Robust reinsurance contracts with risk constraint

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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.
Original languageEnglish
Pages (from-to)419-453
Number of pages35
JournalScandinavian Actuarial Journal
Volume2020
Issue number5
Early online date30 Oct 2019
DOIs
Publication statusPublished - 27 May 2020

Keywords

  • ambiguity
  • Karush-Kuhn-Tucker (KKT) conditions
  • Optimal reinsurance
  • principal-agent problem
  • proportional reinsurance
  • risk constraint

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