The Library
Coupling and the policy improvement algorithm for controlled diffusion processess
Tools
Širaj, Dejan (2015) Coupling and the policy improvement algorithm for controlled diffusion processess. PhD thesis, University of Warwick.
|
PDF
WRAP_Thesis_Širaj_2015.pdf - Requires a PDF viewer. Download (744Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b2844845~S1
Abstract
The thesis deals with the mirror and synchronous couplings of geometric Brownian motions, the policy improvement (or iteration) algorithm in completely continuous settings, and an application where the latter is applied to the former.
First we investigate whether the mirror and synchronous couplings of Brownian motions minimise and maximise, respectively, the coupling time of the corresponding geometric Brownian motions. We prove (via Bellman's principle) that this is indeed the case in the infinite horizon and ergodic average problems, but not necessarily in the finite horizon and exponential efficiency problems, for which we characterise when the two couplings are suboptimal.
Then we describe the policy improvement algorithm for controlled diffusion processes in the framework of the discounted infinite horizon problem, both in one and several dimensions. Under some assumptions on the data of the problem, we prove that the algorithm yields a sequence of Markov policies such that its accumulation point is an optimal policy, and that the corresponding payoff functions converge monotonically to the value function. We use no discretisation procedures at any stage. We show that a large class of data satisfies the assumptions, and an example implemented in Matlab demonstrates that the convergence is numerically fast.
Next we study the policy improvement algorithm for continuous finite horizon problem. We obtain analogous results as for the infinite horizon problem. Finally we apply the algorithm to a certain sequence of data to approximate the value function of the (partially unsolved) finite horizon problem for geometric Brownian motions.
Item Type: | Thesis (PhD) | ||||
---|---|---|---|---|---|
Subjects: | H Social Sciences > HA Statistics | ||||
Library of Congress Subject Headings (LCSH): | Brownian motion processes, Markov processes, Statistical decision | ||||
Official Date: | March 2015 | ||||
Dates: |
|
||||
Institution: | University of Warwick | ||||
Theses Department: | Department of Statistics | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Jacka, Saul D. ; Mijatović, Aleksandar | ||||
Sponsors: | Slovene Human Resources Development and Scholarship Fund ; University of Warwick | ||||
Extent: | v, 102 leaves | ||||
Language: | eng |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year