Results in stochastic control: optimal prediction problems and Markov decision processes

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Pérez López, Iker (2015) Results in stochastic control: optimal prediction problems and Markov decision processes. PhD thesis, University of Nottingham.

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Abstract

The following thesis is divided in two main topics. The first part studies variations of optimal prediction problems introduced in Shiryaev, Zhou and Xu (2008) and Du Toit and Peskir (2009) to a randomized terminal-time set up and different families of utility measures. The work presents optimal stopping rules that apply under different criteria, introduces a numerical technique to build approximations of stopping boundaries for fixed terminal time problems and suggest previously reported stopping rules extend to certain generalizations of measures.

The second part of the thesis is concerned with analysing optimal wealth allocation techniques within a defaultable financial market similar to Bielecki and Jang (2007). It studies a portfolio optimization problem combining a continuous time jump market and a defaultable security; and presents numerical solutions through the conversion into a Markov Decision Process and characterization of its value function as a unique fixed point to a contracting operator. This work analyses allocation strategies under several families of utilities functions, and highlights significant portfolio selection differences with previously reported results.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Le, H.
Hodges, D.J.
Keywords: optimal prediction problems, Markov decision process, MDP, stochastic control theory
Subjects: Q Science > QA Mathematics > QA273 Probabilities
Q Science > QA Mathematics > QA299 Analysis
Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID: 28395
Depositing User: Pérez López, Iker
Date Deposited: 16 Oct 2015 13:30
Last Modified: 15 Dec 2017 11:16
URI: https://eprints.nottingham.ac.uk/id/eprint/28395

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