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Ioannis Karatzas
Researcher at Columbia University
Publications - 190
Citations - 26325
Ioannis Karatzas is an academic researcher from Columbia University. The author has contributed to research in topics: Stochastic control & Optimal stopping. The author has an hindex of 58, co-authored 189 publications receiving 25152 citations. Previous affiliations of Ioannis Karatzas include University of North Carolina at Chapel Hill & Princeton University.
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Book
Brownian Motion and Stochastic Calculus
TL;DR: In this paper, the authors present a characterization of continuous local martingales with respect to Brownian motion in terms of Markov properties, including the strong Markov property, and a generalized version of the Ito rule.
Book ChapterDOI
Stochastic Differential Equations
TL;DR: In this paper, the authors explore questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties, using diffusion processes as a model of a Markov process with continuous sample paths.
Book
Methods of Mathematical Finance
TL;DR: A Brownian Motion of financial markets is used in this paper to describe the relationship between single-agent consumption and investment in a complete market and equilibrium in complete markets, where the single agent consumption is constrained by a Brownian motion.
Journal ArticleDOI
Optimal portfolio and consumption decisions for a “small investor” on a finite horizon
TL;DR: In this paper, a general consumption/investment problem is considered for an agent whose actions cannot affect the market prices, and who strives to maximize total expected discounted utility of both consumption and investment.
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Martingale and duality methods for utility maximization in a incomplete market
TL;DR: In this paper, the authors studied the problem of maximizing the expected utility from terminal wealth in the context of a complete financial market and showed that there is a way to complete the market by introducing additional "fictitious" stocks so that the optimal portfolio for the thus completed market coincides with the original incomplete market.