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Dynamic mean-variance problem with constrained risk control for the insurers. (English) Zbl 1156.93037

Summary: 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 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 equations, which is different from that given in X. Y. Zhou, J. Yong and X. Li [SIAM J. Control Optimization 35, No. 1, 243–253 (1997; Zbl 0880.93059)]. Furthermore, by comparisons, we find that they are identical under the two risk models.

MSC:

93E20 Optimal stochastic control
91B30 Risk theory, insurance (MSC2010)
60J60 Diffusion processes
49L20 Dynamic programming in optimal control and differential games

Citations:

Zbl 0880.93059
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References:

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