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Optimal per-loss reinsurance and investment to minimize the probability of drawdown

  • *Corresponding author: Zhibin Liang

    *Corresponding author: Zhibin Liang 

This research was supported by the National Natural Science Foundation of China (Grant No.12071224)

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  • In this paper, we study an optimal reinsurance-investment problem in a risk model with two dependent classes of insurance business, where the two claim number processes are correlated through a common shock component. We assume that the insurer can purchase per-loss reinsurance for each line of business and invest its surplus in a financial market consisting of a risk-free asset and a risky asset. Under the criterion of minimizing the probability of drawdown, the closed-form expressions for the optimal reinsurance-investment strategy and the corresponding value function are obtained. We show that the optimal reinsurance strategy is in the form of pure excess-of-loss reinsurance strategy under the expected value principle, and under the variance premium principle, the optimal reinsurance strategy is in the form of pure quota-share reinsurance. Furthermore, we extend our model to the case where the insurance company involves $ n $ $ (n\geq3) $ dependent classes of insurance business and the optimal results are derived explicitly as well.

    Mathematics Subject Classification: Primary: 93E20; Secondary: 91G05, 91G10.


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  • Figure 1.  The function $ G(7,d) $

    Figure 2.  The effect of $ u $ on optimal strategy

    Figure 3.  The effect of η1 on optimal strategy (η2 = 0.25)

    Figure 4.  The effect of $ \eta_2 $ on optimal strategy ($ \eta_1 = 0.4 $)

    Figure 5.  The effect of $ \lambda $ on optimal strategy

    Figure 6.  The effect of $ \lambda $ on correlation coefficient

    Figure 7.  Comparison between the optimal strategies

    Figure 8.  Comparison between the value functions

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