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Optimal stopping and randomisation

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Zeng, Matthew (2020) Optimal stopping and randomisation. PhD thesis, University of Warwick.

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Official URL: http://webcat.warwick.ac.uk/record=b3494562~S15

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Abstract

This thesis is a collection of four individual works on optimal stopping problems in junction with stochastic behaviours. Chapter 2 introduces the classical optimal stopping problem. In the classical model, the optimal strategy is to stop at some predetermined threshold, and thus there is no stochastic behaviours involved. Chapter 3 established a dynamic Cautious Stochastic Choice (CSC) model for an optimal stopping problem. Randomised strategies outperform threshold strategies in the CSC model, and thus, stochastic behaviours are predicted by our CSC model. Chapter 4 discussed the sufficiency of randomised threshold strategies and pointed out that the desire of stochastic behaviours stems from quasi-convexity. Chapter 5 considered a stopping problem where the agent doesn’t stop with probability one. Instead, the stopping probability depends on the relative values of stopping and continuing. We discussed the case where stopping opportunities are constrained to be event times of an independent Poisson process. Dupuis and Wang introduced constraint on the class of admissible stopping times which they had to take values in the set of event times of an exogenous, time-homogeneous Poisson process. Chapter 6 extended the analysis of Dupuis and Wang (2005) to allow the agent to choose the rate of the Poisson process. Even for a simple model for the stopped process and a simple call-style payoff, the problem leads to a rich range of optimal behaviours which depend on the form of the cost function.

Item Type: Thesis or Dissertation (PhD)
Subjects: Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH): Optimal stopping (Mathematical statistics), Stochastic processes
Official Date: January 2020
Dates:
DateEvent
January 2020UNSPECIFIED
Institution: University of Warwick
Theses Department: Department of Statistics
Thesis Type: PhD
Publication Status: Unpublished
Supervisor(s)/Advisor: Hobson, David ; Henderson, Vicky
Sponsors: University of Warwick
Format of File: pdf
Extent: vi, 129 leaves : colour illustrations
Language: eng

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