Boldyrіeva V. Modeling and analysis of the insurance companies that operate in the (B,S)-market

The aim of the thesis is to study the construction and operation of insurance companies under uncertainty and risk. The object of study - activities of insurance companies. Methods based on the using methods of probability theory, mathematical analysis, the theory of stochastic differential equations and stochastic optimal control systems, methods of stochastic calculus methods of the theory of random processes and methods for solving stochastic differential equations. The balance equations for insurance companies models of under different conditions were obtained, it was taking into account advertising costs in order to attract new customers. It was founded the equations for the probabilities of non-bankruptcy on finite and infinite time intervals of the company existence. Different methods for deriving the equations for the probability of the insurance company non-bankruptcy which operates in the (B, S)-market were received and substantiated. For the classical risk model, it was obtained an homogeneous linear differential equation with constant coefficients for finding approximate non-bankruptcy probability distribution function for any insurance claims. The rate of convergence of the solution of this equation to the original was built.