Abstract
The paper is devoted to solving problems of optimal choice of client’s risk bearing by the insurer at the level insurer-client and at the level insurer-reinsurer. It was shown that in the model of additional restrictions, the most profitable for the insurer will be the refusal from reinsurance and application of stop-loss insurance strategy. In the problem that takes the restriction on insurer’s risk into account, reinsurance of excess of loss and insurance that is a combination of the stop-loss strategy and deductible are optimal. Necessary and sufficient conditions of optimality of parameters of the stated strategies are obtained; an example illustrating the proved results in case of exponential utility functions is given.
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Original Russian Text © A.Yu. Golubin, V.N. Gridin, A.I. Gazov, 2009, published in Avtomatika i Telemekhanika, 2009, No. 8, pp. 133–144.
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Golubin, A.Y., Gridin, V.N. & Gazov, A.I. Optimization of risk bearing in a statistical model with reinsurance. Autom Remote Control 70, 1385–1395 (2009). https://doi.org/10.1134/S0005117909080116
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DOI: https://doi.org/10.1134/S0005117909080116