What is he best known for?
The fields of study he is best known for:
- Mathematical analysis
- Geometry
- Probability theory
His primary areas of investigation include Mathematical economics, Stochastic control, Mathematical optimization, Portfolio and Financial market.
His Mathematical economics research is multidisciplinary, incorporating elements of Valuation of options, Semimartingale, Decision theory, Market price and Incomplete markets.
His Optimal stopping and Optimal control study in the realm of Mathematical optimization interacts with subjects such as Duality.
His biological study spans a wide range of topics, including Dynkin's formula, Applied mathematics and Stochastic game.
His work in Portfolio covers topics such as Martingale which are related to areas like Hedge, Marginal utility and Infimum and supremum.
His Mathematical analysis course of study focuses on Brownian bridge and Geometric Brownian motion.
His most cited work include:
- Brownian Motion and Stochastic Calculus (8395 citations)
- Graduate Texts in Mathematics (7753 citations)
- Methods of Mathematical Finance (1656 citations)
What are the main themes of his work throughout his whole career to date?
His primary scientific interests are in Mathematical economics, Mathematical optimization, Stochastic control, Optimal stopping and Mathematical analysis.
His work on Expected utility hypothesis as part of general Mathematical economics research is frequently linked to Financial market, thereby connecting diverse disciplines of science.
His work in the fields of Mathematical optimization, such as Stochastic optimization, Singular control and Variational inequality, intersects with other areas such as Probabilistic logic.
The concepts of his Stochastic control study are interwoven with issues in Stochastic game, Convex analysis and Bellman equation.
His Optimal stopping research includes elements of Martingale, Applied mathematics, Unobservable and Probability measure.
His work focuses on many connections between Mathematical analysis and other disciplines, such as Diffusion process, that overlap with his field of interest in Statistical physics.
He most often published in these fields:
- Mathematical economics (23.93%)
- Mathematical optimization (21.37%)
- Stochastic control (19.23%)
What were the highlights of his more recent work (between 2015-2020)?
- Applied mathematics (19.66%)
- Trading strategy (11.11%)
- Market portfolio (12.39%)
In recent papers he was focusing on the following fields of study:
His main research concerns Applied mathematics, Trading strategy, Market portfolio, Arbitrage and Portfolio.
Ioannis Karatzas combines subjects such as Optimal stopping, Quadratic equation, Uniqueness and Distribution with his study of Applied mathematics.
His research investigates the connection between Market portfolio and topics such as Mathematical finance that intersect with problems in Calculus, Differential equation and Girsanov theorem.
His Arbitrage study incorporates themes from Volatility, Current, Mathematical economics and Bounded function.
His studies in Portfolio integrate themes in fields like Lyapunov function and Econometrics.
His Ambient space research is under the purview of Mathematical analysis.
Between 2015 and 2020, his most popular works were:
- Distribution of the time to explosion for one-dimensional diffusions (21 citations)
- Trading strategies generated by Lyapunov functions (20 citations)
- Trading strategies generated by Lyapunov functions (20 citations)
In his most recent research, the most cited papers focused on:
- Mathematical analysis
- Geometry
- Probability theory
Ioannis Karatzas focuses on Arbitrage, Mathematical finance, Trading strategy, Market portfolio and Stochastic portfolio theory.
His Arbitrage study integrates concerns from other disciplines, such as Volatility, Mathematical economics, Bounded function and Combinatorics.
His Mathematical economics research is multidisciplinary, incorporating elements of Current, Differentiable function and Momentum.
His Mathematical finance study combines topics from a wide range of disciplines, such as Local martingale, Distribution and Girsanov theorem.
His Trading strategy research is multidisciplinary, relying on both Lyapunov function, Mathematical optimization and Portfolio.
His study deals with a combination of Portfolio and Moment.
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