Comonotonic Approximations for the Sum of Log Unified Skew Normal Random Variables: Application in Finance and Actuarial Science

Journal of Data Science

article

Arjun K. Gupta¹  Mohammad A. Azizb² 

[1] Department of Mathematics and Statistics, Bowling Green State University;Department of Mathematics, University of Wisconsin-Eau Claire

关键词: Unified skew normal distribution;    additive properties;    log unified skew normal distribution;    convex order;    comonotonicity;    value at risk;   

DOI  :  10.6339/JDS.201504_13(2).0008

学科分类：土木及结构工程学

来源: JDS

【 摘 要 】

The classical works in finance and insurance for modeling asset returns is the Gaussian model. However, when modeling complex random phenomena, more flexible distributions are needed which are beyond the normal distribution. This is because most of the financial and economic data are skewed and have “fat tails”. Hence symmetric distributions like normal or others may not be good choices while modeling these kinds of data. Flexible distributions like skew normal distribution allow robust modeling of high-dimensional multimodal and asymmetric data. In this paper, we consider a very flexible financial model to construct comonotonic lower convex order bounds in approximating the distribution of the sums of dependent log skew normal random variables. The dependence structure of these random variables is based on a recently developed generalized multivariate skew normal distribution, known as unified skew normal distribution. The approximations are used to calculate the risk measure related to the distribution of terminal wealth. The accurateness of the approximation is investigated numerically. Results obtained from our methods are competitive with a more time consuming method known as Monte Carlo method.

【 授权许可】

CC BY