TAKUJI ARAI () (Department of Economics, Keio University, 2-15-45 Mita, Minato-ku, Tokyo, 108-8345, Japan)
Abstract
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.
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