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We investigate two discrete-time risk models under quota share reinsurance. For the first model we study the finite-time and ultimate ruin probabilities of the insurer and the reinsurer. B.K. Dam and N.Q. Chung introduced the upper bounds of these probabilities in their article (Dam and Chung, Applied Mathematical Sciences, 11(53), 2609–2629 (2017)). In our work, the lower bounds are presented. Moreover, upper and lower bounds of the joint ruin probability of the insurer and the reinsurer are provided. The second model treats (in addition to reinsurance) investment in risky and non-risky assets. In the framework of cost approach we establish the optimal investment strategy in the case of linear return functions. One-period survival probability is considered as well.

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Stochastic Insurance Models with Investment and Reinsurance

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  • 发表日期：

    2025年

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  • Ekaterina Bulinskaya,
  • Alexey Shatokhin

摘要

We investigate two discrete-time risk models under quota share reinsurance. For the first model we study the finite-time and ultimate ruin probabilities of the insurer and the reinsurer. B.K. Dam and N.Q. Chung introduced the upper bounds of these probabilities in their article (Dam and Chung, Applied Mathematical Sciences, 11(53), 2609–2629 (2017)). In our work, the lower bounds are presented. Moreover, upper and lower bounds of the joint ruin probability of the insurer and the reinsurer are provided. The second model treats (in addition to reinsurance) investment in risky and non-risky assets. In the framework of cost approach we establish the optimal investment strategy in the case of linear return functions. One-period survival probability is considered as well.