Integral representations of risk functions for basket derivatives

Michał Barski. "Integral representations of risk functions for basket derivatives." Applicationes Mathematicae 39.4 (2012): 489-514. <http://eudml.org/doc/280038>.

@article{MichałBarski2012,
abstract = {The risk minimizing problem $E[l((H-X_T^\{x,π\})⁺)] \overset\{π\}\{→\} min$ 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.},
author = {Michał Barski},
journal = {Applicationes Mathematicae},
keywords = {shortfall risk; basket options; correlated assets; quantile hedging},
language = {eng},
number = {4},
pages = {489-514},
title = {Integral representations of risk functions for basket derivatives},
url = {http://eudml.org/doc/280038},
volume = {39},
year = {2012},
}

TY - JOUR
AU - Michał Barski
TI - Integral representations of risk functions for basket derivatives
JO - Applicationes Mathematicae
PY - 2012
VL - 39
IS - 4
SP - 489
EP - 514
AB - The risk minimizing problem $E[l((H-X_T^{x,π})⁺)] \overset{π}{→} min$ 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.
LA - eng
KW - shortfall risk; basket options; correlated assets; quantile hedging
UR - http://eudml.org/doc/280038
ER -