Ioannis Karatzas studied at the Ionideion Gymnaseion in Piraeus (Apolyterion 1970), at the
Technical University of Athens (Diploma 1975), and at Columbia University (M.Sc. 1976,
M.Phil. 1978, Ph.D. 1980). He is the Eugene Higgins Professor of Applied Probability at
Columbia’s Departments of Mathematics and Statistics. He works on Probability Theory and
on several of its Applications.
SELECTED BOOKS:
I. KARATZAS & S.E. SHREVE (1988) Brownian Motion and Stochastic Calculus. Volume

I. KARATZAS & C.KARDARAS (2021) Portfolio Theory and Arbitrage. Book series
Graduate Studies in Mathematics, American Mathematical Society, Providence, RI. To appear.
SELECTED PUBLICATIONS:
I. KARATZAS & S.E. SHREVE (1984) Connections between optimal stopping and singular
stochastic control. SIAM Journal on Control & Optimization 22, 856-877.
N. El KAROUI & I. KARATZAS (1993) General Gittins index processes in discrete time.
Proceedings of the National Academy of Sciences 90, 1232-1236.
J. CVITANIC & I. KARATZAS (1996) Backwards stochastic differential equations and
Dynkin games. Annals of Probability 24, 2024-2056.
I. KARATZAS & W.D. SUDDERTH (2001) The controller-and-stopper game for a linear
diffusion. Annals of Probability 29, 1111-1127.
E.R. FERNHOLZ, I. KARATZAS & J. RUF (2018) Volatility and arbitrage. Annals of Applied
Probability 28, 378-417.
I. KARATZAS, J. MAAS & W. SCHACHERMAYER (2021) Trajectorial dissipation and
gradient flow for the relative entropy in Markov Chains. Communications in Information and
Systems. To appear.