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Mathematics

D-Index
61
Citations
34910
World Ranking
493
National Ranking
255

Overview

Ioannis Karatzas is affiliated with Columbia University in the United States and has contributed extensively to the fields of mathematics and economics, econometrics, and finance.

The primary areas of Karatzas's research include stochastic processes and financial applications, probability and risk models, geometric analysis and curvature flows, Markov chains and Monte Carlo methods, financial risk and volatility modeling, advanced mathematical modeling in engineering, and stochastic processes and statistical mechanics.

Karatzas has published a total of 22 works in mathematics and 16 in economics, econometrics, and finance. Specific subfields engaged include finance, statistics and probability, applied mathematics, management science and operations research, and computational theory and mathematics.

Frequent publication venues for Karatzas's research encompass:

  • arXiv (Cornell University)
  • Theory of Probability and Its Applications
  • Теория вероятностей и ее применения
  • Mathematical Finance
  • Probability Uncertainty and Quantitative Risk

The scientist's recent notable papers are:

  • "Open markets" (2020) in Mathematical Finance
  • "A Trajectorial Approach to the Gradient Flow Properties of Langevin--Smoluchowski Diffusions" (2022) in Theory of Probability and Its Applications
  • "A Weak Law of Large Numbers for Dependent Random Variables" (2023) in Theory of Probability and Its Applications
  • "Trajectorial dissipation and gradient flow for the relative entropy in Markov chains" (2021) in Communications in Information and Systems
  • "A sequential estimation problem with control and discretionary stopping" (2022) in Probability Uncertainty and Quantitative Risk

Karatzas has collaborated frequently with a number of colleagues, including Walter Schachermayer, Bertram Tschiderer, Tomoyuki Ichiba, Erik Ekström, and Václav E. Beneš.

In addition to articles, Karatzas has published a book titled Portfolio Theory and Arbitrage (2021) through the American Mathematical Society.

Best Publications

  • Brownian Motion and Stochastic Calculus

    Ioannis Karatzas;Steven E. Shreve

  • Methods of Mathematical Finance

    Ioannis Karatzas;Steven E. Shreve

  • Optimal portfolio and consumption decisions for a “small investor” on a finite horizon

    Ioannis Karatzas;John P. Lehoczky;Steven E. Shreve

  • Martingale and duality methods for utility maximization in a incomplete market

    Ioannis Karatzas;John P. Lehoczky;Steven E. Shreve;Gan-Lin Xu

  • Convex Duality in Constrained Portfolio Optimization

    Jakša Cvitanić;Ioannis Karatzas

  • On the pricing of American options

    Ioannis Karatzas

  • Optimization problems in the theory of continuous trading

    I. Karatzas

  • Backward stochastic differential equations with reflection and Dynkin games

    Jakša Cvitanić;Ioannis Karatzas

  • Explicit Solution of a General Consumption/Investment Problem

    Ioannis Karatzas;John P. Lehoczky;Suresh P. Sethi;Steven E. Shreve

  • The numéraire portfolio in semimartingale financial models

    Ioannis Karatzas;Constantinos Kardaras

  • HEDGING AND PORTFOLIO OPTIMIZATION UNDER TRANSACTION COSTS: A MARTINGALE APPROACH ⁄

    Jakša Cvitanić;Ioannis Karatzas

  • Lectures on the Mathematics of Finance

    Ioannis Karatzas

  • Hedging Contingent Claims with Constrained Portfolios

    Jaksa Cvitanic;Ioannis Karatzas

  • A generalized clark representation formula, with application to optimal portfolios

    Daniel L. Ocone;Ioannis Karatzas

  • On the optimal stopping problem for one-dimensional diffusions

    Savas Dayanik;Ioannis Karatzas

  • Utility Maximization with Discretionary Stopping

    Ioannis Karatzas;Hui Wang

  • ANTICIPATIVE PORTFOLIO OPTIMIZATION

    Igor Pikovsky;Ioannis Karatzas

  • On dynamic measures of risk

    Jakša Cvitanić;Ioannis Karatzas

  • On the pricing of contingent claims under constraints

    I. Karatzas;S. G. Kou

  • Existence and Uniqueness of Multi-Agent Equilibrium in a Stochastic, Dynamic Consumption/Investment Model

    Ioannis Karatzas;John P. Lehoczky;Steven E. Shreve

Frequent Co-Authors

Steven E. Shreve
Steven E. Shreve Carnegie Mellon University
Martin Shubik
Martin Shubik Yale University
Jakša Cvitanić
Jakša Cvitanić California Institute of Technology
John P. Lehoczky
John P. Lehoczky Carnegie Mellon University
John Geanakoplos
John Geanakoplos Yale University
Walter Schachermayer
Walter Schachermayer University of Vienna
Erhan Bayraktar
Erhan Bayraktar University of Michigan–Ann Arbor
Suresh P. Sethi
Suresh P. Sethi The University of Texas at Dallas
Albert N. Shiryaev
Albert N. Shiryaev Steklov Mathematical Institute
Béla Bollobás
Béla Bollobás University of Memphis

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