Pricing and hedging in incomplete markets

We present a new approach for positioning, pricing, and hedging in incomple te markets that bridges standard arbitrage pricing and expected utility max imization. Our approach for determining whether an investor should undertak e a particular position involves specifying a set of probability measures a nd associated floors which expected payoffs must exceed in order for the in vestor to consider the hedged and financed investment to be acceptable. By assuming that the liquid assets are priced so that each portfolio of assets has negative expected return under at least one measure, we derive a count erpart to the first fundamental theorem of asset pricing. We also derive a counterpart to the second fundamental theorem, which leads to unique deriva tive security pricing and hedging even though markets are incomplete. For p roducts that are not spanned by the liquid assets of the economy, we show h ow our methodology provides more realistic bid-ask spreads. (C) 2001 Publis hed by Elsevier Science S.A.