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Hedging of contingent claims and maximum price. (Couverture des actifs contingents et prix maximum.) (French) Zbl 0796.60056

Summary: The problem of pricing contingent claims from the price dynamics of some securities is well understood in the context of a complete financial market. In order to avoid any arbitrage opportunity, we assume the existence of a martingale measure which is unique in a complete market. Then the price of a contingent claim is its expectation with respect to this martingale measure. On the other hand when the market is incomplete there are several martingale measures and therefore several prices of a contingent claim. We study the relationship between the maximum price and the existence of a hedging strategy and we give necessary and sufficient conditions for a contingent claim to be representable with respect to the discounted price process.

MSC:

60H05 Stochastic integrals
60H30 Applications of stochastic analysis (to PDEs, etc.)
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