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Cybernetics And Systems Analysis
International Theoretical Science Journal
Volume 56 >>> № 1 JANUARY — FEBRUARY 2020
UDC 368:519.21
Yu.M. Ermoliev1, V.I. Norkin2, B.V. Norkin3


1 International Institute for Applied Systems Analysis, Laxenburg, Austria

 ermoliev@iiasa.ic.it

2 V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine,
and National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute,” Kyiv, Ukraine

 vladimir.norkin@gmail.com

3 V.M. Glushkov Institute of Cybernetics, National Academy
of Sciences of Ukraine, Kyiv, Ukraine

 bogdan.norkin@gmail.com

STOCHASTIC OPTIMIZATION MODELS OF ACTUARIAL MATHEMATICS

Abstract. 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 payment levels, i.e., the ratio of paid claims to the corresponding premiums per unit of time. Optimization variables are the structure of the insurance portfolio (the gross premium structure) and the size of dividends. As efficiency criteria indicators of the profitability of the insurance business are used, and, as risk indicators the probability of ruin and the recourse capital necessary to prevent the ruin are taken. The goal of optimization is to find Pareto-optimal solutions. Methods for finding these solutions are proposed.

Keywords: insurance mathematics, risk process, ruin probability, stochastic programming, multicriteria problems, two-stage problems, probabilistic constraints, stochastic optimal control, mixed-integer programming, dynamic programming.



FULL TEXT

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