On applying approximations to find optimal excess of loss reinsurance

Abstract

Mikhail Batsyn  – Associate Professor, Department of Applied Mathematics and Informatics, Faculty of Business Informatics and Applied Mathematics, National Research University Higher School of Economics.
Address: 25/12, Bolshaya Pecherskaya str., Nizhniy Novgorod, 603155, Russian Federation.
E-mail: mbatsyn@hse.ru

Ekaterina Batsyna  – Assistant Professor, Department of Applied Mathematics and Informatics, Faculty of Business Informatics and Applied Mathematics, National Research University Higher School of Economics.
Address: 25/12, Bolshaya Pecherskaya str., Nizhniy Novgorod, 603155, Russian Federation.
E-mail: batcyna@hse.ru 

In this paper we consider the problem of finding an optimal excess of loss reinsurance which maximizes the reliability (probability of no ruin) of the insurance company. We apply two approximate approaches to calculate the distribution of total payments. The first approach is based on normal approximation of the payments distribution. Using this approximation we have derived an integral equation on the optimal retention limit. The second approach is based on simulation techniques. To test the precision of our approaches we use an exact formula for the distribution of total payments known for the case when losses
in one insured event are distributed uniformly.

The article is published in English. Full text in English is available (see the file attached).