Financial Mathematics - Department of Mathematics

The mathematical finance group includes probabilists and stochastic analysts working in problems directly motivated and/or applicable to finance and economics, or supervising PhD students working in those problems. From mathematical side, the members’ specialized research areas include stochastic differential equations (both forward and backward, both ordinary and partial), their related areas such as stochastic control and stochastic filtering, stochastic numerics, and statistics. From the finance/economics side, several research topics include, but are not limited to: option pricing and hedging theory; financial markets with frictions (including transaction cost, liquidity cost, credit risk, and model uncertainty); utility optimization theory with portfolio/consumption control, and contract theory.

The faculty members in the group are also responsible for teaching and advising graduate students at both Master and Ph.D. levels. The Master program of mathematical finance at USC College, a joint venture of Mathematics department and Economics department, prepares students a careers in the quantitative finance industry. Many members of the group have been responsible for teaching courses in the program, and advising Ph.D. students specializing in mathematical finance. The biweekly Mathematical Finance Colloquium brings in experts from both academia and financial industry, providing valuable contacts and opportunities for graduate students.

REGULAR FACULTY

Lototsky, Sergey: Stochastic partial differential equations, optimal nonlinear filtering of diffusion processes, statistical inference for continuous-time processes.
Ma, Jin: Stochastic analysis, stochastic differential equations, stochastic control theory, mathematical finance and insurance.
Minsker, Stanislav (Stas): Statistical learning theory, non-parametric statistics, concentration inequalities, mathematical finance.
Zhang, Jianfeng: Stochastic analysis, backward stochastic differential equations, stochastic numerics, and mathematical finance.

EMERITUS FACULTY

Baxendale, Peter (emeritus): Stochastic dynamical systems; equilibrium, stability and bifurcation for solutions of stochastic differential equations; applications to stochastic neuronal models.
Mikulevicius, Remigijus (Remi): Stochastic differential equations, stochastic analysis.

POST DOCS and VISITORS

Xia, Weixuan (NTT Assistant Professor): investment decisions under incomplete preferences, exotic derivatives, cryptocurrency markets, optimal control of set-valued stochastic processes, Lévy functionals and illiquidity measures, and neural network architectures applicable in these areas.

CURRENT GRADUATE STUDENTS:

Bixing Qiao (Zhang)
Gaozhan Wang (Ma/Zhang)
Zihao Gu (Zhang)

SEMINARS

RECENT GRADUATES, THEIR ADVISORS, AND DISSERTATIONS

2024

Atiqah Almuzaini (Ma), Set-Valued Stochastic Differential Equations with Unbounded Coefficients and Applications
Thejani Gamage (Ma), Reinforcement Learning for the Optimal Dividend Problem

2023

Iseri, Melih (Zhang), Set Values for Mean Field Games and Set Valued PDEs
Tan, Ying (Ma), Stochastic Two-point Boundary Value Problem and Application in Kyle-Back Equilibrium Model

2022

Pollok, Austin (Zhang), High-Frequency Kelly Criterion and Fat-Tails: Gambling with an Edge

2021

Feng, Pengbin (Ma/Zhang), Dynamic Network Models for Systemic Risk
Luo, Man (Ma), Topics on Dynamic Limit Order Book and its Related Computation
Wu, Wenqian (Ma), Topics on Set-Valued Backward Stochastic Differential Equations
Zhu, Zimu (Zhang), Some Topics on Continuous Time Principal-Agent Problem

2020

Phonsom, Chukiat (Mikulevicius), On Stochastic Integro-Differential Equations
Ruan, Jie (Zhang), Numerical Methods for High-Dimensional Path-Dependent PDEs Driven by Stochastic Volterra Equations

2019

Xu, Fanhui (Mikulevicius), On the parabolic Kolmogorov integro-differential equation and its applications

2018

Kim, Hyun-Jung (Lototsky), Time-Homogeneous Parabolic Anderson Model
Noh, Eunjung (Ma), Equilibrium Model of Limit Order Book and Optimal Execution Problem
Sun, Rentao (Ma), Conditional Mean-Field Stochastic Differential Equations and Their Applications
Wang, Jian (Lototsky), Statistical Inference For Second-Order Ordinary Differential Equation Driven by Additive Gaussian White Noise

2017

Sun, Rentao (Ma), Conditional Mean-Field Stochastic Differential Equations and Their Application
Wu, Cong (Zhang), Controlled McKean-Vlasov Equations and Related Topics
Xing, Xiaojing (Ma), Optimal Investment and Dividend under Sparre Andersen Model

2016

Kang, Yongjian (Lv/Zhang), Large-Scale Inference in Multiple Gaussian Graphical Models
Karnam, Chandrasekhar (Ma/Zhang), Dynamic Approaches for some Time Inconsistent Problems
Tsilifis, Panagiotis (Ghanem/Mikulevicius), Design, Adaptation and Variational Methods in Uncertainty Quantification
Xie, Weisheng (Ma), Stochastic Differential Equations Driven by Fractional Brownian Motion and Poisson Point Processes

2015

Keller, Christian (Zhang), Pathwise Stochastic Analysis and Related Topics
Zhang, Tian (Ma), Optimal Investment and Reinsurance Problems and Related Non-Markovian FBSDEs With Constraints

2014

Bessam, Diogo (Lototsky), Large Deviations Rates in a Gaussian Setting and Related Topics
Ekren, Ibrahim (Zhang), Path-Dependent Partial Differential Equations and Related Topics
Sokolov, Grigory (Tartakovsky/Lototsky), Multi-Population Optimal Change-Point Detection
Zhuo, Jia (Zhang), Probabilistic Numerical Methods for Fully Nonlinear PDEs and Related Topics

2013

Pham, Triet (Zhang), Zero-Sum Stochastic Differential Games in Weak Formulation and Related Norms for Semi-Martingales
Wang, Huanhuan (Ma), Asset Management with Incomplete Information
Wang, Xin (Ma), Nonlinear Expectations for Continuous Time Model with Jumps and Applications
Xu, Li (Lototsky), Parameter Estimate for Hyperbolic SPDE’s with Stochastic Coefficients
Zhong, Jie (Lototsky), Second Order in Time Stochastic Evolution Equation and Wiener Chaos Approach

2012

Du, Jie (Zhang), Stochastic Games on Stopping Times
Kaligotla, Sivaditya (Lototsky), Asymptotic Problems in Stochastic Partial Differential Equations: A Wiener Chaos Approach
Lin, Ning (Lototsky), Estimation of Coefficients in Stochsatic Differential Equations
Moers, Michael (Lototsky), Statistical Inference of Stochastic Differential Equations Driven by Gaussian Noise
Xu, Shanshan (Lototsky/Wilcox), Initiative Non-Parametric Multivariate Regression Hypothesis Testing

2011

Chen, Jianfu (Ma), Regime Switch Term Structure model with Forward-Backward Stochastic Differential Equations
Wang, Xinyang (Ma/Zhang), Dynamic Model for Limit Order Books and Optimal Liquidation Problems
Yun, Youngyun (Ma), Analysis of Correlated Defaults and Joint Default Probability in a Contagion Model

2010

Liu, Wei (Lototsky), Statistical Inference for Stochastic Hyperbolic Equations
Zhang, Changyong (Mikulevicius), Numerical Weak Approximation of Stochastic Differential Equations Driven by Levy Processes

2009

Knape, Mathias (Mikulevicius/Zapatero), A General Equilibrium Model for Exchange Rates and Asset Prices in an Economy Subject to Jump-Diffusion Uncertainty
Polunchenko, Aleksey (Mikulevicius/Tartakovsky), Quickest Change Detection with Applications to Distributed Multi-Sensor Systems

THE FIRST JOB OF SOME OF OUR RECENT GRADUATES