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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Previous articles were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence, and they are hosted by MDPI on mdpi.com as a courtesy and upon agreement with Association for Scientific Research (ASR).
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Article

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

by
Ismail Iyigunler
1,*,
Mine Çağlar
1,* and
Gazanfer Ünal
2,*
1
Koç University, 34450 Istanbul, Turkey
2
Department of International Finance, Yeditepe University, 34755 Istanbul, Turkey
*
Authors to whom correspondence should be addressed.
Math. Comput. Appl. 2012, 17(1), 68-82; https://doi.org/10.3390/mca17010068
Published: 1 April 2012
Versions Notes

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

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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. https://doi.org/10.3390/mca17010068

AMA Style

Iyigunler I, Çağlar M, Ünal G. Exact Solvability of Stochastic Differential Equations Driven by Finite Activity Levy Processes. Mathematical and Computational Applications. 2012; 17(1):68-82. https://doi.org/10.3390/mca17010068

Chicago/Turabian Style

Iyigunler, Ismail, Mine Çağlar, and Gazanfer Ünal. 2012. "Exact Solvability of Stochastic Differential Equations Driven by Finite Activity Levy Processes" Mathematical and Computational Applications 17, no. 1: 68-82. https://doi.org/10.3390/mca17010068

APA Style

Iyigunler, I., Çağlar, M., & Ünal, G. (2012). Exact Solvability of Stochastic Differential Equations Driven by Finite Activity Levy Processes. Mathematical and Computational Applications, 17(1), 68-82. https://doi.org/10.3390/mca17010068

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