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Optimal proportional reinsurance and investment with regime-switching for mean–variance insurers

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Listed author(s):
  • Chen, Ping
  • Yam, S.C.P.
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    Abstract

    Following the framework of Promislow and Young (2005), this paper considers an optimal investment–reinsurance problem of an insurer facing a claim process modeled by a Brownian motion with drift under the Markowitz mean–variance criterion. The market modes are divided into a finite number of regimes. All the key parameters change according to the value of different market modes. The insurer chooses to purchase proportional reinsurance to reduce the underlying risk. In addition to reinsurance, we suppose that the insurer is allowed to invest its surplus in a financial market consisting of a risk-free asset (bond or bank account) and a risky asset whose price process is modeled by a geometric Brownian motion. We investigate the feasibility of the problem, obtain an analytic expression for the optimal strategy, delineate the efficient frontier and demonstrate our results with numerical examples.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167668713001583
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    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 53 (2013)
    Issue (Month): 3 ()
    Pages: 871-883

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    Handle: RePEc:eee:insuma:v:53:y:2013:i:3:p:871-883
    DOI: 10.1016/j.insmatheco.2013.10.004
    Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505554

    Keywords: Proportional reinsurance; Optimal investment–reinsurance; Geometric Brownian motion; Mean–variance; Efficient frontier;

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    1. Zeng, Yan & Li, Zhongfei, 2011. "Optimal time-consistent investment and reinsurance policies for mean-variance insurers," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 145-154, July.
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    12. Raymond, Jennie E & Rich, Robert W, 1997. "Oil and the Macroeconomy: A Markov State-Switching Approach," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(2), pages 193-213, May.
    13. Duan Li & Wan-Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean-Variance Formulation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 387-406.
    14. Chen, Ping & Yang, Hailiang & Yin, George, 2008. "Markowitz's mean-variance asset-liability management with regime switching: A continuous-time model," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 456-465, December.
    15. Cao, Yusong & Wan, Nianqing, 2009. "Optimal proportional reinsurance and investment based on Hamilton-Jacobi-Bellman equation," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 157-162, October.
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    Cited by:

    1. Shen, Yang & Zeng, Yan, 2015. "Optimal investment–reinsurance strategy for mean–variance insurers with square-root factor process," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 118-137.
    2. Meng, Hui & Li, Shuanming & Jin, Zhuo, 2015. "A reinsurance game between two insurance companies with nonlinear risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 91-97.
    3. Chen, Lv & Qian, Linyi & Shen, Yang & Wang, Wei, 2016. "Constrained investment–reinsurance optimization with regime switching under variance premium principle," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 253-267.
    4. Pun, Chi Seng & Wong, Hoi Ying, 2015. "Robust investment–reinsurance optimization with multiscale stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 245-256.

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