Many problems in mathematical finance (such as the pricing and hedging of complex financial derivatives) can be formulated as high-dimensional integration with dimension as high as hundreds or even thousands. In this talk I will discuss the advances for tackling such high-dimensional problems in mathematical finance. It is shown how the curse of dimensionality can be broken with the optimal convergence rate by using low discrepancy sequences and by properly introducing weights to characterize the importance of variables. I also try to answer why high-dimensional problems in mathematical finance are often of low effective dimension. The necessity and the methods for choosing the right weights in constructing good lattice rules and the methods for dimension reduction are highlighted.
About the Speaker:
王小群，清华大学数学科学系长聘教授，2009年获国家杰出青年科学基金，2011年被聘为教育部长江学者特聘教授。研究领域为金融数学、计算金融学、数据科学和统计计算、计算机模拟算法和计算复杂性理论。在金融资产定价和金融风险管理、高维积分计算和降维、拟蒙特卡洛(Quasi-Monte Carlo)方法和计算复杂性方面进行了系统研究，取得一系列研究成果。学术成果发表在Management Science, Operations Research, INFORMS Journal on Computing, European Journal of Operational Research, SIAM Journal on Numerical Analysis, SIAM Journal on Scientific Computing, Mathematics of Computation, Numerische Mathematik, IMA Journal of Numerical Analysis, Journal of Complexity, Quantitative Finance等国际权威刊物上。
Tencent Meeting: https://meeting.tencent.com/dm/7rnwMgIVkZdQ
Your participation is warmly welcomed!