Date of Award

August 2020

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Richard Stockbridge

Committee Members

Vytaras Brazauskas, Istvan Lauko, Wei Wei, Chao Zhu

Keywords

continuity, probability, stochastic

Abstract

In order to study model uncertainty of an optimal stopping problem of a stochastic process with a given state dependent drift rate and volatility, we analyze the effects of perturbing the parameters of the problem. This is accomplished by translating the original problem into a semi-infinite linear program and its dual. We then approximate this dual linear program by a countably constrained sub-linear program as well as an infinite sequence of finitely constrained linear programs. We find that in this framework the value function will be lower semi-continuous with respect to the parameters. If in addition we restrict ourselves to a compact set of constraints and add smoothness conditions to the gain function, we have full continuity of the value function.

Included in

Mathematics Commons

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