金融工程研究中心学术报告：Approximations for random sums with equally correlated summands

**报告人：**Dr. Fraser Daly Associate
Professor Heriot-Watt University

**时 间：**2023年3月30 星期四 19：00 -- 20:00

**地 点：**腾讯会议：499-258-340

**报告摘要:**

Let $Y=X_1+\cdots+X_N$ be a sum of a random number of random variables, where the random variable $N$ is independent of the $X_j$. Such random sums arise in many applications, including in the areas of financial risk, hypothesis testing and physics. Classically, the $X_j$ are assumed to be independent, in which case central limit theorems and other distributional approximation results for $Y$ are well known. However, this assumption of independent $X_j$ may be unrealistic in some applications. We relax this restriction, instead assuming that these random variables come from a generalized multinomial model. In this setting, we prove error bounds in Gaussian, Gamma and Poisson approximations for $Y$ which allow us to investigate the effect of the correlation parameter on the quality of the approximation, while also providing competitive bounds in the special case of independent $X_j$. Proofs make use of Stein's method in conjunction with size-biased and zero-biased couplings.

**个人简介:**

Dr Fraser Daly is Associate Professor in the Department of Actuarial Mathematics and Statistics at Heriot-Watt University. He completed his PhD at the University of Nottingham in 2008, and held postdoctoral positions at the Universities of Zurich and Bristol before taking up his position at Heriot-Watt University in 2013. His research is in applied probability. Much of his work has been focussed on establishing limit theorems with explicit error bounds for a variety of stochastic systems.