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Optimal Investment for the Insurers in Markov-Modulated Jump-Diffusion Models

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  • Jinzhi Li
  • Haiying Liu

Abstract

This paper investigates the optimal portfolio investment policies of an insurer with Markov-modulated jump-diffusion risk process. Assume that there are two asset available for the insurer: a risk-free asset and a risky asset. The market interest rate, the drift and the volatility of the risky asset, and the premium rate of the insurer and claim arrival intensity switch over time according to transitions of the Markov chain. Given an insurer maximizing utility from terminal wealth, we present a verification result for portfolio problems, and obtain the explicit forms of the optimal policy with CARA utility function. And we conduct Monte Carlo simulation and perform a sensitivity analysis of the optimal asset allocation strategies and the terminal expected utility. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Jinzhi Li & Haiying Liu, 2015. "Optimal Investment for the Insurers in Markov-Modulated Jump-Diffusion Models," Computational Economics, Springer;Society for Computational Economics, vol. 46(1), pages 143-156, June.
    • Handle: RePEc:kap:compec:v:46:y:2015:i:1:p:143-156
    DOI: 10.1007/s10614-014-9454-7
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    References listed on IDEAS

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    1. Siu, Tak Kuen & Yang, Hailiang & Lau, John W., 2008. "Pricing currency options under two-factor Markov-modulated stochastic volatility models," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 295-302, December.
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    4. Robert Elliott & Carlton-James Osakwe, 2006. "Option Pricing for Pure Jump Processes with Markov Switching Compensators," Finance and Stochastics, Springer, vol. 10(2), pages 250-275, April.
    5. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    6. Robert J. Elliott & Carlton-James U. Osakwe, 2006. "Option Pricing for Pure Jump Processes with Markov Switching Compensators," Finance and Stochastics, Springer, vol. 10(2), pages 250-275, April.
    7. Robert J. Elliott & Leunglung Chan & Tak Kuen Siu, 2005. "Option pricing and Esscher transform under regime switching," Annals of Finance, Springer, vol. 1(4), pages 423-432, October.
    8. Thaleia Zariphopoulou, 2001. "A solution approach to valuation with unhedgeable risks," Finance and Stochastics, Springer, vol. 5(1), pages 61-82.
    9. Yang, Hailiang & Zhang, Lihong, 2005. "Optimal investment for insurer with jump-diffusion risk process," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 615-634, December.
    10. Bo, Lijun & Wang, Yongjin & Yang, Xuewei, 2010. "Markov-modulated jump-diffusions for currency option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 461-469, June.
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    Cited by:

    1. Weiwei Shen & Juliang Yin, 2022. "Optimal Investment and Risk Control Strategies for an Insurer Subject to a Stochastic Economic Factor in a Lévy Market," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2913-2931, December.

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