Files in this item



application/pdfZhi_Zheng.pdf (491kB)
(no description provided)PDF


Title:Stochastic Stefan problems: existence, uniqueness, and modeling of market limit orders
Author(s):Zheng, Zhi
Director of Research:Sowers, Richard B.
Doctoral Committee Chair(s):DeVille, Robert E.
Doctoral Committee Member(s):Sowers, Richard B.; Zharnitsky, Vadim; Rapti, Zoi
Department / Program:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):stochastic partial differential equations (PDEs)
moving boundaries
market limit orders
parameter estimation
Maximum-Likelihood Estimator (MLE)
Mean-Square Errors (MSE)
Akaike information criterion (AIC)
investment optimization
dynamic optimization
Abstract:In this thesis we study the effect of stochastic perturbations on moving boundary value PDE's with Stefan boundary conditions, or Stefan problems, and show the existence and uniqueness of the solutions to a number of stochastic equations of this kind. We also derive the space and time regularities of the solutions and the associated boundaries via Kolmogorov's Continuity Theorem in a defined normed space. Moreover, we model the evolution of market limit orders in completely continuous settings using such equations, derive parameter estimation schemes using maximum likelihood and least mean-square-errors methods under certain criteria, and settle the investment optimization problem in both static and dynamic sense when taking the model as exogenous.
Issue Date:2013-02-03
Rights Information:Copyright 2012 by Zhi Zheng. All rights reserved.
Date Available in IDEALS:2013-02-03
Date Deposited:2012-12

This item appears in the following Collection(s)

Item Statistics