Robust reinsurance contracts with risk constraint

Research output: Contribution to journalArticleResearchpeer-review

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.
LanguageEnglish
Number of pages35
JournalScandinavian Actuarial Journal
DOIs
Publication statusE-pub ahead of print - 30 Oct 2019

Fingerprint

Reinsurance
Expected Utility
Maximise
Proportional Reinsurance
Exponential Utility
Value at Risk
Hamilton-Jacobi
Utility Function
Insurance
Dynamic Programming
Continuous Time
Optimal Solution
Economics
Optimization Problem
Numerical Examples
Requirements
Modeling
Insurer
Expected utility
Optimal reinsurance

Keywords

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

Cite this

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title = "Robust reinsurance contracts with risk constraint",
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.",
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Robust reinsurance contracts with risk constraint. / Wang, Ning; Siu, Tak Kuen.

In: Scandinavian Actuarial Journal, 30.10.2019.

Research output: Contribution to journalArticleResearchpeer-review

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