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Equilibrium mean–variance reinsurance and investment strategies for a general insurance company under smooth ambiguity

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  • Guan, Guohui
  • Hu, Xiang

Abstract

This work investigates the equilibrium investment and reinsurance strategies for a general insurance company under smooth ambiguity. The general insurance company holds shares of an insurance company and a reinsurance company. The claims of the insurer follow a compound Poisson process. The insurer can divide part of the insurance risk to the reinsurer. Besides, the insurer and reinsurer both participate in the financial market and invest in cash and stock. However, the general insurance company is ambiguous about the insurance and financial risks and is an ambiguity-averse manager (AAM). The uncertainties over the insurance and financial risks are described by second-order distributions. The AAM aims to maximize the average performance of the weighted sum surplus process of the insurer and reinsurer under the mean–variance criterion and smooth ambiguity. We present the extended Hamilton–Jacobi–Bellman (HJB) system for the optimization problem combining the mean–variance criterion and smooth ambiguity. In the case that the second-order distributions are Gaussian, we obtain the closed-forms of the equilibrium reinsurance and investment strategies. At the end of this work, sensitivity analyses are presented to show the economic behaviors of the AAM.

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  • Guan, Guohui & Hu, Xiang, 2022. "Equilibrium mean–variance reinsurance and investment strategies for a general insurance company under smooth ambiguity," The North American Journal of Economics and Finance, Elsevier, vol. 63(C).
    • Handle: RePEc:eee:ecofin:v:63:y:2022:i:c:s1062940822001310
    DOI: 10.1016/j.najef.2022.101793
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    More about this item

    Keywords

    Proportional reinsurance; Investment; Equilibrium strategy; Smooth ambiguity; Mean–variance;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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