Abstract: High dimensionality and discontinuity are two outstanding challenges in computational finance, such as in the problems of pricing and hedging of complex financial derivatives. In this talk I will touch briefly on recent advances in understanding the success of quasi-Monte Carlo (QMC) methods for high dimensional problems in mathematical finance, and propose new dimension reduction methods and smoothing methods that deal with the “curse of dimensionality” and discontinuity for typical problems in mathematical finance. Numerical experiments demonstrate that the proposed methods significantly increase the efficiency of QMC methods for pricing options and estimating the Greeks (or sensitivities).
 

Bio: 王小群，清华大学数学科学系教授，2009年获国家杰出青年科学基金。王小群教授从事金融数学、计算金融学、统计计算、计算机随机模拟算法和计算复杂性研究，在国际权威刊物Management Science, Operations Research, SIAM Journal on Numerical Analysis, SIAM Journal on Scientific Computing, Mathematics of Computation, Numerische Mathematik, Journal of Complexity, Quantitative Finance等上发表数十篇学术论文。