Numerical Solution of Stochastic Differential Equations with Jumps in Finance

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 P.E. Kloeden & E. Platen: Numerical Solution of Stochastic Differential Equations, Springer 1992. The present volume builds on the above-mentioned volume 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 requires an undergraduate background in mathematical or quantitative methods and is accessible to a broad readership, including those who are only seeking numerical recipes.§The Wagner-Platen expansion provides the key for discrete-time numerical methods for stochastic differential equations with jumps. This work 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, chapters on exact simulation, estimation and filtering have been included. Besides serving as a basic text on quantitative methods, this research monograph offers ready access to a large number of potential research problems in an area that is widely applicable and rapidly expanding.§Finance was 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, which provides a general framework for modeling in finance and insurance beyond the standard risk-neutral approach.§To help the reader develop a deeper understanding of the underlying mathematics, exercises with solutions are included.