A Utility Function Derived from a Survival Game

Karl Borch
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Karl Borch: University of California, Los Angeles

Management Science, 1966, vol. 12, issue 8, B287-B295

Abstract: The starting point of the paper is a firm engaged in a risky business. It is assumed that the firm's gain in each operating period is a stochastic variable. It is further assumed that these stochastic variables are independent and identically distributed. If the capital of the firm becomes negative, the firm is ruined, and must go out of business. The optimal dividend policy is defined as the policy which will maximize the expected discounted value of the dividends paid before ruin occurs. It is then shown that the solution of the dividend problem gives the utility function, which will govern the firm's decisions under uncertainty. From this result it appears that a number of decisions which seem irrational when studied in isolation, become perfectly rational when analysed in their proper dynamic setting.

Date: 1966
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