Backward Stochastic PDE and Imperfect Hedging

M. Mania () and R. Tevzadze
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M. Mania: A. Razmadze Mathematical Institute, Georgian Academy of Sciences, 1, M. Aleksidze St., Tbilisi 0193, Georgia
R. Tevzadze: Institute of Cybernetics, Georgian Academy of Sciences, 5, S. Euli St., Tbilisi 0186, Georgia

International Journal of Theoretical and Applied Finance (IJTAF), 2003, vol. 06, issue 07, 663-692

Abstract: We consider a problem of minimization of a hedging error, measured by a positive convex random function, in an incomplete financial market model, where the dynamics of asset prices is given by anRd-valued continuous semimartingale. Under some regularity assumptions we derive a backward stochastic PDE for the value function of the problem and show that the strategy is optimal if and only if the corresponding wealth process satisfies a certain forward-SDE. As an example the case of mean-variance hedging is considered.

Keywords: Backward stochasic partial differential equation; semimartinggale market model; incomplete markets; mean-variance hedging (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (28)

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DOI: 10.1142/S0219024903002122

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