Theory of Stochastic Differential Equations with Jumps and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Theory of Stochastic Differential Equations with Jumps and Applications write by Rong SITU. This book was released on 2006-05-06. Theory of Stochastic Differential Equations with Jumps and Applications available in PDF, EPUB and Kindle. Stochastic differential equations (SDEs) are a powerful tool in science, mathematics, economics and finance. This book will help the reader to master the basic theory and learn some applications of SDEs. In particular, the reader will be provided with the backward SDE technique for use in research when considering financial problems in the market, and with the reflecting SDE technique to enable study of optimal stochastic population control problems. These two techniques are powerful and efficient, and can also be applied to research in many other problems in nature, science and elsewhere.
Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications
Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications write by Łukasz Delong. This book was released on 2013-06-12. Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications available in PDF, EPUB and Kindle. Backward stochastic differential equations with jumps can be used to solve problems in both finance and insurance. Part I of this book presents the theory of BSDEs with Lipschitz generators driven by a Brownian motion and a compensated random measure, with an emphasis on those generated by step processes and Lévy processes. It discusses key results and techniques (including numerical algorithms) for BSDEs with jumps and studies filtration-consistent nonlinear expectations and g-expectations. Part I also focuses on the mathematical tools and proofs which are crucial for understanding the theory. Part II investigates actuarial and financial applications of BSDEs with jumps. It considers a general financial and insurance model and deals with pricing and hedging of insurance equity-linked claims and asset-liability management problems. It additionally investigates perfect hedging, superhedging, quadratic optimization, utility maximization, indifference pricing, ambiguity risk minimization, no-good-deal pricing and dynamic risk measures. Part III presents some other useful classes of BSDEs and their applications. This book will make BSDEs more accessible to those who are interested in applying these equations to actuarial and financial problems. It will be beneficial to students and researchers in mathematical finance, risk measures, portfolio optimization as well as actuarial practitioners.
Reflecting Stochastic Differential Equations with Jumps and Applications
Reflecting Stochastic Differential Equations with Jumps and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Reflecting Stochastic Differential Equations with Jumps and Applications write by Situ Rong. This book was released on 1999-08-05. Reflecting Stochastic Differential Equations with Jumps and Applications available in PDF, EPUB and Kindle. Many important physical variables satisfy certain dynamic evolution systems and can take only non-negative values. Therefore, one can study such variables by studying these dynamic systems. One can put some conditions on the coefficients to ensure non-negative values in deterministic cases. However, as a random process disturbs the system, the components of solutions to stochastic differential equations (SDE) can keep changing between arbitrary large positive and negative values-even in the simplest case. To overcome this difficulty, the author examines the reflecting stochastic differential equation (RSDE) with the coordinate planes as its boundary-or with a more general boundary. Reflecting Stochastic Differential Equations with Jumps and Applications systematically studies the general theory and applications of these equations. In particular, the author examines the existence, uniqueness, comparison, convergence, and stability of strong solutions to cases where the RSDE has discontinuous coefficients-with greater than linear growth-that may include jump reflection. He derives the nonlinear filtering and Zakai equations, the Maximum Principle for stochastic optimal control, and the necessary and sufficient conditions for the existence of optimal control. Most of the material presented in this book is new, including much new work by the author concerning SDEs both with and without reflection. Much of it appears here for the first time. With the application of RSDEs to various real-life problems, such as the stochastic population and neurophysiological control problems-both addressed in the text-scientists dealing with stochastic dynamic systems will find this an interesting and useful work.
Numerical Solution of Stochastic Differential Equations
Numerical Solution of Stochastic Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Numerical Solution of Stochastic Differential Equations write by Peter E. Kloeden. This book was released on 2013-04-17. Numerical Solution of Stochastic Differential Equations available in PDF, EPUB and Kindle. The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations. From the reviews: "The authors draw upon their own research and experiences in obviously many disciplines... considerable time has obviously been spent writing this in the simplest language possible." --ZAMP
Numerical Solution of Stochastic Differential Equations with Jumps in Finance
Numerical Solution of Stochastic Differential Equations with Jumps in Finance - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Numerical Solution of Stochastic Differential Equations with Jumps in Finance write by Eckhard Platen. This book was released on 2010-07-23. Numerical Solution of Stochastic Differential Equations with Jumps in Finance available in PDF, EPUB and Kindle. In financial and actuarial modeling and other areas of application, stochastic differential equations with jumps have been employed to describe the dynamics of various state variables. The numerical solution of such equations is more complex than that of those only driven by Wiener processes, described in Kloeden & Platen: Numerical Solution of Stochastic Differential Equations (1992). The present monograph builds on the above-mentioned work and provides an introduction to stochastic differential equations with jumps, in both theory and application, emphasizing the numerical methods needed to solve such equations. It presents many new results on higher-order methods for scenario and Monte Carlo simulation, including implicit, predictor corrector, extrapolation, Markov chain and variance reduction methods, stressing the importance of their numerical stability. Furthermore, it includes chapters on exact simulation, estimation and filtering. Besides serving as a basic text on quantitative methods, it offers ready access to a large number of potential research problems in an area that is widely applicable and rapidly expanding. Finance is chosen as the area of application because much of the recent research on stochastic numerical methods has been driven by challenges in quantitative finance. Moreover, the volume introduces readers to the modern benchmark approach that provides a general framework for modeling in finance and insurance beyond the standard risk-neutral approach. It requires undergraduate background in mathematical or quantitative methods, is accessible to a broad readership, including those who are only seeking numerical recipes, and includes exercises that help the reader develop a deeper understanding of the underlying mathematics.
