The Bargaining Set of a Reinsurance Market

Abstract

This paper uses the same notations and some of the results of BATON and LE~IAIRE (1981). The reader is referred to that work for more details about the classical risk exchange model, which will not be recalled here. The main result of that former paper was to characterize the core of the market in the case of exponential utdities, and to show that it is never empty. Since the core always exists, and since ~t ~s such an intuitive notion, one m~ght wonder why we introduce here a much more complicated concept. The reason is that the core is presently subject to a heavy fire of critmisms-both experimental and theore-t mal-from leading researchers in game theory ; they claim that tile core is much too static, that ~t does not take into account the real dynamics of the bargaining process, that it does not introduce the full spectrum of negotiation threats of the traders. Indeed, experimental data consistently produce final payoffs that he outside the core, but within the bargaining set (abbreviated:b.s.) We shall attempt to illustrate those cntmisms in 4- We shall define the b.s. m a general non transferable game in 2, and characterize it in the specml case of a 3-company reinsurance market in 3, but first of all we would hke to explain intuitively the basic mechanisms of the b s. by means of a simple example (with transferable utilitms).

Volume
12:2
Page
101-114
Year
1981
Description
This paper uses the same notations and some of the results of BATON and LE~IAIRE (1981). The reader is referred to that work for more details about the classical risk exchange model, which will not be recalled here. The main result of that former paper was to characterize the core of the market in the case of exponential utdities, and to show that it is never empty. Since the core always exists, and since ~t ~s such an intuitive notion, one m~ght wonder why we introduce here a much more complicated concept. The reason is that the core is presently subject to a heavy fire of critmisms-both experimental and theore-
t mal-from leading researchers in game theory ; they claim that tile core is much too static, that ~t does not take into account the real dynamics of the bargaining process, that it does not introduce the full spectrum of negotiation threats of the traders. Indeed, experimental data consistently produce final payoffs that he outside the core, but within the bargaining set (abbreviated:b.s.) We shall attempt to illustrate those cntmisms in 4- We shall define the b.s. m a general non transferable game in 2, and characterize it in the specml case of a 3-company reinsurance market in 3, but first of all we would hke to explain intuitively the basic mechanisms of the b s. by means of a simple example (with transferable utilitms).
Categories
Financial and Statistical Methods
Risk Pricing and Risk Evaluation Models
Utility Theory
Business Areas
Reinsurance
Publications
ASTIN Bulletin
Authors
Bernard Baton
Jean Lemaire
Formerly on syllabus
Off