Game Theory and Life Insurance

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Astln Bulletin 11 (198o) 1-16 A GAME T H E O R E T I C LOOK AT L I F E I N S U R A N C E UNDERWRITING* JEAN LEMAIRE Universit6 Libre de Bruxelles Tim decision problem o[ acceptance or rejection of life insurance proposals is formulated as a ~vo-person non cooperattve game between the insurer and the set of the proposers Using the mmtmax criterion or the Bayes criterion, ~t ~s shown how the value and the optunal stxateg~es can be computed, and how an optimal s e t of medina!, mformatmns can be selected and utlhzed 1. FORMULATIONOF THE GAME The purpose of this paper, whose m a t h e m a t i c a l level is elementary, is to d e m o n s t r a t e how g a m e t h e o r y can help the insurers to formulate a n d solve some of their…show more content…
P2's optmml strategy is to present a proportion of good risks. 2.2. Introduction of Medical Information The preceding model is extremely naive (and vv1Lt only be used as reference for comparisons) since it does not take into account P,'s possibility to gather some information about the proposer's health, by asking him to fill in an health questmnnaire, or by requiring him to undertake a medical examination. This information is of course only partially reliable. But, however imperfect, it can be used to improve P~'s guaranteed payoff. How can the insurer make optimal use of the information lie does have ? It is sufficient for our purposes to characterize tile medical information by two parameters : Ps, tile probability of successfully noticing a bad risk, and PF, tile false alarm probability of detecting a non-existant illness. Let us introduce a third pure strategy for P , : to follow the indications of tile medical information. If tile proposer is not healthy, his illness is detected with a probabihty Ps, and remains undetected with a probability 1 - - P S . . P i ' S expected payoff thus equals E = Dps + C(1-ps). Smailarly, his payoff m case the proposer is healthy is F = (1--pF)A + t~FB. Fig. 2 represents a "detector" with a .7 success probability and a .4 false alarm