ℒp-Projections of random variables and its application to finance

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Abstract

The aim of this paper is to give an extension of the mean-variance hedging problem to the $ ℒp-setting, where 1 < p < ∞. Remark that the mean-variance hedging is corresponding to the case where p = 2. Firstly, we prove that the unique existence of the optimal hedging strategy in the ℒp-sense, which is the ℒp-projection of the underlying contingent claim onto a suitable space of stochastic integrations. Next, we obtain its feedback representation under some additional assumptions. Moreover, the valuation problem induced by the ℒp-projections naturally is discussed.

Original languageEnglish
Pages (from-to)869-888
Number of pages20
JournalInternational Journal of Theoretical and Applied Finance
Volume11
Issue number8
DOIs
Publication statusPublished - 2008 Dec 1

Keywords

  • Mathematical finance
  • Option pricing
  • Q-optimal martingale measure
  • Semimartingales
  • Stochastic integrals

ASJC Scopus subject areas

  • Finance
  • Economics, Econometrics and Finance(all)

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