Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets
AbstractLet M(X) be a family of all equivalent local martingale measures for some locally bounded d-dimensional process X, and V be a positive process. Main result of the paper (Theorem 2.1) states that the process V is a supermartingale whatever Q in M(X), if and only if this process admits the following decomposition: V_t = V_0 + \int_0^t H_s dX_s - C_t, t>= 0, where H is an integrand for X, and C is an adapted increasing process. We call such a representation the optional because, in contrast to Doob-Meyer decomposition, it generally exists only with an adapted (optional) process C. We apply this decomposition to the problem of hedging European and American style contingent claims in a setting of incomplete security markets.
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Bibliographic InfoPaper provided by University of Bonn, Germany in its series Discussion Paper Serie B with number 294.
Date of creation: Oct 1994
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Doob-Meyer decomposition; optional decomposition; martingale measure; stochastic integral; semimartingale topology; incomplete market; hedging; options;
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- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
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