2004•Journal of Applied ProbabilityRequires access

Optimal stopping rules for correlated random walks with a discount

Pieter C. Allaart

Abstract

Optimal stopping rules are developed for the correlated random walk when future returns are discounted by a constant factor per unit time. The optimal rule is shown to be of dual threshold form: one threshold for stopping after an up-step, and another for stopping after a down-step. Precise expressions for the thresholds are given for both the positively and the negatively correlated cases. The optimal rule is illustrated by several numerical examples.

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Key concepts: Mathematics, Optimal stopping, Random walk, Stopping time, Stopping rule, Constant (computer programming), Optional stopping theorem, Dual (grammatical number)