Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets

摘要: LetM(X) be the family of all equivalent local martingale measuresQ for some locally boundedd-dimensional processX, andV a positive process. The main result paper (Theorem 2.1) states that processV is supermartingale whateverQ∈M(X), if and only this process admits following decomposition: $$V_t $$ whereH an integrand forX, andC adapted increasing We call such representationoptional because, in contrast to Doob-Meyer decomposition, it generally exists with (optional) processC. apply decomposition problem hedging European American style contingent claims setting ofincomplete security markets.