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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.
Acknowledgements
The authors would like to sincerely thank the editor and the referees for evaluating the paper and providing insightful comments and suggestions. This paper is based on a thesis by the first author for a Master of Research at Macquarie University.
Disclosure statement
No potential conflict of interest was reported by the authors.
Notes
1 We would like to thank the comments from a referee for stimulating the discussions here.