Some stochastic models of actuarial mathematics

We study three models of insurance company performance that differ in financial instruments which can be applied. The first chapter of the thesis is devoted to the problem of optimal control in the classical risk model. It is assumed that each insurable event can cause several claims corresponding to different risks. Furthermore, each risk can be reinsured according to the arbitrary reinsurance treaty. Parameters of such reinsurance treaties can be changed dynamically. The second and the third chapters deal with the performance of stock insurance companies. Such characteristics as total dividends paid until ruin and the probability of ruin are investigated. In the framework of the second chapter we assume that the insurance company is using the excess of loss reinsurance treaty with the limited liability of reinsurer. In the third chapter we examine barrier dividend strategies with a step barrier function, according to which the dividend barrier can be changed throughout the operation of the insurance company.