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Article

Оптимальные стратегии страхования в процессе риска с ограничениями на риски cтрахователей

Голубин А. Ю., Гридин В. Н.

The paper studies a problem of optimal insurer’s choice of a risk-sharing policy in a dynamic risk model, so-called Cramer-Lundberg process, over infinite time interval. Additional constraints are imposed on residual risks of insureds: on mean value or with probability one. An optimal control problem of  minimizing a functional  of the form  of variation coefficient is solved.  We show that: in the first case the optimum is achieved at stop loss insurance  policies,  in the second case  the  optimal insurance is a combination of stop loss and deductible policies.  It is proved that the obtained results can be easily applied to problems with other optimization criteria: maximization of  long-run utility and minimization of  probability of  a deviation from mean trajectory.