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Some applications of optimal stopping and control in finance and economics
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Liu, Ruiqi (2022) Some applications of optimal stopping and control in finance and economics. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3872167
Abstract
In this thesis, we consider some applications of optimal stopping and control problems in specific scenarios. In Chapter 1, a review of the established general results is provided. In Chapter 2, we study a mathematical model capturing the support/ resistance line method (a technique in technical analysis) where the underlying stock price transitions between two states of nature in a path-dependent manner. For optimal stopping problems with respect to a general class of reward functions and dynamics, using probabilistic methods, we show that the value function is C1 and solves a general free boundary problem. Moreover, for a wide range of utilities, we prove that the best time to buy and sell the stock is obtained by solving free boundary problems corresponding to two linked optimal stopping problems. We use this to numerically compute optimal trading strategies and compare the strategies with the standard trading rule to investigate the viability of this form of technical analysis. In Chapter 3, the model studied in Chapter 2 is extended by adding a partial reflection boundary and an additional regime (the 0 regime). In Chapter 4, we study a two dimensional continuous-time infinite horizon singular control problem related with the optimal management of inventory and production. The primary source of production is modeled as an uncontrolled one-dimensional diffusion process with general dynamics. By controlling the accumulated secondary source of production and output, which are both finite variation processes, we aim to optimise the inventory process under a general concave running reward function and maximise the profit generated from the production. By solving the associated Dynkin game, we obtain two non-intersecting bounded and monotone free-boundaries where one is directly computable and the other is characterised by a free-boundary problem with smooth-pasting conditions. By restricting the volatility term of the diffusion to linear functions with no intercepts, desired smoothness of the value function is obtained by utilising its viscosity property. This leads to the verification of the proposed candidate optimal control that keeps the state process within the inaction set by reflecting the inventory process at the free-boundaries with the minimum effort.
Item Type: | Thesis (PhD) | ||||
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Subjects: | H Social Sciences > HG Finance Q Science > QA Mathematics |
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Library of Congress Subject Headings (LCSH): | Optimal stopping (Mathematical statistics), Stocks -- Prices -- Mathematical models, Boundary value problems, Stochastic control theory | ||||
Official Date: | October 2022 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Department of Statistics | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Jacka, Saul D. ; Henderson, Vicky | ||||
Sponsors: | University of Warwick. Department of Statistics | ||||
Format of File: | |||||
Extent: | vi, 116 pages | ||||
Language: | eng |
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