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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 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)
first two authors are grateful for financial support from Banker's Trust. We are particularly grateful to Henry McKean for many valuable discussions.
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 . We offer an approach which both simplifies and extends the results of existing theory on this topic.
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)
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)
An equity market is called " diverse " if no single stock is ever allowed to dominate the entire market in terms of relative capitalization. In the context of the standard Itô-process model initiated by Samuelson (1965) we formulate this property (and the allied, successively weaker notions of " weak diversity " and " asymptotic weak diversity ") in precise… (More)
We discuss the finite-fuel, singular stochastic control problem of optimally tracking the standard Brownian motion x + W (·) started at x ∈ IR, by an adapted process ξ(·) = ξ + (·) − ξ − (·) of bounded total variatioň ξ(t) = ξ + (t) + ξ − (t) ≤ y, ∀ 0 ≤ t < ∞, so as to minimize the total expected discounted cost IE τ 0 e −αt λX 2 (t) dt + [0,τ ] e −αt d ˇ… (More)