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<p>In this paper, we study an investment decision problem for an insurance company who controls risk exposure through reinsurance. The insurer’s surplus can be invested into a risky asset and a risk-free asset with zero interest rate. Moreover, funds can be transferred between the two assets, but the insurer should pay fees on each transaction, equaling to a fixed percentage of the amount transacted. In addition, the insurer is allowed to purchase proportional reinsurance to reduce its claim risks. The insurer’s objective is to determine an optimal investment and reinsurance strategy to maximize the probability of reaching a predetermined target before bankruptcy. Using the dynamic programming approach, we first prove a verification lemma and then, we derive the explicit expressions of the value function and optimal strategy by solving the associated Hamilton-Jacobi-Bellman equation.</p>

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Maximizing the Probability of Reaching a Goal Before Ruin with Transaction Costs

  • 期刊论文

  • 发表日期：

    2026年2月23日

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  • Xiaoqing Liang,
  • Junyi Guo

摘要

In this paper, we study an investment decision problem for an insurance company who controls risk exposure through reinsurance. The insurer’s surplus can be invested into a risky asset and a risk-free asset with zero interest rate. Moreover, funds can be transferred between the two assets, but the insurer should pay fees on each transaction, equaling to a fixed percentage of the amount transacted. In addition, the insurer is allowed to purchase proportional reinsurance to reduce its claim risks. The insurer’s objective is to determine an optimal investment and reinsurance strategy to maximize the probability of reaching a predetermined target before bankruptcy. Using the dynamic programming approach, we first prove a verification lemma and then, we derive the explicit expressions of the value function and optimal strategy by solving the associated Hamilton-Jacobi-Bellman equation.