EXPLICIT SOLUTION PROCESSES FOR NONLINEAR JUMP-DIFFUSION EQUATIONS

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.