The risk minimizing problem E[l((H-X_T^{x,\pi})^{+})]\pi{\longrightarrow}\min in the  Black-Scholes framework with correlation is studied. General formulas for the minimal risk function and the cost reduction function for the option H depending on multiple underlying are derived. The case of a linear and a strictly convex loss function l are examined. Explicit computation for l(x)=x and l(x)=x^p, with p>1 for digital, quantos, outperformance and spread options are presented. The method is based on the quantile hedging approach presented in \mbox{%DIFAUXCMD FL10pt%DIFAUXCMD , \mbox{%DIFAUXCMD FL2 }0pt%DIFAUXCMD and developed for the multidimensional options in \mbox{%DIFAUXCMD Barski}0pt%DIFAUXCMD }  .
The risk minimizing problem E[l((H-X_T^{x,\pi})^{+})]\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 0pt%DIFAUXCMD , \mbox{%DIFAUXCMD FL2 }0pt%DIFAUXCMD and developed for the multidimensional options in \mbox{%DIFAUXCMD Barski}0pt%DIFAUXCMD } derived .
A
multidimensional
D
with correlation
R
General
Specific
R
the option H depending on multiple underlying are derived. The case of a linear and a strictly convex loss function l are examined. Explicit computation for
basket derivatives are shown. Explicit integral representations for the risk functions for
D
presented. The method is based on the quantile hedging approach presented in \mbox{%DIFAUXCMD FL1
A
derived