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Numerical Method for a Markov‐Modulated Risk Model with Two‐Sided Jumps

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  • Hua Dong
  • Xianghua Zhao

Abstract

This paper considers a perturbed Markov‐modulated risk model with two‐sided jumps, where both the upward and downward jumps follow arbitrary distribution. We first derive a system of differential equations for the Gerber‐Shiu function. Furthermore, a numerical result is given based on Chebyshev polynomial approximation. Finally, an example is provided to illustrate the method.

Suggested Citation

  • Hua Dong & Xianghua Zhao, 2012. "Numerical Method for a Markov‐Modulated Risk Model with Two‐Sided Jumps," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:401562
    DOI: 10.1155/2012/401562
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    References listed on IDEAS

    as
    1. Yi Lu & Cary Tsai, 2007. "The Expected Discounted Penalty at Ruin for a Markov-Modulated Risk Process Perturbed by Diffusion," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(2), pages 136-149.
    2. Li, Shuanming & Lu, Yi, 2008. "The Decompositions of the Discounted Penalty Functions and Dividends-Penalty Identity in a Markov-Modulated Risk Model," ASTIN Bulletin, Cambridge University Press, vol. 38(1), pages 53-71, May.
    3. Xing, Xiaoyu & Zhang, Wei & Jiang, Yiming, 2008. "On the time to ruin and the deficit at ruin in a risk model with double-sided jumps," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2692-2699, November.
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