### Abstract

Language | English |
---|---|

Number of pages | 35 |

Journal | Scandinavian Actuarial Journal |

DOIs | |

Publication status | E-pub ahead of print - 30 Oct 2019 |

### Fingerprint

### Keywords

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

### Cite this

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**Robust reinsurance contracts with risk constraint.** / Wang, Ning; Siu, Tak Kuen.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Robust reinsurance contracts with risk constraint

AU - Wang, Ning

AU - Siu, Tak Kuen

PY - 2019/10/30

Y1 - 2019/10/30

N2 - 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.

AB - 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.

KW - ambiguity

KW - Karush-Kuhn-Tucker (KKT) conditions

KW - Optimal reinsurance

KW - principal-agent problem

KW - proportional reinsurance

KW - risk constraint

U2 - 10.1080/03461238.2019.1683761

DO - 10.1080/03461238.2019.1683761

M3 - Article

JO - Scandinavian Actuarial Journal

T2 - Scandinavian Actuarial Journal

JF - Scandinavian Actuarial Journal

SN - 0346-1238

ER -