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An extended Fatou equation and continuous-time gambling

Published online by Cambridge University Press:  01 July 2016

Victor C. Pestien
Victor C. Pestien*
Affiliation:
The University of Miami
*
∗Postal address: Department of Mathematics, The University of Miami, P.O. Box 249085, Coral Gables, FL 33124, U.S.A.
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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.

Keywords

GAMBLING THEORYSTOCHASTIC CONTROL
Type
Research Article
Information
Advances in Applied Probability , Volume 14 , Issue 2 , June 1982 , pp. 309 - 323
Copyright
Copyright © Applied Probability Trust 1982 

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