Explicit Representation of Cost-Efficient Strategies

Abstract

In this paper, we give an explicit representation of the lowest cost strategy (or "cost-efficient" strategy) to achieve a given payoff distribution. For any inefficient strategy, we are able to construct financial derivatives which dominate in the sense of first-order or second-order stochastic dominance. We highlight the connections between cost-efficiency and dependence (copulas). This allows us to extend the theory to deal with state-dependent constraints to better reflect real world preferences. We show in particular that path-dependent strategies (although inefficient in the Black Scholes setting) may become optimal in the presence of state-dependent constraints.

Keywords: Law-invariant increasing preferences, Stochastic Dominance, Expected Utility, State-dependent preferences, Copulas

JEL Classification: D81, D91, G11, G12, G13