Publication: Explicit Solution Processes for Nonlinear Jump-Diffusion Equations
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Springer Science and Business Media LLC
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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.
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Journal of Nonlinear Mathematical Physics
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OPEN
Keywords
explicit solution process, linearization conditions, stochastic integrating factor, stochastic differential equation, compound Poisson process, Financial applications of other theories, Stochastic ordinary differential equations (aspects of stochastic analysis)