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Optimal proportional reinsurance with a loss-dependent premium principle

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  • Duni Hu
  • Hailong Wang

Abstract

Empirical studies suggest that many insurance companies recontract with their clients on premiums by extrapolating past losses: a client is offered a decrease in premium if the monetary amounts of his claims do not exceed some prespecified quantities, otherwise, an increase in premium. In this paper, we formulate the empirical studies and investigate optimal reinsurance problems of a risk-averse insurer by introducing a loss-dependent premium principle, which uses a weighted average of history losses and the expectation of future losses to replace the expectation in the expected premium principle. This premium principle satisfies the bonus-malus and smoothes the insurer's wealth. Explicit expressions for the optimal reinsurance strategies and value functions are derived. If the reinsurer applies the loss-dependent premium principle to continuously adjust his premium, we show that the insurer always needs less reinsurance when he also adopts this premium principle than when he adopts the expected premium principle.

Suggested Citation

  • Duni Hu & Hailong Wang, 2019. "Optimal proportional reinsurance with a loss-dependent premium principle," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2019(9), pages 752-767, October.
    • Handle: RePEc:taf:sactxx:v:2019:y:2019:i:9:p:752-767
    DOI: 10.1080/03461238.2019.1604426
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    Cited by:

    1. Tong Qian & Cuixia Chen & Weijun Yin & Bing Liu, 2024. "Optimal Investment-reinsurance Strategies for an Insurer with Options Trading Under Model Ambiguity," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-21, December.

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