The Annals of Probability

Optimal Switching Between Two Random Walks

R. Cairoli and Robert C. Dalang

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This paper is motivated by remarkable results of Mandelbaum, Shepp and Vanderbei concerning an optimal switching problem for two Brownian motions. In this paper, the discrete form of this problem, in which the Brownian motions are replaced by random walks, is studied and solved without any restriction on the boundary data. The method proposed here involves uncovering the structure of the solution using combinatorial and geometric arguments, and then providing a characterization for the two types of possible solutions, as well as explicit formulas for computing the solution. The extension of these methods and results to the continuous time problem will be considered in a subsequent paper.

Article information

Ann. Probab., Volume 23, Number 4 (1995), 1982-2013.

First available in Project Euclid: 19 April 2007

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Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]
Secondary: 62L15: Optimal stopping [See also 60G40, 91A60] 49L25: Viscosity solutions

Stochastic control optimal switching random walk value function


Cairoli, R.; Dalang, Robert C. Optimal Switching Between Two Random Walks. Ann. Probab. 23 (1995), no. 4, 1982--2013. doi:10.1214/aop/1176987812.

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