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Optimal premium pricing for a heterogeneous portfolio of insurance risks. (English) Zbl 1200.91144
Summary: 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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