Gambling Models with Concave Utility Functions.
Abstract
The author examines the problem of a gambler desiring to maximize the expected value of a concave increasing utility function after a fixed, finite number of plays against a casino which offers favourable bets (in the sense of positive expected gains). The gambles are assumed to have any distribution, which may change from play to play according to a Markov chain, but is known to the player previous to his placing each wager. Although the optimal wager does not exhibit simple monotonicity properties as a function of the gambler's current fortune, the author exhibits two linear functions of the wager and fortune that are indeed monotone and allow to bound above and below the optimal wager for any fortune, given that for any other fortune. These functions generalize the statements 'the richer you are the more you save' and 'the richer you are the more you should try to get.' The dependence of the optimal bet on the gamble currently available is examined, and, in the case of coin tossing games, it is shown that 'the better the gamble, the more you should bet.' The case in which the distribution of the gamble is unknown, except for a prior distribution over a set of possible alternatives is also analyzed and results similar to the above are exhibited.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1976
- Accession Number
- ADA035734
Entities
People
- Eduardo J. Subelman
Organizations
- University of California, Berkeley