Pricing and Hedging in Incomplete Markets
Professor Dilip Madan, Robert H. Smith School of Business, University of Maryland at College Park

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 leads to unique derivative security pricing and hedging even though markets are incomplete. For products that are not spanned by the liquid assets of the economy, we show how our methodology provides more realistic bid-ask spreads.