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Robust reinsurance contracts with risk constraint

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  • Ning Wang
  • Tak Kuen Siu

Abstract

This paper aims to investigate optimal reinsurance contracts in a continuous-time modelling framework from the perspective of a principal-agent problem. The reinsurer plays the role of the principal and aims to determine an optimal reinsurance premium to maximize the expected utility on terminal wealth. It is supposed that the reinsurer faces ambiguity about the insurance claim process. The insurer acts as the agent whose objective is to determine an optimal retention level in a proportional reinsurance to maximize the expected utility on terminal wealth. It is postulated that the insurer is subject to a dynamic Value-at-Risk constraint, which may be attributed to capital requirements specified by Solvency II. The Hamilton-Jacobi-Bellman (HJB) dynamic programming is adopted to discuss the optimization problems of the reinsurer and insurer. Explicit expressions for the optimal solutions of the problems are obtained in the case of exponential utility functions. Numerical examples are provided to illustrate economic intuition and insights.

Suggested Citation

  • Ning Wang & Tak Kuen Siu, 2020. "Robust reinsurance contracts with risk constraint," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2020(5), pages 419-453, May.
    • Handle: RePEc:taf:sactxx:v:2020:y:2020:i:5:p:419-453
    DOI: 10.1080/03461238.2019.1683761
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