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

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  • Lihua Bai
  • Huayue Zhang

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. Copyright Springer-Verlag 2008

Suggested Citation

  • Lihua Bai & Huayue Zhang, 2008. "Dynamic mean-variance problem with constrained risk control for the insurers," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(1), pages 181-205, August.
    • Handle: RePEc:spr:mathme:v:68:y:2008:i:1:p:181-205
    DOI: 10.1007/s00186-007-0195-4
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    References listed on IDEAS

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