数学科学院学术报告[2024] 057号

(高水平大学建设系列报告937号)

报告题目: A Generalized Tail Mean-Variance Model for Optimal Capital Allocation

报告人：姚经，特聘教授，苏州大学

报告时间：2024.06.28 11:00-12:00pm

报告地点：汇星楼（科技楼）514

报告内容：Capital allocation is a core task in financial and actuarial risk management. Some well-known capital allocation principles, such as the "Euler principle" and the "haircut principle", have been widely used in the banking and insurance industry. The partitions of allocated capital not only serve as the buffer against the potential loss but also provide certain risk pricing and performance measurement to the underlying risks. Dhaene et al. (2012) proposed a unified distance-minimizing capital allocation framework. Their objective function in the optimization only considers the magnitude of the loss function but not the variability. In this paper, we propose a general tail mean-variance (GTMV) model, which employs the Bregman divergences to construct distance-minimizing function, and takes both the magnitude and the variability into account. We prove the existence and uniqueness of the optimal allocation and provide the general system of equations that characterizes the optimal solution. In this context, we further introduce the Mahalanobis tail mean-variance (MTMV) model and provide explicit distribution-free optimal allocation formulas, which cover many existing results as special cases. In particular, we derive the parametric analytical solutions for multivariate generalized hyperbolic distributed risks. For multivariate log-generalized hyperbolic distributed non-negative risks, we use the convex approximation method to solve the explicit solutions. We present two numerical examples showing the good performance of our optimal capital allocation rules. The first one analyzes the market risk of S&P 500 industry sector indices. We show that our optimal capital allocation framework is applicable for various scenario analyses and provides a performance measure for the indices and financial market. The other example is based on insurance claims from an Australian insurance company, showing our approximate formulas are both robust and accurate.

报告人简历：姚经是苏州大学特聘教授和博士生导师，教育部引才计划专家，江苏省特聘教授，重庆市“巴渝学者”讲座教授，以色列海法大学精算研究中心研究员。 于2013年5月获得比利时布鲁塞尔自由大学应用经济学博士学位。曾先后任职于比利时FWO基金研究员，比利时布鲁塞尔自由大学科研教授，英国麦克斯韦数学科学研究所和赫瑞瓦特大学统计精算系准教授。主持国家自然科学基金面上项目、比利时FWO科研基金、以色列Zimmerman基金、欧盟伊拉斯莫斯科研基金、英国伦敦数学学会、爱丁堡数学学会等多个国内外科研项目。主要研究方向包括量化金融风险管理与定价、最优投资，资产配置和控制、高维风险模型与系统风险、绿色金融等。

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邀请人：李婧超

数学科学学院

　　　　　　　　　　　　　　　　　　　2024年06月26日