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Stochastic Optimization Models of Actuarial Mathematics

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Cybernetics and Systems Analysis Aims and scope

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 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.

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Authors and Affiliations

  1. International Institute for Applied Systems Analysis, Luxenburg, Austria

    Yu. M. Ermoliev

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

    V. I. Norkin & B. V. Norkin

Authors
  1. Yu. M. Ermoliev
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  2. V. I. Norkin
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  3. B. V. Norkin
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Corresponding author

Correspondence to Yu. M. Ermoliev.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 1, January–February, 2020, pp. 70–81.

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Ermoliev, Y.M., Norkin, V.I. & Norkin, B.V. Stochastic Optimization Models of Actuarial Mathematics. Cybern Syst Anal 56, 58–67 (2020). https://doi.org/10.1007/s10559-020-00221-0

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  • DOI: https://doi.org/10.1007/s10559-020-00221-0

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