EXPLICIT SOLUTION PROCESSES FOR NONLINEAR JUMP-DIFFUSION EQUATIONS

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

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, vol.17, no.3, pp.281-310, 2010 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 17 Issue: 3
• Publication Date: 2010
• Doi Number: 10.1142/s1402925110000908
• Journal Name: JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Page Numbers: pp.281-310
• Istanbul Technical University Affiliated: Yes

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.