### 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) |
---|---|

Pages (from-to) | 85-96 |

Number of pages | 12 |

Journal | Stochastic Processes and their Applications |

Volume | 12 |

Issue number | 1 |

DOIs | |

State | Published - 1981 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Statistics, Probability and Uncertainty
- Mathematics(all)
- Modeling and Simulation
- Statistics and Probability

### Cite this

*Stochastic Processes and their Applications*,

*12*(1), 85-96. https://doi.org/10.1016/0304-4149(81)90013-2

**Optimum excess-loss reinsurance : a dynamic framework.** / Tapiero, Charles; Zuckerman, Dror.

Research output: Contribution to journal › Article

*Stochastic Processes and their Applications*, vol. 12, no. 1, pp. 85-96. https://doi.org/10.1016/0304-4149(81)90013-2

}

TY - JOUR

T1 - Optimum excess-loss reinsurance

T2 - a dynamic framework

AU - Tapiero, Charles

AU - Zuckerman, Dror

PY - 1981

Y1 - 1981

N2 - 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.

AB - 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.

KW - diffusion approximation

KW - excess-loss

KW - loading factor

KW - Reinsurance

KW - Stackelberge solution

UR - http://www.scopus.com/inward/record.url?scp=49049152845&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=49049152845&partnerID=8YFLogxK

U2 - 10.1016/0304-4149(81)90013-2

DO - 10.1016/0304-4149(81)90013-2

M3 - Article

AN - SCOPUS:49049152845

VL - 12

SP - 85

EP - 96

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

IS - 1

ER -