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Optimal Investment and Reinsurance to Maximize the Probability of Drawup Before Drawdown

Author

Listed:
  • Yakun Liu

    (Hunan Normal University
    Hunan Universtiy)

  • Jingchao Li

    (Shenzhen University)

  • Jieming Zhou

    (Hunan Normal University)

  • Yingchun Deng

    (Hunan University of Information Technology)

Abstract

In this paper, we study the optimal investment and proportional reinsurance problem for an insurer with short-selling and borrowing constraints under the expected value premium principle. The claim process follows a Brownian risk model with a drift. The insurer’s surplus is allowed to invest in one risk-free asset and one risky asset. By using the dynamic programming approach and solving the corresponding boundary-value problems, the optimization objective of maximizing the probability of drawup before drowdown is considered initially. The optimal strategy and the corresponding value function are derived through solving the Hamilton-Jacobi-Bellman (HJB) equation. Moreover, numerical examples are performed to illustrate the effects of model parameters on the optimal strategy. In addition, we verify the optimality of the strategies obtained from the dynamic programming principle by Euler method.

Suggested Citation

  • Yakun Liu & Jingchao Li & Jieming Zhou & Yingchun Deng, 2024. "Optimal Investment and Reinsurance to Maximize the Probability of Drawup Before Drawdown," Methodology and Computing in Applied Probability, Springer, vol. 26(3), pages 1-34, September.
    • Handle: RePEc:spr:metcap:v:26:y:2024:i:3:d:10.1007_s11009-024-10096-9
    DOI: 10.1007/s11009-024-10096-9
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