Особенности формирования спроса на страховой продукт
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.
The points of view of modern writers on the ideas of "insurance product", "insurance service", and “insurance goods" are analyzed. Either the contradictions in different authors’ interpretations of these ideas, or groundlessness of some approaches to them have been discovered.
Authors, using economic approach, reveal a ratio of these conceptions and prove legitimacy of their synthesis in the category "insurance goods".
The monograph includes selected articles of the studies on the theory and practice of insurance and risk management in Russia and abroad. The modern condition and perspective directions of scientific researches in the field of insurance, risk management insurance education. The monograph allows to obtain a fairly complete picture of the most pressing issues in the field of insurance business, as well as about directions of finding possible answers to them. The book is intended for senior students, postgraduates and teachers of economic universities, researchers and practitioners interested in the issues of insurance, risk management, and insurance.
The chapter studies a dynamic risk model defined on infinite time interval, where both insurance and per-claim reinsurance policies are chosen by the insurer in order to minimize a functional of the form of variation coefficient under constraints imposed with probability one on insured's and reinsurer's risks. We show that the optimum is achieved at constant policies, the optimal reinsurance is a partial stop loss reinsurance and the optimal insurance is a combination of stop loss and deductible policies. The results are illustrated by a numerical example involving uniformly distributed claim sizes.
A singular boundary value problem for a second order linear integrodifferential equation with Volterra and nonVolterra integral operators is formulated and analyzed. The problem arises in the study of the survival probability of an insurance company over infinite time (as a function of its initial surplus) in a dynamic insurance model that is a modification of the classical Cramer–Lundberg model with a stochastic process rate of premium under a certain investment strategy in the financial market.