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An effective method for the explicit solution of sequential problems on the real line

Journal article
Authors Sören Christensen
Published in Sequential Analysis
Volume 36
Issue 1
Pages 2-18
ISSN 0747-4946
Publication year 2017
Published at Department of Mathematical Sciences
Pages 2-18
Language en
Links dx.doi.org/10.1080/07474946.2016.12...
Keywords Generalized parking problems, Lorden’s test, Markov processes, monotone stopping rules, optimal stopping, running maximum process, threshold times, Continuous time systems, Continuous time Markov process, Mathematical Finance, Optimal stopping problem, Sequential problems, Stopping rule, Problem solving
Subject categories Mathematical statistics

Abstract

A general method for solving optimal stopping problems for continuous-time Markov processes on the real line is developed. The basic idea is to first study an auxiliary problem for the two-dimensional process consisting of the underlying Markov process and its running maximum. It turns out that this auxiliary problem is much easier to solve using standard methods such as the monotonicity of the problem, and an optimal strategy in the class of threshold times can be found. The optimality of the time carries over to original problem. This two-step procedure gives a unifying approach for solving problems from different fields such as mathematical finance and sequential analysis. © 2017 Taylor & Francis.

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