Carnegie Mellon University

Dmitry Kramkov

Mellon College of Science Professor of Mathematical Finance, Director of Center for Computational Finance

6126 Wean Hall
Department of Mathematical Sciences
Carnegie Mellon University
5000 Forbes Avenue
Pittsburgh, PA 15213

P: 412-268-5912



Dmitry Kramkov


Ph.D., Steklov Mathematical Institute


  • European Mathematical Society Prize


My research interests are related with problems of Mathematical Finance and Theory of Stochastic Processes and, particularly, with the mathematical challenges presented by equilibrium-based models. The recent results include the development of continuous-time price impact model with Peter Bank, the necessary and sufficient conditions for the existence of (static) Arrow-Debreu equilibria, sufficient conditions for the existence of complete (dynamic) Radner equilibria, sufficient conditions for the existence of backward martingale representation (with Silviu Predoiu), local existence and asymptotic analysis of BSDE's in BMO spaces (with Sergio Pulido).

Select Publications

Dmitry Kramkov and Mihai Sirbu. Sensitivity analysis of utility based prices and risk-tolerance wealth processes. Annals of Applied Probability, 16(4):2140-2194, 2006.

Dmitry Kramkov and Walter Schachermayer. The asymptotic elasticity of utility functions and optimal investment in incomplete markets. Annals of Applied Probability, 9(3):904-950, 1999.

Dmitry Kramkov. Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets. Probability Theory and Related Fields, 105:459-479, 1996.