We propose an approach to the valuation of payoffs in general semimartingale models of financial markets where prices are nonnegative. Each asset price can hit 0; we only exclude that this ever happens simultaneously for all assets. We start from two simple, economically motivated axioms, namely...

In this paper, we examine an exchange economy with a financial market composed of three assets: a share of a stock, an European call option written on the stock, and a riskless bond.

Market participants use leveraged derivatives to gain access to equity market exposure through broker banks. Leverage and interconnectedness via overlapping portfolios of dealer banks can amplify adverse market movements, potentially causing sizeable losses. I propose a model, based on granular...

The valuation theory for American Contingent Claims, due to Bensoussan (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...

Prices of financial options in a market with liquidity risk are shown to be weak solutions of a class of semilinear parabolic partial differential equations with nonnegative characteristic form. We prove the existence and uniqueness of such solutions, and then show the solutions correspond to...

We study the exponential utility indifference valuation of a contingent claim B in an incomplete market driven by two Brownian motions. The claim depends on a nontradable asset stochastically correlated with the traded asset available for hedging. We use martingale arguments to provide upper and...

This paper reconsiders the predictions of the standard option pricing models in the context of incomplete markets. We relax the completeness assumption of the Black-Scholes (1973) model and as an immediate consequence we can no longer construct a replicating portfolio to price the option....

The high volatility of electricity markets gives producers and retailers an incentive to hedge their exposure to electricity prices. This paper studies how welfare and investment incentives are affected when markets for derivatives are introduced, and to what extent this depends on market...

We give an explicit PDE characterization for the solution of the problemof maximizing the utility of both terminal wealth and intertemporal consumption under model uncertainty. The underlying market model consists of a risky asset, whose volatility and long-term trend are driven by an external...

This paper publishes results on the convergence for hedging strategies in the setting of incomplete financial markets.