensional diffusions analyzed in this book are significant for many areas of application beyond finance. The book is aimed at a wide readership, and develops an intuitive and rigorous understanding of the mathematics underlying the derivation of explicit formulas for functionals of multidimensional diffusions.​

Author : Jacques Janssen
Publisher : John Wiley & Sons
Page : 412 pages
File Size : 23,34 MB
Release : 2013-04-08
Category : Mathematics
ISBN : 1118578341

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The aim of this book is to promote interaction between engineering, finance and insurance, as these three domains have many models and methods of solution in common for solving real-life problems. The authors point out the strict inter-relations that exist among the diffusion models used in engineering, finance and insurance. In each of the three fields, the basic diffusion models are presented and their strong similarities are discussed. Analytical, numerical and Monte Carlo simulation methods are explained with a view to applying them to obtain the solutions to the different problems presented in the book. Advanced topics such as nonlinear problems, Lévy processes and semi-Markov models in interactions with the diffusion models are discussed, as well as possible future interactions among engineering, finance and insurance. Contents 1. Diffusion Phenomena and Models. 2. Probabilistic Models of Diffusion Processes. 3. Solving Partial Differential Equations of Second Order. 4. Problems in Finance. 5. Basic PDE in Finance. 6. Exotic and American Options Pricing Theory. 7. Hitting Times for Diffusion Processes and Stochastic Models in Insurance. 8. Numerical Methods. 9. Advanced Topics in Engineering: Nonlinear Models. 10. Lévy Processes. 11. Advanced Topics in Insurance: Copula Models and VaR Techniques. 12. Advanced Topics in Finance: Semi-Markov Models. 13. Monte Carlo Semi-Markov Simulation Methods.

Author : Wolfgang Siegert
Publisher : Springer Science & Business Media
Page : 264 pages
File Size : 32,83 MB
Release : 2009
Category : Mathematics
ISBN : 3540859632

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Establishing a new concept of local Lyapunov exponents the author brings together two separate theories, namely Lyapunov exponents and the theory of large deviations. Specifically, a linear differential system is considered which is controlled by a stochastic process that during a suitable noise-intensity-dependent time is trapped near one of its so-called metastable states. The local Lyapunov exponent is then introduced as the exponential growth rate of the linear system on this time scale. Unlike classical Lyapunov exponents, which involve a limit as time increases to infinity in a fixed system, here the system itself changes as the noise intensity converges, too.

Author : Peter Tankov
Publisher : CRC Press
Page : 552 pages
File Size : 10,5 MB
Release : 2003-12-30
Category : Business & Economics
ISBN : 1135437947

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WINNER of a Riskbook.com Best of 2004 Book Award! During the last decade, financial models based on jump processes have acquired increasing popularity in risk management and option pricing. Much has been published on the subject, but the technical nature of most papers makes them difficult for nonspecialists to understand, and the mathematic

Author : Carlos A. Braumann
Publisher : John Wiley & Sons
Page : 335 pages
File Size : 50,55 MB
Release : 2019-02-25
Category : Mathematics
ISBN : 111916608X

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A comprehensive introduction to the core issues of stochastic differential equations and their effective application Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance offers a comprehensive examination to the most important issues of stochastic differential equations and their applications. The author — a noted expert in the field — includes myriad illustrative examples in modelling dynamical phenomena subject to randomness, mainly in biology, bioeconomics and finance, that clearly demonstrate the usefulness of stochastic differential equations in these and many other areas of science and technology. The text also features real-life situations with experimental data, thus covering topics such as Monte Carlo simulation and statistical issues of estimation, model choice and prediction. The book includes the basic theory of option pricing and its effective application using real-life. The important issue of which stochastic calculus, Itô or Stratonovich, should be used in applications is dealt with and the associated controversy resolved. Written to be accessible for both mathematically advanced readers and those with a basic understanding, the text offers a wealth of exercises and examples of application. This important volume: Contains a complete introduction to the basic issues of stochastic differential equations and their effective application Includes many examples in modelling, mainly from the biology and finance fields Shows how to: Translate the physical dynamical phenomenon to mathematical models and back, apply with real data, use the models to study different scenarios and understand the effect of human interventions Conveys the intuition behind the theoretical concepts Presents exercises that are designed to enhance understanding Offers a supporting website that features solutions to exercises and R code for algorithm implementation Written for use by graduate students, from the areas of application or from mathematics and statistics, as well as academics and professionals wishing to study or to apply these models, Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance is the authoritative guide to understanding the issues of stochastic differential equations and their application.

Author : Arturo Kohatsu-Higa
Publisher : Springer Science & Business Media
Page : 427 pages
File Size : 18,97 MB
Release : 2011-07-22
Category : Mathematics
ISBN : 3034800975

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Stochastic analysis has a variety of applications to biological systems as well as physical and engineering problems, and its applications to finance and insurance have bloomed exponentially in recent times. The goal of this book is to present a broad overview of the range of applications of stochastic analysis and some of its recent theoretical developments. This includes numerical simulation, error analysis, parameter estimation, as well as control and robustness properties for stochastic equations. The book also covers the areas of backward stochastic differential equations via the (non-linear) G-Brownian motion and the case of jump processes. Concerning the applications to finance, many of the articles deal with the valuation and hedging of credit risk in various forms, and include recent results on markets with transaction costs.