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Title: Optimal stopping and control problems using the Legendre transform
Author: Sexton, Jennifer
ISNI:       0000 0004 5354 9646
Awarding Body: University of Manchester
Current Institution: University of Manchester
Date of Award: 2014
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This thesis addresses some aspects of the connection between convex analysis andoptimal stopping and control problems. The first chapter contains a summary of theoriginal contributions made in subsequent chapters. The second chapter uses elementary tools from convex analysis to establish anextension of the Legendre transformation. These results complement the results in[66] and are used to provide an alternative proof that Nash equilibria exist in optimalstopping games driven by diffusions. In the third chapter a ‘maximum principle’ for singular stochastic control is es-tablished using methods from convex analysis which is a generalisation of the firstorder conditions derived in [18]. This ‘maximum principle’ is used to show that thesolution to certain singular stochastic control problems can be expressed in termsof a family of associated optimal stopping problems. These results connect the firstorder conditions in [3] and the representation result originating in [5] to variationalanalysis. In particular, the Legendre transform is used to derive first order conditionsfor a class of constrained optimisation problems. Sections 2.1-2.4 and Example 30 have been accepted for publication to the ‘Journalof Convex Analysis’ as [75] subject to minor corrections. The suggested revision hasbeen implemented in this thesis.
Supervisor: Peskir, Goran Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available