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Optimal proportional reinsurance and investment based on Hamilton-Jacobi-Bellman equation

Author

Listed:
  • Cao, Yusong
  • Wan, Nianqing

Abstract

In the whole paper, the claim process is assumed to follow a Brownian motion with drift and the insurer is allowed to invest in a risk-free asset and a risky asset. In addition, the insurer can purchase the proportional reinsurance to reduce the risk. The paper concerns the optimal problem of maximizing the utility of terminal wealth. By solving the corresponding Hamilton-Jacobi-Bellman equations, the optimal strategies about how to purchase the proportional reinsurance and how to invest in the risk-free asset and risky asset are derived respectively.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:45:y:2009:i:2:p:157-162
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    References listed on IDEAS

    as
    1. 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.
    2. Sid Browne, 1995. "Optimal Investment Policies for a Firm With a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin," Mathematics of Operations Research, INFORMS, vol. 20(4), pages 937-958, November.
    3. 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.
    4. Gajek, Leslaw & Zagrodny, Dariusz, 2000. "Insurer's optimal reinsurance strategies," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 105-112, August.
    5. S. David Promislow & Virginia Young, 2005. "Minimizing the Probability of Ruin When Claims Follow Brownian Motion with Drift," North American Actuarial Journal, Taylor & Francis Journals, vol. 9(3), pages 110-128.
    Full references (including those not matched with items on IDEAS)

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