Numerical Solution of Stochastic Differential Equations with Jumps in Finance

Abstract

This research monograph concerns the design and analysis of discrete-time approximations for stochastic differential equations (SDEs) driven by ·Wiener processes and Poisson processes or Poisson jump measures, In financial and actuarial modeling and other areas of application I such jump difrusions are often used to d¿Scribe the dynamics of ',.-arious state variables. In finance these may represent, for instance, asset prices, credit ratings, stock indices, luterest rates, exchange rates or commodity prices. The jump component can capture event-driven unC<'xtainties, such as corporato defaults, operational failures or insured events.