# Integral representations of risk functions for basket derivatives

## Author Info

Listed author(s):
• Micha{\l} Barski
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## Abstract

The risk minimizing problem $\mathbf{E}[l((H-X_T^{x,\pi})^{+})]\overset{\pi}{\longrightarrow}\min$ 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.

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File URL: http://arxiv.org/pdf/1102.3928

## Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 1102.3928.

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 Length: Date of creation: Feb 2011 Date of revision: Jan 2016 Publication status: Published in Applicationes Mathematicae, 2012, 39, 489-514 Handle: RePEc:arx:papers:1102.3928 Contact details of provider: Web page: http://arxiv.org/

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