Stochastic Differential Equations with Jumps
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Stochastic differential equations (SDEs) with jumps provide the most flexible, numerically accessible, mathematical framework that allows us to model the evolution of financial and other random quantities over time. In particular, feedback effects can be easily modeled and jumps enable us to model events. This chapter introduces SDEs driven by Wiener processes, Poisson processes and Poisson random measures. We also discuss the Itô formula, the Feyman-Kac formula and the existence and uniqueness of solutions of SDEs. These tools and results provide the basis for the application and numerical solution of stochastic differential equations with jumps.
KeywordsPoisson Process Asset Price Wiener Process Quadratic Variation Local Martingale
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