Dynamic mean-variance problem with constrained risk control for the insurers

被引：129

作者：

Bai, Lihua ^{[1
]}

Zhang, Huayue ^{[2
]}

机构：

[1] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China

[2] Nankai Univ, Dept Finance, Sch Econ, Tianjin 300071, Peoples R China

来源：

MATHEMATICAL METHODS OF OPERATIONS RESEARCH | 2008年 / 68卷 / 01期

基金：

中国国家自然科学基金;

关键词：

mean-variance; efficient frontier; efficient strategy; Hamilton-Jacobi- Bellman equation; Riccati equation; viscosity solution; Lagrange multiplier;

D O I：

10.1007/s00186-007-0195-4

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

In this paper, we study optimal reinsurance/new business and investment (no-shorting) strategy for the mean-variance problem in two risk models: a classical risk model and a diffusion model. The problem is firstly reduced to a stochastic linear-quadratic (LQ) control problem with constraints. Then, the efficient frontiers and efficient strategies are derived explicitly by a verification theorem with the viscosity solutions of Hamilton-Jacobi-Bellman (HJB) equations, which is different from that given in Zhou et al. (SIAM J Control Optim 35:243-253, 1997). Furthermore, by comparisons, we find that they are identical under the two risk models.

引用

页码：181 / 205

页数：25

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