Geodesic
Integral representations of risk functions for basket derivatives
Michał Barski 1
1 Faculty of Mathematics and Computer Science Leipzig University D-04009 Leipzig, Germany and Faculty of Mathematics Cardinal Stefan Wyszyński University 01-938 Warszawa, Poland
Applicationes Mathematicae, Tome 39 (2012) no. 4, pp. 489-514 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/am39-4-6
Keywords: risk minimizing problem mathbf h x overset rightarrow min multidimensional black scholes framework studied specific formulas minimal risk function cost reduction function basket derivatives shown explicit integral representations risk functions digital quantos outperformance spread options derived

Michał Barski  1

1 Faculty of Mathematics and Computer Science Leipzig University D-04009 Leipzig, Germany and Faculty of Mathematics Cardinal Stefan Wyszyński University 01-938 Warszawa, Poland 
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Michał Barski. Integral representations of risk functions for basket derivatives. Applicationes Mathematicae, Tome 39 (2012) no. 4, pp. 489-514. doi: 10.4064/am39-4-6

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