Mathematical Methods of Operations Research

, Volume 68, Issue 1, pp 181–205 | Cite as

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

Original Article
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Abstract

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.

Keywords

Mean-variance Efficient frontier Efficient strategy Hamilton–Jacobi– Bellman equation Riccati equation Viscosity solution Lagrange multiplier 

Mathematics Subject Classification (2000)

93E20 91B30 
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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.School of Mathematical SciencesNankai UniversityTianjinPeople’s Republic of China
  2. 2.Department of Finance, School of EconomicsNankai UniversityTianjinPeople’s Republic of China

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