On Sums of Claims and their Applications in Analysis of Pension Funds and Insurance Products

The problem that assets of a fund are not sufficient to cover its liabilities is of extreme importance both for its members as well as for fund managers. We show that this problem can be solved via total claims distributions and give answers to the following questions: How much money will be needed in the first pillar in order to satisfy the requirements of pensioners in a time horizon and which groups of working people should join also the second pillar because their benefits from it will be greater than those from the first pillar? Though the paper concentrates primarily on the situation with Slovakian pension funds we believe that our findings are more general. We show that the alternative methods should be used for calculation of extremes. We discuss the so-called barrier strategy for treating the surplus of an insurance company and bring some new results concerning it. Reprinted by permission of the University of Economics, Prague