Abstract
Let be a stochastic process starting at which changes by i.i.d. dichotomous increments with mean 0 and variance 1. The cost of proceeding one step is one and the payoff is zero unless steps are taken and the final value of is negative in which case the payoff is . The optimal procedure consists of stopping as soon as where is the number of steps left to be taken. The limit of as is desired as a function of . This limit is evaluated for rational and proved to be continuous in . One can use to relate the solution of optimal stopping problems involving a Wiener process to those involving certain discrete-time discrete-process stopping problems. Thus is useful in calculating simple numerical approximations to solutions of various stopping problems.
Citation
H. Chernoff. A. J. Petkau. "An Optimal Stopping Problem for Sums of Dichotomous Random Variables." Ann. Probab. 4 (6) 875 - 889, December, 1976. https://doi.org/10.1214/aop/1176995933
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