Optimal premium pricing for a heterogeneous portfolio of insurance risks.

*(English)*Zbl 1200.91144Summary: The paper revisits the classical problem of premium rating within a heterogeneous portfolio of insurance risks using a continuous stochastic control framework. The portfolio is divided into several classes where each class interacts with the others. The risks are modelled dynamically by the means of a Brownian motion. This dynamic approach is also transferred to the design of the premium process. The premium is not constant but equals the drift of the Brownian motion plus a controlled percentage of the respective volatility. The optimal controller for the premium is obtained using advanced optimization techniques, and it is finally shown that the respective pricing strategy follows a more balanced development compared with the traditional premium approaches.

##### MSC:

91B30 | Risk theory, insurance (MSC2010) |

60J70 | Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) |

93E20 | Optimal stochastic control |

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\textit{A. A. Pantelous} et al., J. Probab. Stat. 2009, Article ID 451856, 18 p. (2009; Zbl 1200.91144)

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