报告人：邵嗣烘 教授（北京大学）

时间：2025年09月10日 10:30-

地点：理科楼LA103

摘要：The need for a fast and accurate numerical evaluation of the multivariate normal cumulative distribution function arises in many applications from statistics, computational physics to mathematical finance. Yet, the famous “curse of dimensionality” makes this problem uneasy. This talk presents a new and efficient deterministic method for multivariate normal probabilities with high accuracy as well as the analysis for the convergence rate. With the help of the Laguerre function of the second kind, we prove that an upper bound of the error depends only on the number of variables and the order l, thereby implying that the new algorithm has uniform convergence rate for different covariance matrix，even near singular cases, and different evaluated point d. Numerical experiments demonstrate that the proposed algorithm may achieve double precision when l = 21, and can get accurate results even in 11-variate cases. Finally, we show some typical applications in the calculation of expected European option returns and the pricing of rainbow European options.

邀请人：数学研究中心

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