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arXiv · 1005.0160

Constructing Time-Homogeneous Generalised Diffusions Consistent with Optimal Stopping Values

David Hobson·Martin Klimmek
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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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David Hobson, Martin Klimmek. 2010-05-02. Constructing Time-Homogeneous Generalised Diffusions Consistent with Optimal Stopping Values. https://arxiv.org/abs/1005.0160

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