Affiliation:
1. Department of Mathematics and Industrial Engineering, Polytechnique Montréal, 2500, Chemin de Polytechnique, Montréal, QC H3T 1J4, Canada
Abstract
A stochastic difference game is considered in which a player wants to minimize the time spent by a controlled one-dimensional symmetric random walk {Xn,n=0,1,…} in the continuation region C:={1,2,…}, and the second player seeks to maximize the survival time in C. The process starts at X0=x>0 and the game ends the first time Xn≤0. An exact expression is derived for the value function, from which the optimal solution is obtained, and particular problems are solved explicitly.
Funder
Natural Sciences and Engineering Research Council of Canada
Subject
Applied Mathematics,Statistics, Probability and Uncertainty,Statistics and Probability
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