## Abstract

The purpose of this article is to consider a two firms excess-loss reinsurance problem. The first firm is defined as the direct underwriter while the second firm is the reinsurer. As in the classical model of collective risk theory it is assumed that premium payments are received deterministically from policyholders at a constant rate, while the claim process is determined by a compound Poisson process. The objective of the underwriter is to maximize the expected present value of the long run terminal wealth (investments plus cash) of the firm by selecting an appropriate excess-loss coverage strategy, while the reinsurer seeks to maximize its total expected discounted profit by selecting an optimal loading factor. Since both firms' policies are interdependent we define an insurance game, solved by employing a Stackelberg solution concept. A diffusion approximation is used in order to obtain tractable results for a general claim size distribution. Finally, an example is presented illustrating computational procedures.

Original language | English (US) |
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Pages (from-to) | 85-96 |

Number of pages | 12 |

Journal | Stochastic Processes and their Applications |

Volume | 12 |

Issue number | 1 |

DOIs | |

State | Published - Oct 1981 |

## Keywords

- Reinsurance
- Stackelberge solution
- diffusion approximation
- excess-loss
- loading factor

## ASJC Scopus subject areas

- Statistics and Probability
- Modeling and Simulation
- Applied Mathematics