Modelling of technical reserves of an insurance company

Анотація

In the modern rapidly evolving society, the science and the business are facing new needs and challenges constantly. The insurance industry and its mathematical foundation, the actuarial science, are not exceptions. Currently, the greatest challenge that the insurance system has to cope with is the issue of the new international financial standard that affects the calculation of reserves among other things. So far, insurers have mainly used common classical deterministic methods. However, the new standard emphasizes the necessity of the realistic prognosis that is best achieved with stochastic modelling tools since deterministic models do not represent the uncertainty and the random nature of future possible losses. This article considers the advantage of using stochastic modelling for reserve calculation in comparison to the deterministic approach. The article consists of five sections. In the first section, we briefly present the technique that lies in the basis of technical reserves calculation. The second section is devoted to such deterministic methods of reserve calculation as the Bornhuetter-Ferguson method and the chain-ladder method. In the third section, we consider modifications of two stochastic models – the Mack method and the bootstrapping technique. The fourth section considers the adjustment of reserves for the time value of money and inflation. In the fifth section, the results of modelling in the programming language R are presented.

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