Financial Mathematics

Financial mathematics concerns mathematical models and problems arising in financial markets and applies tools from probability, optimization, stochastic analysis and statistics. Specific areas of research include risk management, pricing and hedging in incomplete markets, stochastic volatility models, markets with transaction costs, energy markets, credit risk, portfolio optimization, utility indifference valuation, and stochastic differential games.

Research Area Faculty

René Carmona
Paul M. Wythes '55 Professor of Engineering and Finance

Research Interests: Stochastic analysis (SPDEs, BSDEs, FBSDEs, stochastic control and large stochastic differential games such as mean field games), high frequency markets, energy and commodity markets, environmental finance and financial mathematics models.

Jianqing Fan
Frederick L. Moore Professor in Finance

Research Interests: High-dimensional statistics, Machine Learning, financial econometrics, computational biology, biostatistics, graphical and network modeling, portfolio theory, high-frequency finance, time series.

Emma Hubert
Assistant Professor

Research Interests: Financial Math and Probability

John Mulvey
Professor

Research Interests: Financial optimization models and associated algorithms, asset management strategies for global pension plans, (re)insurance companies, and other long-term investors, dynamic portfolio tactics for hedge funds, replicating performance of active managers

Mykhaylo Shkolnikov
Associate Professor

Research Interests: Financial mathematics (stochastic portfolio theory, optimal investment, systemic risk), probability theory (interacting particle systems, random matrix theory, and their applications to finance, neuroscience, and physics), partial differential equations (parabolic PDEs/SPDEs, free boundary problems,…

Ronnie Sircar
Eugene Higgins Professor of Operations Research & Financial Engineering

Research Interests: Financial mathematics, stochastic models, especially for market volatility, optimal investment and hedging strategies, analysis of financial data, credit risk; employee stock options, dynamic game theory, energy and commodities markets

Mete Soner
Professor

Research Interests: Decisions under uncertainty, Knigthian uncertainty, stochastic optimal control, financial mathematics, robust techniques in quantitative finance.

Ludovic Tangpi
Assistant Professor

Research Interests: Financial mathematics (risk management, model uncertainty, optimal investment); Stochastic analysis (stochastic control, SDEs, BSDEs, FBSDEs, probabilistic representations of parabolic/elliptic PDEs); Probability theory (optimal transportation, functional inequalities)

Robert Vanderbei
Professor

Research Interests: Interior-point methods for linear, convex, nonconvex, semidefinite optimization, robust optimization, the parametric simplex method, and constraint matrix sparsification (e.g. fast Fourier optimization). Applications include high-contrast imaging (to design a NASA space telescope), finding new stable…