Stochastic Differential Equations with Jumps

  • Eckhard PlatenEmail author
  • Nicola Bruti-Liberati
Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 64)


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.


Poisson Process Asset Price Wiener Process Quadratic Variation Local Martingale 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.School of Finance and Economics, Department of Mathematical SciencesUniversity of Technology, SydneyBroadwayAustralia

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