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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.

91B30 Risk theory, insurance (MSC2010)
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
93E20 Optimal stochastic control
Full Text: DOI EuDML
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