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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)

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)

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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)

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)

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)

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)

We provide simple, easy-to-test criteria for the existence of relative arbitrage in equity markets. These criteria postulate essentially that the excess growth rate of the market portfolio, a positive quantity that can be estimated or even computed from a given market structure, be " sufficiently large ". We show that conditions which satisfy these criteria… (More)