Stochastic Stefan problems: existence, uniqueness, and modeling of market limit orders

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2013

Author dc:creator

• Zheng, Zhi

Contributors dc:contributor

• Sowers, Richard B.
• DeVille, Robert E.
• Zharnitsky, Vadim
• Rapti, Zoi

• 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

Statement dc:rights

• Copyright 2012 by Zhi Zheng. All rights reserved.

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/42335

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/42335