Explicit Solution Processes for Nonlinear Jump-Diffusion Equations

Abstract

Jump-diffusion equations with compound Poisson processes are often used to model financial data with spiky behavior. As many models are nonlinear, it is interesting to obtain linearization criteria together with the linearizing transformations, if any. Furthermore, the method of stochastic integrating factors is presented to solve linear jump-diffusion equations. Extended Cox-Ingersoll-Ross, Brennan-Schwartz and Epstein models are shown to be linearizable and their explicit solutions are given.