Optimum excess-loss reinsurance: a dynamic framework

Charles Tapiero, Dror Zuckerman

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)85-96
Number of pages12
JournalStochastic Processes and their Applications
Volume12
Issue number1
DOIs
StatePublished - 1981

Fingerprint

Reinsurance
Excess
Insurance
Profitability
Maximise
Risk Theory
Compound Poisson Process
Diffusion Approximation
Solution Concepts
Long-run
Rate Constant
Profit
Coverage
Business
Framework
Game

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

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

In: Stochastic Processes and their Applications, Vol. 12, No. 1, 1981, p. 85-96.

Research output: Contribution to journalArticle

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