University of Illinois Urbana-Champaign

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

Zheng, Zhi

Content Files
Zhi_Zheng.pdf

Permalink

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

Description

Title
Stochastic Stefan problems: existence, uniqueness, and modeling of market limit orders
Author(s)
Zheng, Zhi
Issue Date
2013-02-03T19:35:41Z
Director of Research (if dissertation) or Advisor (if thesis)
Sowers, Richard B.
Doctoral Committee Chair(s)
DeVille, Robert E.
Committee Member(s)
  • Sowers, Richard B.
  • Zharnitsky, Vadim
  • Rapti, Zoi
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Date of Ingest
2013-02-03T19:35:41Z
Keyword(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.
Graduation Semester
2012-12
Permalink
http://hdl.handle.net/2142/42335
Copyright and License Information
Copyright 2012 by Zhi Zheng. All rights reserved.

Owning Collections

Graduate Dissertations and Theses at Illinois PRIMARY
Graduate Theses and Dissertations at Illinois
Dissertations and Theses - Mathematics