Integral representations of risk functions for basket derivatives

Volume 39 / 2012

Michał Barski Applicationes Mathematicae 39 (2012), 489-514 MSC: Primary 91B30, 91B24; Secondary 91B70. DOI: 10.4064/am39-4-6


The risk minimizing problem $\mathbf{E}[l((H-X_T^{x,\pi})^{+})]\overset{\pi}{\rightarrow}\min$ in the multidimensional Black–Scholes framework is studied. Specific formulas for the minimal risk function and the cost reduction function for basket derivatives are shown. Explicit integral representations for the risk functions for $l(x)=x$ and $l(x)=x^p$, with $p>1$ for digital, quantos, outperformance and spread options are derived.


  • Michał BarskiFaculty of Mathematics and Computer Science
    Leipzig University
    D-04009 Leipzig, Germany
    Faculty of Mathematics
    Cardinal Stefan Wyszyński University
    01-938 Warszawa, Poland

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