Ioannis Karatzas

Ioannis Karatzas is the Eugene Higgins Professor of Applied Probability at Columbia University, holding appointments in both the Department of Mathematics and Department of Statistics. His work bridges Stochastic Analysis, Mathematical Finance, and Optimization, with a focus on utility maximization, market equilibrium, and stochastic control problems.

• Research Interests: Stochastic processes, financial mathematics, optimal stopping, singular control, and portfolio optimization. His contributions include foundational work on martingale methods in incomplete markets and the development of stochastic portfolio theory.
• Books: Co-authored Brownian Motion and Stochastic Calculus and Methods of Mathematical Finance, both standard references in stochastic analysis and quantitative finance.
• Teaching: Taught advanced courses like Stochastic Methods in Finance and Probability, covering topics from arbitrage theory to optimal consumption.
• Doctoral Students: Advised 18 PhD students, including notable researchers in stochastic control, financial economics, and optimal stopping.