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Optimal time-consistent investment and reinsurance policies for mean-variance insurers

  • Zeng, Yan
  • Li, Zhongfei
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    This paper investigates the optimal time-consistent policies of an investment-reinsurance problem and an investment-only problem under the mean-variance criterion for an insurer whose surplus process is approximated by a Brownian motion with drift. The financial market considered by the insurer consists of one risk-free asset and multiple risky assets whose price processes follow geometric Brownian motions. A general verification theorem is developed, and explicit closed-form expressions of the optimal polices and the optimal value functions are derived for the two problems. Economic implications and numerical sensitivity analysis are presented for our results. Our main findings are: (i) the optimal time-consistent policies of both problems are independent of their corresponding wealth processes; (ii) the two problems have the same optimal investment policies; (iii) the parameters of the risky assets (the insurance market) have no impact on the optimal reinsurance (investment) policy; (iv) the premium return rate of the insurer does not affect the optimal policies but affects the optimal value functions; (v) reinsurance can increase the mean-variance utility.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167668711000023
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    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 49 (2011)
    Issue (Month): 1 (July)
    Pages: 145-154

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    Handle: RePEc:eee:insuma:v:49:y:2011:i:1:p:145-154
    Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505554

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    1. Gu, Mengdi & Yang, Yipeng & Li, Shoude & Zhang, Jingyi, 2010. "Constant elasticity of variance model for proportional reinsurance and investment strategies," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 580-587, June.
    2. 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.
    3. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    4. repec:spr:compst:v:68:y:2008:i:1:p:181-205 is not listed on IDEAS
    5. Browne, S., 1995. "Optimal Investment Policies for a Firm with a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin," Papers 95-08, Columbia - Graduate School of Business.
    6. 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.
    7. Bai, Lihua & Guo, Junyi, 2008. "Optimal proportional reinsurance and investment with multiple risky assets and no-shorting constraint," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 968-975, June.
    8. repec:spr:compst:v:62:y:2005:i:1:p:159-165 is not listed on IDEAS
    9. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
    10. repec:spr:compst:v:66:y:2007:i:2:p:339-367 is not listed on IDEAS
    11. Chen, Shumin & Li, Zhongfei & Li, Kemian, 2010. "Optimal investment-reinsurance policy for an insurance company with VaR constraint," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 144-153, October.
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