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An extended Fatou equation and continuous-time gambling
Published online by Cambridge University Press: 01 July 2016
Abstract
Let be an optional stochastic process and let be the directed set of almost-surely-finite stopping times. If lim , then
This equality is employed in studying the continuous-time gambler's problem, as formulated by Heath and Sudderth (1974). The optimal return function is shown to be upper semi-analytic and excessive whenever the utility function is Borel.
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- Copyright © Applied Probability Trust 1982
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