The Pricing And Hedging Of Contingent Claims In An Incomplete Market

The problem of pricing and hedging of contingent claims in an incomplete market is discussed in this paper. We define the price of contingent claim via utility indiffer-ence pricing:the price of contingent claim is defined as the smallest pt, which is Ft-measurable such that ess sup πE[u(XT(x+Pt,π)-B)|Ft]≥ess supπE[u(XT(x,π)|Ft], where u is the utility function of the investor and X(x,π) is the wealth process associated with initial wealth x and portfolio strategy π. The filtration in this model is discontinuous and the trading strategies are constrained to a closed, convex set. We consider the in-vestor of a negative exponential utility function and the dynamic equation for the price process is proved to be a BSDE with jumps, whose generator is quadratic in the second unknown variable Z. Finally,we get the properties of the price process with respect to the parameters by the comparison theorem of BSDEs.