English, Article, Journal or magazine article edition: Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets Kramkov, D.O.

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Bookmark: http://trove.nla.gov.au/version/52070
Physical Description
  • preprint
Language
  • English

Edition details

Title
  • Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets
Author
  • Kramkov, D.O.
Physical Description
  • preprint
Notes
  • Let 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.
  • Doob-Meyer decomposition, optional decomposition, martingale measure, stochastic integral, semimartingale topology, incomplete market, hedging, options
  • RePEc:bon:bonsfb:294
Language
  • English
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