标题： 风险函数的篮子衍生品积分表示 显示英文标题

标题： Integral representations of risk functions for basket derivatives

摘要： 风险最小化问题 $\mathbf{E}[l((H-X_T^{x,\pi})^{+})]\overset{\pi}{\longrightarrow}\min$在多维 Black-Scholes 框架中被研究。 展示了篮子衍生品的最小风险函数和成本减少函数的具体公式。 推导了对于$l(x)=x$和$l(x)=x^p$的风险函数的显式积分表示，其中$p>1$用于数字、定量、表现优于和价差期权。 显示英文摘要

摘要： 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.