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A Compensated Numerical Method for Solving Stochastic Differential Equations with Variable Delays and Random Jump Magnitudes

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  • Ying Du
  • Changlin Mei

Abstract

Stochastic differential equations with jumps are of a wide application area especially in mathematical finance. In general, it is hard to obtain their analytical solutions and the construction of some numerical solutions with good performance is therefore an important task in practice. In this study, a compensated split-step method is proposed to numerically solve the stochastic differential equations with variable delays and random jump magnitudes. It is proved that the numerical solutions converge to the analytical solutions in mean-square with the approximate rate of 1/2. Furthermore, the mean-square stability of the exact solutions and the numerical solutions are investigated via a linear test equation and the results show that the proposed numerical method shares both the mean-square stability and the so-called A-stability.

Suggested Citation

  • Ying Du & Changlin Mei, 2015. "A Compensated Numerical Method for Solving Stochastic Differential Equations with Variable Delays and Random Jump Magnitudes," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-11, July.
    • Handle: RePEc:hin:jnlmpe:810160
    DOI: 10.1155/2015/810160
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