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The paper overviews stochastic optimization models of actuarial mathematics and methods for their solution from the point of view of the methodology of multicriteria stochastic programming and optimal control. The evolution of the capital of an insurance company is considered in discrete time. The main random parameters of the models are insurance payouts, i.e., the ratios of paid insurance claims to the corresponding premiums per unit time. Optimization variables are the structure of the insurance portfolio (gross premium structure) and amount of dividends. As efficiency criteria, indicators of the profitability of the insurance business are used, and, as risk indicators the ruin probability and the recourse capital necessary to prevent the ruin are taken. The goal of the optimization is to find Pareto-optimal solutions. Methods for finding these solutions are proposed. [ABSTRACT FROM AUTHOR]

The paper presents an algorithm to search for the lower bound of the Bayesian estimate of the parameter of exponential distribution in the case where it is known that a priori distribution belongs to the class of all distribution functions with two equal quantiles. This problem arises in sensivity analysis of Bayesian estimates of failure rates to the choice of a priori distribution in the exponential failure model. [ABSTRACT FROM AUTHOR]