The Reduction of Initial Reserves Using the Optimal Reinsurance Chains in Non-Life Insurance

Galina Horáková, František Slaninka and Zsolt Simonka
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Galina Horáková: Department of Mathematics & Actuarial Science, Faculty of Economic Informatics, University of Economics in Bratislava, Dolnozemská Cesta 1/b, 852 35 Bratislava, Slovakia
František Slaninka: Department of Mathematics & Actuarial Science, Faculty of Economic Informatics, University of Economics in Bratislava, Dolnozemská Cesta 1/b, 852 35 Bratislava, Slovakia
Zsolt Simonka: Department of Mathematics & Actuarial Science, Faculty of Economic Informatics, University of Economics in Bratislava, Dolnozemská Cesta 1/b, 852 35 Bratislava, Slovakia

Mathematics, 2021, vol. 9, issue 12, 1-20

Abstract: The aim of the paper is to propose, and give an example of, a strategy for managing insurance risk in continuous time to protect a portfolio of non-life insurance contracts against unwelcome surplus fluctuations. The strategy combines the characteristics of the ruin probability and the values VaR and CVaR . It also proposes an approach for reducing the required initial reserves by means of capital injections when the surplus is tending towards negative values, which, if used, would protect a portfolio of insurance contracts against unwelcome fluctuations of that surplus. The proposed approach enables the insurer to analyse the surplus by developing a number of scenarios for the progress of the surplus for a given reinsurance protection over a particular time period. It allows one to observe the differences in the reduction of risk obtained with different types of reinsurance chains. In addition, one can compare the differences with the results obtained, using optimally chosen parameters for each type of proportional reinsurance making up the reinsurance chain.

Keywords: compound Poisson process; surplus process; Brownian motion; inverse Gaussian distribution; ruin probability; conditional value at risk; reinsurance chain; optimisation criteria; reserves (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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