Mathematical Finance Seminar

April 12, 2001 , 5:30 PM to 7:00 PM

Peter Carr, Banc of America Securities

Pricing and Hedging in Incomplete Markets

We present a new approach for positioning, pricing, and hedging in incomplete markets, which bridges standard arbitrage pricing and expected utility maximization. Our approach for determining whether to undertake a particular position involves specifying a set of probability measures and associated floors which expected payoffs must exceed in order that the hedged and financed investment be acceptable. By assuming that the liquid assets are priced so that each portfolio of them has negative expected return under at least one measure, we derive a counterpart to the first fundamental theorem of asset pricing. We also derive a counterpart to the second fundamental theorem, which can lead to unique derivative security pricing and hedging even though markets are incomplete.