Arbitrage pricing of American contingent claims in incomplete markets - a convex optimization approach

Abstract

Convex optimization provides a natural framework for pricing and hedging financial instruments in incomplete market models. Duality theory of convex optimization has been shown to yield elementary proofs of well-known martingale-expressions for prices of European contingent claims. This paper extends the analysis to American contingent claims in incomplete markets. The pricing problems of the seller and the buyer of an American contingent claim are first expressed as convex optimization problems, after which martingale-expressions for the buyer's and seller's prices are obtained by inspecting the dual optimization problems. Besides its simplicity, one of the main advantages of the present approach is that it is computational. Indeed, many algorithms are available for pricing problems as soon as they are set up as convex optimization problems. Also, portfolio constraints and transaction costs can be immediately incorporated to the definitions of the buyer's and seller's prices and into computational approaches based on optimization.