Оптимизация размера премии с учетом кривой спроса на страховые услуги
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.
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.
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.
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 concept of economic equilibrium under uncertainty is applied to a model of insurance market where, in distinction to the classic Borch's model of a reinsurance market, risk exchanges are allowed between the insurer and each insured only, not among insureds themselves. Conditions characterizing an equilibrium are found. A variant of the conditions, based on the Pareto optimality notion and involving risk aversion functions of the agents, is derived. An existence theorem is proved. Computation of the market premiums and optimal indemnities is illustrated by an example with exponential utility functions.
Smoking is a problem, bringing signifi cant social and economic costs to Russiansociety. However, ratifi cation of the World health organization Framework conventionon tobacco control makes it possible to improve Russian legislation accordingto the international standards. So, I describe some measures that should be taken bythe Russian authorities in the nearest future, and I examine their effi ciency. By studyingthe international evidence I analyze the impact of the smoke-free areas, advertisementand sponsorship bans, tax increases, etc. on the prevalence of smoking, cigaretteconsumption and some other indicators. I also investigate the obstacles confrontingthe Russian authorities when they introduce new policy measures and the public attitudetowards these measures. I conclude that there is a number of easy-to-implementanti-smoking activities that need no fi nancial resources but only a political will.
One of the most important indicators of company's success is the increase of its value. The article investigates traditional methods of company's value assessment and the evidence that the application of these methods is incorrect in the new stage of economy. So it is necessary to create a new method of valuation based on the new main sources of company's success that is its intellectual capital.