Optimal switching between two random walks

• 成果类型: Article
• 署名作者: Cairoli, R; Dalang, RC
• 署名单位: Tufts University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176987812
• 发表日期: 1995
• 页码: 1982-2013
• 关键词: brownian motions

摘要

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.