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

@inproceedings{Kramkov1996OptionalDO,
  title={Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets},
  author={Dmitry O. Kramkov},
  year={1996}
}
t Vt = Vo + f H, dX~ Ct, t > O , o where H is an integrand for X, and C is an adapted increasing process. We call such a representation optional because, in contrast to the Doob-Meye r 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 the setting of incomplete security markets. 
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