EXPLICIT SOLUTION PROCESSES FOR NONLINEAR JUMP-DIFFUSION EQUATIONS


Uenal G., Turkeri H., Khalique C. M.

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, vol.17, no.3, pp.281-310, 2010 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 3
  • Publication Date: 2010
  • Doi Number: 10.1142/s1402925110000908
  • Title of Journal : JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS
  • Page Numbers: pp.281-310

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.