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Brownian Motion and Stochastic Calculus

- I. Karatzas
- Mathematics, Computer Science
- 1987

TLDR

Stochastic Differential Equations

- I. Karatzas, S. Shreve
- Mathematics
- 1998

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion… Expand

Methods of Mathematical Finance

- I. Karatzas, S. Shreve
- Economics
- 2010

A Brownian Motion of Financial Markets.- Contingent Claim Valuation in a Complete Market.- Single-Agent Consumption and Investment.- Equilibrium in a Complete Market.- Contingent Claims in Incomplete… Expand

Convex Duality in Constrained Portfolio Optimization

- J. Cvitanić, I. Karatzas
- Mathematics
- 1 November 1992

We study the stochastic control problem of maximizing expected utility from terminal wealth and/or consumption, when the portfolio is constrained to take values in a given closed, convex subset of… Expand

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

- I. Karatzas, J. Lehoczky, S. Shreve
- Mathematics
- 1 November 1987

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 ...

The numéraire portfolio in semimartingale financial models

- I. Karatzas, C. Kardaras
- Economics, MathematicsFinance Stochastics
- 8 August 2007

TLDR

On the optimal stopping problem for one-dimensional diffusions

- Savas Dayanik, I. Karatzas
- Mathematics
- 1 October 2003

A new characterization of excessive functions for arbitrary one-dimensional regular diffusion processes is provided, using the notion of concavity. It is shown that excessivity is equivalent to… Expand

Martingale and duality methods for utility maximization in a incomplete market

- I. Karatzas, J. Lehoczky, S. Shreve, Ganlin Xu
- Mathematics
- 1 March 1991

The problem of maximizing the expected utility from terminal wealth is well understood in the context of a complete financial market. This paper studies the same problem in an incomplete market… Expand

Backward stochastic differential equations with reflection and Dynkin games

- J. Cvitanić, I. Karatzas
- Mathematics
- 1 October 1996

We establish existence and uniqueness results for adapted solutions of backward stochastic differential equations (BSDE's) with two reflecting barriers, generalizing the work of El Karoui,… Expand

On the pricing of American options

- I. Karatzas
- Mathematics
- 1988

The problem of valuation for contingent claims that can be exercised at any time before or at maturity, such as American options, is discussed in the manner of Bensoussan [1]. We offer an approach… Expand

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