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- Ioannis Karatzas, Constantinos Kardaras
- Finance and Stochastics
- 2007

We study the existence of the numéraire portfolio under predictable convex constraints in a general semimartingale model of a financial market. The numéraire portfolio generates a wealth process, with respect to which the relative wealth processes of all other portfolios are supermartingales. Necessary and sufficient conditions for the existence of the… (More)

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 concavity in some suitable generalized sense. This permits a characterization of the value function of the optimal stopping problem as " the smallest nonnegative… (More)

Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Each copy of any part of a JSTOR transmission must contain the same copyright notice that… (More)

Stochastic Portfolio Theory is a flexible framework for analyzing portfolio behavior and equity market structure. This theory is descriptive, as opposed to normative; it is consistent with observable characteristics of actual portfolios and markets; and it provides a theoretical tool which is useful for practical applications. As a theoretical tool, this… (More)

- Ioannis Karatzas, John P. Lehoczky, Suresh P. Sethi, Steven E. Shreve
- Math. Oper. Res.
- 1986

We consider the problem of maximizing expected utility from consumption in a constrained incomplete semimartingale market with a random endowment process, and establish a general existence and uniqueness result using techniques from convex duality. The notion of " as-ymptotic elasticity " of Kramkov and Schachermayer is extended to the time-dependent case.… (More)

- IOANNIS KARATZAS
- 2006

We derive a formula for the minimal initial wealth needed to hedge an arbitrary contingent claim in a continuous-time model with proportional transaction costs; the expression obtained can be interpreted as the supremum of expected discounted values of the claim, over all (pairs of) probability measures under which the " wealth process " is a… (More)

- Ioannis Karatzas
- 2005

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 which both simplifies and extends the results of existing theory on this topic.

- Ioannis Karatzas, Hui Wang
- SIAM J. Control and Optimization
- 2000

Utility maximization problems of mixed optimal stopping /control type are considered, which can be solved by reduction to a family of related pure optimal stopping problems. Sufficient conditions for the existence of optimal strategies are provided in the context of continuous-time, Itô process models for complete markets. The mathematical tools used are… (More)

- Ioannis Karatzas, Steven Kou
- Finance and Stochastics
- 1998

The valuation theory for American Contingent Claims, due to Bensous-san (1984) and Karatzas (1988), is extended to deal with constraints on portfolio choice, including incomplete markets and borrowing/short-selling constraints, or with different interest rates for borrowing and lending. In the unconstrained case, the classical theory provides a single… (More)