Contingent Claims in Incomplete Markets

Abstract

The subject of this chapter is the arbitrage pricing and almost sure hedging of contingent claims in markets which are incomplete due to portfolio constraints. It often occurs in such markets that a given contingent claim cannot be hedged perfectly, no matter how large the initial wealth of the would-bG hedging agent. However, it can be the case that with sufficient initial wealth, a hedging agent can construct a portfolio which respects the constraints and still leads to a final wealth that dominates almost surely the payoff of the contingent claim. This chapter distinguishes these two cases and shows how, when possible, to construct the superreplicating portfolio of the second case.