Regression and convex switching system methods for stochastic control problems with applications to multiple-exercise options

Yap, SG

Regression and convex switching system methods for stochastic control problems with applications to multiple-exercise options

Yap, SG

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Publication Type:: Thesis
Issue Date:: 2015

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Field	Value	Language
dc.contributor.author	Yap, SG
dc.date.accessioned	2015-11-30T22:53:46Z
dc.date.available	2015-11-30T22:53:46Z
dc.date.issued	2015
dc.identifier.uri	http://hdl.handle.net/10453/39183
dc.description	University of Technology Sydney. Faculty of Business.	en_AU
dc.description.abstract	In this thesis, we develop several new simulation-based algorithms for solving some important classes of optimal stochastic control problems. In particular, these methods are aimed at providing good approximate solutions to problems that involve a high-dimensional underlying processes. These algorithms are of the primal-dual kind and therefore provide a gauge of the distance to optimality of the given approximate solutions to the optimal one. These methods will be used in the pricing of the multiple-exercise option. In Chapter 1, we conduct a review of the literature that is relevant to the pricing of the multiple-exercise option and the primal and dual methods that we will be developing in this thesis. In the next two chapters of the thesis, we focus on regression-based dual methods for optimal multiple stopping problems in probability theory. In particular, we concentrate on finding upper bounds on the price of the multiple-exercise option as it sits within this framework. In Chapter 2, we derive an additive dual for the multiple-exercise options using financial arguments, and see that this approach leads to the construction of an algorithm that has greater computational efficiency than other methods in the literature. In Chapter 3, we derive the first known dual of the multiplicative kind for the multiple-exercise option and devise a tractable algorithm to compute it. In the penultimate chapter of the thesis, we focus on a new class of algorithms that are based on what is known as convex switching system. These algorithms provide approximate solutions to the more general class of optimal stochastic switching problems. In Chapter 4, techniques based on combinations of rigorous theory and heuristics arguments are used to improve the efficiency and applicability of the method. We then devise algorithms of the primal-dual kind to assess the accuracy of this approach. Chapter 5 concludes.	en_AU
dc.format	Thesis (PhD)
dc.language.iso	en_AU	en_AU
dc.relation	https://opus.lib.uts.edu.au/bitstream/10453/39183/2/02whole.pdf
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	au.edu.uts.lib/ppc
dc.rights	The author owns the copyright in this thesis including all reproduction and reuse rights for the work. The work may not be altered without the permission of the copyright owner. Attribution is essential when quoting or paraphrasing from this thesis.
dc.subject	Simulation-based algorithms.	en
dc.subject	High-dimensional underlying processes.	en
dc.subject	Multiple-exercise option.	en
dc.subject	Primal and dual methods.	en
dc.subject	Regression-based dual methods.	en
dc.subject	Convex switching system.	en
dc.subject	Stochastic control problems.	en
dc.title	Regression and convex switching system methods for stochastic control problems with applications to multiple-exercise options	en_AU
dc.type	Thesis	en_AU
utslib.copyright.status	open_access

Abstract:

In this thesis, we develop several new simulation-based algorithms for solving some important classes of optimal stochastic control problems. In particular, these methods are aimed at providing good approximate solutions to problems that involve a high-dimensional underlying processes. These algorithms are of the primal-dual kind and therefore provide a gauge of the distance to optimality of the given approximate solutions to the optimal one. These methods will be used in the pricing of the multiple-exercise option. In Chapter 1, we conduct a review of the literature that is relevant to the pricing of the multiple-exercise option and the primal and dual methods that we will be developing in this thesis. In the next two chapters of the thesis, we focus on regression-based dual methods for optimal multiple stopping problems in probability theory. In particular, we concentrate on finding upper bounds on the price of the multiple-exercise option as it sits within this framework. In Chapter 2, we derive an additive dual for the multiple-exercise options using financial arguments, and see that this approach leads to the construction of an algorithm that has greater computational efficiency than other methods in the literature. In Chapter 3, we derive the first known dual of the multiplicative kind for the multiple-exercise option and devise a tractable algorithm to compute it. In the penultimate chapter of the thesis, we focus on a new class of algorithms that are based on what is known as convex switching system. These algorithms provide approximate solutions to the more general class of optimal stochastic switching problems. In Chapter 4, techniques based on combinations of rigorous theory and heuristics arguments are used to improve the efficiency and applicability of the method. We then devise algorithms of the primal-dual kind to assess the accuracy of this approach. Chapter 5 concludes.

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http://hdl.handle.net/10453/39183