The problem of optimal portfolio execution has become one of the most important problems in the area of financial mathematics. Over the past two decades, numerous researchers have developed a variety of different models to address this problem. In this dissertation, we extend the LOB (Limit Order Book) model proposed by Obizhaeva and Wang (2013) by incorporating a more realistic assumption on the order book depth; the amount of liquidity provided by a LOB market is finite at all times. We use an algorithmic approach to solve the problem of optimal execution under time-varying constraints on the depth of a LOB. For the simplest case where the order book depth stays at a fixed level for the entire trading horizon, we reduce the optimal execution problem into a one-dimensional root-finding problem which can be readily solved by standard numerical algorithms. When the depth of the LOB is monotone in time, we first apply the KKT (Karush-Kuhn-Tucker) conditions to narrow down the set of candidate strategies and then use a dichotomy-based search algorithm to pin down the optimal one. For the general case that the order book depth doesn't exhibit any particular pattern, we start from the optimal strategy subject to no liquidity constraints and iterate over execution strategy by sequentially adding more constraints to the problem in a specific fashion until primal feasibility is achieved. Numerical experiments indicate that our algorithms give comparable results to those of current existing convex optimization toolbox CVXOPT with significantly lower time complexity. / A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester 2018. / March 22, 2018. / convex programming, limit order market, market impact model, optimal portfolio execution / Includes bibliographical references. / Arash Fahim, Professor Directing Dissertation; Jen Atkins, University Representative; Alec Kercheval, Committee Member; Giray Okten, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_653457 |
| Contributors | Lin, Hua-Yi (author), Fahim, Arash (professor directing dissertation), Atkins, Jennifer (university representative), Kercheval, Alec N. (committee member), Ökten, Giray (committee member), Florida State University (degree granting institution), College of Arts and Sciences (degree granting college), Department of Mathematics (degree granting departmentdgg) |
| Publisher | Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text, doctoral thesis |
| Format | 1 online resource (75 pages), computer, application/pdf |
Page generated in 0.0016 seconds