The influence of consumption on optimal strategies of insurance company under of stochastic uncertainty
Zhurov A.N., Shapoval A.B.
"Математика. Компьютер. Образование". Cб. трудов XVII международной конференции. Под общей редакцией Г.Ю. Ризниченко Ижевск: Научно-издательский центр "Регулярная и хаотическая динамика", 2010 (in press). (accepted)
The aim of this article is to find optimal controls in investments and consumption of insurance company, which deals with insurance and investment risks. It is assumed, that the total loss process is compound Poisson. The investment portfolio consists of risky and free-risky assets. The price of risky asset satisfies the geometric Brown motion. The fraction of wealth, which is invested in risky asset and the value of current consumption are optimal contrls in this model. In this paper the formula of optimal investment and consumption control is analitically determined.
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