# English, Article edition: $\mathcal{L}^p$-PROJECTIONS OF RANDOM VARIABLES AND ITS APPLICATION TO FINANCE TAKUJI ARAI

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Bookmark: http://trove.nla.gov.au/version/83426
Physical Description
• article
Language
• English

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Title
• $\mathcal{L}^p$-PROJECTIONS OF RANDOM VARIABLES AND ITS APPLICATION TO FINANCE
Author
• TAKUJI ARAI
Physical Description
• article
Notes
• The aim of this paper is to give an extension of the mean-variance hedging problem to the $\mathcal{L}^p$-setting, where 1 < p < â. 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 $\mathcal{L}^p$-sense, which is the $\mathcal{L}^p$-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 $\mathcal{L}^p$-projections naturally is discussed.
• Semimartingales, stochastic integrals, q-optimal martingale measure, option pricing, mathematical finance
• RePEc:wsi:ijtafx:v:11:y:2008:i:08:p:869-888
Language
• English
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