Carole Bernard (University of Waterloo)

Title:  Path-dependent inefficient strategies and how to make them efficient

Abstract:  We make the following assumptions. (1) Agents' preferences depend only on the probability distribution of terminal wealth. (2) Agents prefer more to less. (3) The market is perfect and frictionless. (4) The market is arbitrage-free and could be incomplete. Under these assumptions, we show that in general path-dependent strategies are inefficient and not optimal. In addition, we characterize the ones that are cost-efficient. We obtain an explicit formula for the efficiency cost of a strategy as well as for the payoff of the cost-efficient derivative that should be preferred by all investors. Finally, we show that in the Black and Scholes framework, the necessary and sufficient conditions for a strategy to be cost-efficient is that its terminal payoff is an increasing function of the stock price.

This is joint work with Professor Phelim Boyle.