Основы актуарных расчетов
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 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.
The monograph is devoted to the problems arising in the analysis of demographic processes, the calculation of net rates and assessment of reserves in the major life insurance contract. The results of studies involving various related parties of the analyzed issues. For example, given a detailed comparative analysis of pre- and disadvantages of organization of the insurance market in Russia and abroad. With used - vaniem various techniques built a ranking of countries in terms of development of the market under study.
The basis of actuarial calculations in the basic life insurance contracts are demo graphic processes: in particular, information about the mortality rate. The foundation for the construction of a net rates and valuation reserves in the life insurance contract is the data of mortality tables, which are based, in turn, is an indicator of how Vero die before reaching next age interval. In this regard, the authors present the theoretical aspects of the construction of the net rates and valuation reserves in life insurance contracts. The paper discusses methods of constructing mortality tables , raised the problem of statistical analysis of demographic processes in actuarial calculations, an overview of the basic formulas used to derive the net rates and valuation reserves in life insurance contracts.
The authors of the classification of the Russian Federation in terms of economic and demographic character. Some representatives of the obtained clusters The results of the study of the dynamics of demographic processes. It analyzes the main trends in life expectancy at age and sex and the regional context.
Of course, the authors have paid special attention to the analysis of the impact of demographic, financial factors on change of the tariff policy of life insurance contracts, as well as the impact on the rate and size of the allowance conditions of the contract. The research data for the city of Moscow as a financial and information center of Russia, which significantly affects the development of the insurance market as a whole (not only in the life insurance sector).
The results of these studies may be interested in a wide range of professionals in the field of economics, actuarial calculations in life insurance analysts.
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.