Constructing Time-Homogeneous Generalised Diffusions Consistent with Optimal Stopping Values

2010/05/02 by David Hobson, Hobson, David, Martin Klimmek +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60G40 #FOS: Mathematics #Optimization and Control (math.OC) #Point processes and geometric inequalities #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications #math.OC #math.PR #msc:60G40

paper · pdf · doi:10.48550/arxiv.1005.0160

arxiv created 2010/05/02 · openalex publication_date 2010/05/02 · arxiv updated 2010/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider a set of discounted optimal stopping problems for a one-parameter family of objective functions and a fixed diffusion process, started at a fixed point. A standard problem in stochastic control/optimal stopping is to solve for the problem value in this setting. In this article we consider an inverse problem; given the set of problem values for a family of objective functions, we aim to recover the diffusion. Under a natural assumption on the family of objective functions we can characterise existence and uniqueness of a diffusion for which the optimal stopping problems have the specified values. The solution of the problem relies on techniques from generalised convexity theory

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