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

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

Zheng, Zhi

关键词: 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;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/42335/Zhi_Zheng.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

In this thesis we study theeffect 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.