双曲面上重积分的近似及其在含期权二次投资组合中的应用
Approximation of Multiple Integrals over Hyperboloids with Application to a Quadratic Portfolio with Options
AI总结：
针对多元椭圆分布下二次期权投资组合，提出将双曲面重积分变换为径向与球面积分乘积的数值近似方法，并通过金融实例验证。\n
摘要：
我们考虑一个涉及金融二次期权投资组合的应用，其中联合底层对数收益随多元椭圆分布变化。这激发了对双曲面上重积分近似方法的需求。采用一种变换将双曲面积分简化为两个径向积分和两个球面积分的乘积。针对变换后的积分构建了数值近似方法。通过一些金融应用示例展示了这些方法的应用。
英文摘要：
We consider an application involving a financial quadratic portfolio of options, when the joint underlying log-returns changes with multivariate elliptic distribution. This motivates the needs for methods for the approximation of multiple integrals over hyperboloids. A transformation is used to reduce the hyperboloid integrals to a product of two radial integrals and two spherical surface integrals. Numerical approximation methods for the transformed integrals are constructed. The application of these methods is demonstrated using some financial applications examples.
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