Advisor(s)
Ian Knowles
Committee Member(s)
Dongsheng Wu
Marius Nkashama
Nuo Xu
Wei Zhu
School
College of Arts and Sciences
Document Type
Dissertation
Department (new version)
Applied Mathematics
Date of Award
9-11-2025
Abstract
In 2021, Rama Cont and Marvin M¨uller proposed a stochastic partial differential equation (SPDE) that models the density of orders in the limit order book at a given distance from the mid-price. In this thesis, we begin with a generalized version of the Cont–M¨uller SPDE and formulate an associated inverse problem. We present two alternative approaches to framing this inverse problem and establish, under appropriate assumptions, that it is conditionally well-posed. To solve the inverse problem, specifically, to recover the coefficients in the generalized Cont–M¨uller model, we adapt a variational approach involving the minimization of convex functionals. The recovered coefficients can then be used to forecast the density of limit orders by solving the forward problem. However, this process typically involves repeated use of numerical PDE solvers such as MATLAB’s bvp4c, making it computationally expensive. To address this challenge, we explore the use of invariant embedding techniques as a means of accelerating the recovery process.
ProQuest ID
Recommended Citation
Mrigank, Mrigank, "Imaging A Digital Stock Exchange" (2025). All ETDs from UAB. 7409.
https://digitalcommons.library.uab.edu/etd-collection/7409
