Indexation of pensions in Hungary: A simple cohort model

Pensions;Indexation

New results in pension modelling

In a former paper (Simonovits, 1999), I have discussed the problems of the new Hungarian pension system verbally. In this paper I will present some new results obtained by others and myself with mathematical models, which are related to the Hungarian pension reform (see e.g. Palacios and Rocha, 1998). (1) How can one model a pension system with the life-cycle theory? (Of course, this is introduction rather than new result.) (2) How is the model of a funded system modified if volatility of yields and operating costs are taken into account? (3) What would the actuarially fair model be in an unfunded pension system with flexible age of retirement, and how much saving (and damage) is to be expected from replacing the indexation of pensions in progress to earnings by the combined indexation? (4) How is the efficiency of the pension system affected if the unfunded system is replaced by a partially or fully funded system

The critical window for the classical Ramsey-Tur\'an problem

The first application of Szemer\'edi's powerful regularity method was the following celebrated Ramsey-Tur\'an result proved by Szemer\'edi in 1972: any K_4-free graph on N vertices with independence number o(N) has at most (1/8 + o(1)) N^2 edges. Four years later, Bollob\'as and Erd\H{o}s gave a surprising geometric construction, utilizing the isoperimetric inequality for the high dimensional sphere, of a K_4-free graph on N vertices with independence number o(N) and (1/8 - o(1)) N^2 edges. Starting with Bollob\'as and Erd\H{o}s in 1976, several problems have been asked on estimating the minimum possible independence number in the critical window, when the number of edges is about N^2 / 8. These problems have received considerable attention and remained one of the main open problems in this area. In this paper, we give nearly best-possible bounds, solving the various open problems concerning this critical window.Comment: 34 page

The history of degenerate (bipartite) extremal graph problems

This paper is a survey on Extremal Graph Theory, primarily focusing on the case when one of the excluded graphs is bipartite. On one hand we give an introduction to this field and also describe many important results, methods, problems, and constructions.Comment: 97 pages, 11 figures, many problems. This is the preliminary version of our survey presented in Erdos 100. In this version 2 only a citation was complete

Socially optimal contribution rate and cap in a proportional (DC) pension system

In our model, the government operates a mandatory proportional (DC) pension system to substitute for the low life-cycle savings of the lower-paid myopic workers, while maintaining the incentives of the higher-paid far-sighted ones in contributing to the system. The introduction of an appropriate cap on pension contribution (or its base)—excluding the earnings above the cap from the contribution base—raises the optimal contribution rate, helping more the lower-paid myopic workers and reserving enough room for the saving of higher-paid far-sighted ones. The social welfare is almost independent of the cap in a relatively wide interval but the maximal welfare is higher than the capless welfare by 0.3–4.5 %.info:eu-repo/semantics/publishedVersio