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A merger of pension funds - a stochastic model

100%
Białek J., University of Łódź C. o. S. M.
Acta Universitatis Lodziensis. Folia Oeconomica
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2008
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vol. 216
EN
In Polish law there exists a definition of the average rate of return of a group of pension funds which, as it was proved by Gajek and Kaluszka (2000), does not satisfy some economic postulates. These authors proposed another definition of the average rate of return. In this paper we consider the problem of a merger of pension funds taking into consideration both measures. We will show that relations between the presented definitions can be different in the case of a merger of any funds.
PL
W polskim prawie funkcjonuje definicja przeciętnej rentowności grupy funduszy emerytalnych, która - jak pokazali Gajek i Kałuszka (2000) - nie spełnia pewnych ekonomicznie zasadnych postulatów. Jednocześnie zaproponowali oni nową miarę dla przeciętnego zwrotu grupy funduszy. W niniejszym artykule omówiony zostaje problem fuzji funduszy emerytalnych z punktu widzenia tych różnych miar. Okaże się, że relacje zachodzące pomiędzy miarami są inne w przypadku, gdy dochodzi do przejęcia któregoś z funduszy.
2

The primer on arbitrage conceptions in economics: their logics, roots and some formal models (historical and bibliographical notes)

61%
Rybicki W.
Mathematical Economics
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2011
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issue 7 (14)
173-197
EN
The paper makes up the first part of a larger study devoted to arbitrage ideas, models and pricing methodology in spirit of “no arbitrage” (or fairness or transparency) demands.The work – as a whole – is entitled “Arbitrage in Economics and Elsewhere – Facts Well Known and Less Known” and consists of three papers. In the present essay we intentionally interweave “loose (informal) variations on themes” (of arbitrage theories, their applications and connotations) with (brief) demonstrations of selected formal models and some more rigorous mathematical technicalities. Some efforts are made to highlight significant economic aspects as well as to reveal a piece of mathematical “machinery” hidden behind the stories told. Nevertheless, the introductory character of the current paper causes the descriptive, philosophical and historical elements to prevail: we invoke very old roots such as Aristotle‟s or Aquinata‟s thoughts and then follow Cournot, Walras and Keynes works, up to the crucial paper of Miller, Modigliani. Along the way the very deep considerations on the coherency of subjective probability systems are mentioned – “the probabilistic core” of an arbitrage/no arbitrage questions (thoughts of Ramsey and de Finetti). Subsequently, the basics (finite state-space) of the modern, martingale (no arbitrage) modeling (originated by Harrison, Kreps, Pliska) is presented, as well as the “factor-type” schema of the arbitrage pricing theorem (Ross‟s conception). The role played by the supplemented bibliography should be also pointed out. It significantly enters the planned communication. The author‟s aim was to provide the (selected) basis, and “vocabulary” which will be useful for reading the entirety of the “trilogy” – the presented foreword really constitutes a kind of “a bibliographical note”.
3
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The Average Price Dynamics and Indexes of Price Dynamics - Discrete Time Stochastic Model

61%
Białek J., University of Łódź C. o. S. M.
Acta Universitatis Lodziensis. Folia Oeconomica
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2006
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vol. 196
EN
In this paper we define two indexes of the average price dynamics in a discrete time stochastic model. Several properties of these indexes are proven, the other are presented by examples. In particular, it is shown that one of the indexes is a martingale provides the prices of products form a (vector) martingale. In addition it is also shown that only one definition satisfies all given postulates. We compare this definition with price indexes.
PL
W artykule zaprezentowano dwie definicje indeksu przeciętnej dynamiki cen produktów w modelu stochastycznym z czasem dyskretnym. Przedstawiono ich podstawowe własności; niektóre z nich zostały udowodnione, inne - poparte przykładami. Ponadto udowodniono, iż jedna z definicji stanowi martyngał, jeśli tylko procesy cen poszczególnych produktów również są martyngałami. Jednocześnie okazało się, iż tylko jedna definicja posiada wszystkie wymagane własności. Na końcu niniejszego artykułu dokonano porównania rekomendowanej definicji z klasycznymi agregatowymi indeksami cen. Okazało się, iż w przypadku gdy rozważany interwał czasowy zawiera dwa okresy produkcyjne, to przy pewnych dodatkowych założeniach proponowana definicja daje się aproksymować klasycznymi indeksami Fishera, Tömqvista i innymi.
4

Arbitrage in economics and elsewhere – facts well known and less known (three papers on arbitrage ideas, modeling and pricing – yesterday, today and tomorrow) – introduction to the series

61%
Rybicki W.
Mathematical Economics
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2011
|
issue 7 (14)
169-172
XX
The presented series of articles on arbitrage theories and their methodological aspects consist of three papers entitled as follows: I. The Primer on Arbitrage Conceptions in Economics: Their Logics, Roots and Some Formal Models (Historical and Bibliographical Notes). II. Mathematics of Financial Arbitrage: From Algebraic Geometry at the Turn of the 19th and 20th Centuries to Modern Martingale (Generalized) Considerations III. The Arbitrage in Stochastic Finance, Social Choice Theory and Macroeconomics. The articles are devoted to present – in a historical perspective – the basic ideas and “metamorphoses” of the notion and role of an arbitrage (originated as a kind of clever and rational speculation – the last word is used in a “neutral”, not pejorative sense) as well as to point out its various, important connotations (not merely in finance or even economics) and to demonstrate some mathematical inevitable technicalities, reflecting, in fact, the logical essence and the modern view of the arbitrage (and non arbitrage) conditions.
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