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Optimal Reinsurance and Investment Strategies under Mean-Variance Criteria: Partial and Full Information

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  • Shihao Zhu
  • Jingtao Shi

Abstract

This paper is concerned with an optimal reinsurance and investment problem for an insurance firm under the criterion of mean-variance. The driving Brownian motion and the rate in return of the risky asset price dynamic equation cannot be directly observed. And the short-selling of stocks is prohibited. The problem is formulated as a stochastic linear-quadratic (LQ) optimal control problem where the control variables are constrained. Based on the separation principle and stochastic filtering theory, the partial information problem is solved. Efficient strategies and efficient frontier are presented in closed forms via solutions to two extended stochastic Riccati equations. As a comparison, the efficient strategies and efficient frontier are given by the viscosity solution for the Hamilton-Jacobi-Bellman (HJB) equation in the full information case. Some numerical illustrations are also provided.

Suggested Citation

  • Shihao Zhu & Jingtao Shi, 2019. "Optimal Reinsurance and Investment Strategies under Mean-Variance Criteria: Partial and Full Information," Papers 1906.08410, arXiv.org, revised Jun 2020.
    • Handle: RePEc:arx:papers:1906.08410
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    References listed on IDEAS

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    Cited by:

    1. Nicole Bauerle & Gregor Leimcke, 2021. "Bayesian optimal investment and reinsurance with dependent financial and insurance risks," Papers 2103.05777, arXiv.org.

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