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Math. Comput. Appl. 2012, 17(1), 68-82; doi:10.3390/mca17010068

Exact Solvability of Stochastic Differential Equations Driven by Finite Activity Levy Processes

1
Koç University, 34450 Istanbul, Turkey
2
Department of International Finance, Yeditepe University, 34755 Istanbul, Turkey
*
Authors to whom correspondence should be addressed.
Published: 1 April 2012
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Abstract

We consider linearizing transformations of the one-dimensional nonlinear stochastic differential equations driven by Wiener and compound Poisson processes, namely finite activity Levy processes. We present linearizability criteria and derive the required transformations. We use a stochastic integrating factor method to solve the linearized equations and provide closed-form solutions. We apply our method to a number ofstochastic differential equations including Cox-Ingersoll-Ross short-term interest rate model, log-mean reverting asset pricing model and geometric Ornstein- Uhlenbeck equation all with additional jump terms. We use their analytical solutions to illustrate the accuracy of the numerical approximations obtained from Euler and Maghsoodi discretization schemes. The means of the solutions are estimated through Monte Carlo method.
Keywords: Stochastic differential equations; Levy processes; Stochastic integrating factors; Linearization Stochastic differential equations; Levy processes; Stochastic integrating factors; Linearization
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Iyigunler, I.; Çağlar, M.; Ünal, G. Exact Solvability of Stochastic Differential Equations Driven by Finite Activity Levy Processes. Math. Comput. Appl. 2012, 17, 68-82.

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