EXPLICIT SOLUTION PROCESSES FOR NONLINEAR JUMP-DIFFUSION EQUATIONS

Abstract

Recent studies have shown that the nonlinear jump-diffusion models give results which are in agreement with financial data. Here we provide linearization criteria together with transformations which linearize the nonlinear jump-diffusion models with compound Poisson processes. Furthermore, we introduce the stochastic integrating factor to solve the linear jump-diffusion equations. Extended Cox–Ingersoll–Ross, Brennan–Schwartz and Epstein models are shown to be linearizable and their explicit solutions are presented.

Keywords:

• Compound Poisson processes
• linearization conditions
• stochastic integrating factor
• explicit solution processes
• stochastic differential equations