Optimal investment and risk control in a nonlinear diffusion model





报告摘要In this talk the optimal investment and risk control problems are studied in a diffusion approximation to a non-homogeneous compound Poisson process. Observing from the practice, wefind that there exists an unspecified monotone function describing the relationship between the safety loading of premium and the time-varying claim arrival rate. Using the diffusion approximation, we derive a general nonlinear diffusion model which includes a class stochastic control risk models, like premium control and reinsurance control under various premium principles.Within the nonlinear diffusion model, we firstly consider the optimal investment and premium control problem in two cases: (i) maximizing the expected utility of terminal wealth, (ii) minimizing the probability of ruin. In the two cases, some properties of the value functions are derived, and closed-form expressions for the optimal policies and the value functions are obtained. As a special case of the nonlinear diffusion model, we assume the premium is calculated via the variance principle and investigate the optimal investment and reinsurance for an insurer in three situations. We firstly consider the optimal reinsurance problem when there is no risk asset in the market. And then, the optimal reinsurance and investment policies are considered under the assumption of that there is an accurate modeled risky asset in the financial market. Furthermore, model ambiguity in the financial market is also considered. In particular, the optimal policies in three situations are compared, and numerical examples are given to illustrate our results.

报告人简介:周明,研究员,博导,现任中央财经大学保险学院、中国精算研究院副院长,北美准精算师(ASA),中国精算师协会正会员,中国工业与应用数学学会保险精算青年工作委员会副主任。曾在加拿大滑铁卢大学做博士后1年,美国德克萨斯大学达拉斯分校做访问学者1年,先后多次访问香港大学、香港理工大学等。目前主要研究方向为资产负债管理、风险分析与决策。在《Insurance: Mathematics and Economics》《Quantitative Finance》《Astin Bulletin》《中国科学》等国内外知名期刊发表学术论文30余篇,主持国家、省部级等各类项目10余项