Convex and exact games with non-transferable utility

We generalize exactness to games with non-transferable utility (NTU). A game is exact if for each coalition there is a core allocation on the boundary of its payoff set. Convex games with transferable utility are well-known to be exact. We consider ve generalizations of convexity in the NTU setting. We show that each of ordinal, coalition merge, individual merge and marginal convexity can be uni¯ed under NTU exactness. We provide an example of a cardinally convex game which is not NTU exact. Finally, we relate the classes of Π-balanced, totally Π-balanced, NTU exact, totally NTU exact, ordinally convex, cardinally convex, coalition merge convex, individual merge convex and marginal convex games to one another.

The non-existence of a universal topological type space

The concept of types was introduced by Harsányi[8]. In the literature there are two approaches for formalizing types, type spaces: the purely measurable and the topological models. In the former framework Heifetz and Samet [11] showed that the universal type space exists and later Meier[13] proved that it is complete. In this paper we examine the topological approach and conclude that there is no universal topological type space in the category of topological type spaces.

Determinisztikus és valószínűségi elosztási eljárások (Deterministic and probabilistic rationing methods)

Az életben számtalan olyan esettel találkozunk, amikor egy jószág iránti kereslet meghaladja a rendelkezésre álló kínálatot. Példaként említhetjük a kárpótlási igényeket, egy csődbement cég hitelezőinek igényeit, valamely szerv átültetésére váró betegek sorát stb. Ilyen helyzetekben valamilyen eljárás szerint oszthatjuk el a szűkös mennyiséget a szereplők között. Szokás megkülönböztetni a determinisztikus és a sztochasztikus elosztási eljárásokat, jóllehet sok esetben csak a determinisztikus eljárásokat alkalmazzák. Azonban igazságossági szempontból gyakran használnak sztochasztikus elosztási eljárásokat is, mint például tette azt az Egyesült államok hadserege a második világháború végét követően a külföldön állomásozó katonáinak visszavonásakor, illetve a vietnami háború során behívandó személyek kiválasztásakor. / === / We investigated the minimal variance methods introduced in Tasnádi [6] based on seven popular axioms. We proved that if a deterministic rationing method satisfies demand monotonicity, resource monotonicity, equal treatment of equals and self-duality, than the minimal variance methods associated with the given deterministic rationing method also satisfies demand monotonicity, resource monotonicity, equal treatment of equals and self-duality. Furthermore, we found that the consistency, the lower composition and the upper composition of a deterministic rationing method does not imply the consistency, the lower composition and the upper composition of a minimal variance method associated with the given deterministic rationing method.

A bizonytalanságnak és a vevőkör nagyságának együttes hatása az árakra (Investigating how the number of policies effect the optimum insurance premium)

Ebben a cikkben azzal foglalkozom, hogy a kockázat és a vevőkör nagysága együttesen hogyan hat a termék árára. Kétféle piacot hasonlítok össze: egy biztosítási piacot, és egy termékpiacot. A kétféle piac között az a legfontosabb különbség, hogy termékpiac esetében az eladó számára csak ott jelentkezik kockázat, hogy el tudja-e adni a terméket, míg biztosítási piac esetében az eladó a termék értékesítése után is szembesül kockázattal. A cikk során megmutatom, hogy a vevőkör növekedésének ellentétes hatása lehet a termék árára termék- illetve biztosítási piacok esetében. / === / An economic approach for modeling the insurance markets. The study focuses on the monopolistic market, where one insurance company sells a product with predetermined benefits for the customers. An outline of the company and the insureds' behavior with utility functions is given. The study investigates the problem of policy pricing in relation to the number of clients the company acquires. Analytic tools will be used to further clarify the points.

Bevezetés a sztochasztikus analízisbe közgazdászoknak (Introducing stochastic analysis)

A dolgozat célja, hogy rövid bevezetést adjon a folytonos idejű sztochasztikus analízisbe. A hazai pénzügyi oktatási gyakorlat nagyrészt a diszkrét idejű és gyakran diszkrét állapotterű modellekre épül. Ennek oka a folytonos időparaméterű sztochasztikus folyamatok elméletétől való érthető idegenkedés. A folytonos időparaméterű sztochasztikus analízis a modern matematika egyik csúcsteljesítménye, amely teljeskörű matematikai megértése egyrészt feltételezi, hogy az olvasó tisztában van a modern analízis szinte minden részletével; másrészt a matematikai részletek pontos megértése nem sok segítséget jelent a pénzügyi gondolatok elsajátításakor. / === / In the article we present a short, intuitive introduction to stochastic analysis. Our presentation is aimed for economist and we try to discuss only the most elementary properties of the stochastic analysis. Instead of precise proofs we present some simplified intuitive arguments. The central concept of the discussion is the quadratic variation and the Itō's lemma.

Derivatív pénzügyi termékek árdinamikája és az új típusú kamatlábmodellek (Interest rate models and the price processes of financial derivatives)

Ennek a cikknek az a célja, hogy áttekintést adjon annak a folyamatnak néhány főbb állomásáról, amit Black, Scholes és Merton opcióárazásról írt cikkei indítottak el a 70-es évek elején, és ami egyszerre forradalmasította a fejlett nyugati pénzügyi piacokat és a pénzügyi elméletet. / === / This review article compares the development of financial theory within and outside Hungary in the last three decades starting with the Black-Scholes revolution. Problems like the term structure of interest rate volatilities which is in the focus of many research internationally has not received the proper attention among the Hungarian economists. The article gives an overview of no-arbitrage pricing, the partial differential equation approach and the related numerical techniques, like the lattice methods in pricing financial derivatives. The relevant concepts of the martingal approach are overviewed. There is a special focus on the HJM framework of the interest rate development. The idea that the volatility and the correlation can be traded is a new horizon to the Hungarian capital market.

A diszkrét kiválasztási modell becslése Cox-regresszióval (Parameter estimation for multinomial discrete choice model using Cox-regression)

Considering the so-called "multinomial discrete choice" model the focus of this paper is on the estimation problem of the parameters. Especially, the basic question arises how to carry out the point and interval estimation of the parameters when the model is mixed i.e. includes both individual and choice-specific explanatory variables while a standard MDC computer program is not available for use. The basic idea behind the solution is the use of the Cox-proportional hazards method of survival analysis which is available in any standard statistical package and provided a data structure satisfying certain special requirements it yields the MDC solutions desired. The paper describes the features of the data set to be analysed.

A Dalang, Morton, Willinger tétel (On the theorem of Dalang-Morton-Willinger)

In the article we shortly discuss the proof of the theorem of Dalang-Morton-Willinger. We show that the proof of the theorem depends on some interesting general properties of the stochastic convergence.

A Harrod modell strukturális stabilitása (Structural stability of the Harrod model)

In this study it is shown that the nontrivial hyperbolic fixed point of a nonlinear dynamical system, which is formulated by means of the adaptive expectations, corresponds to the unstable equilibrium of Harrod. We prove that this nonlinear dynamical (in the sense of Harrod) model is structurally stable under suitable economic conditions. In the case of structural stability, small changes of the functions (C1-perturbations of the vector field) describing the expected and the true time variation of the capital coefficients do not influence the qualitative properties of the endogenous variables, that is, although the trajectories may slightly change, their structure is the same as that of the unperturbed one, and therefore these models are suitable for long-time predictions. In this situation the critique of Lucas or Engel is not valid. There is no topological conjugacy between the perturbed and unperturbed models; the change of the growth rate between two levels may require different times for the perturbed and unperturbed models.

Osztozkodási játékok (Games of fair division)

In this survey we presented several proportional and envy-free cake-cutting algorithms. We also mentioned some interesting open problems.

Analysis of operational risk of banks – catastrophe modelling

Nowadays financial institutions due to regulation and internal motivations care more intensively on their risks. Besides previously dominating market and credit risk new trend is to handle operational risk systematically. Operational risk is the risk of loss resulting from inadequate or failed internal processes, people and systems or from external events. First we show the basic features of operational risk and its modelling and regulatory approaches, and after we will analyse operational risk in an own developed simulation model framework. Our approach is based on the analysis of latent risk process instead of manifest risk process, which widely popular in risk literature. In our model the latent risk process is a stochastic risk process, so called Ornstein- Uhlenbeck process, which is a mean reversion process. In the model framework we define catastrophe as breach of a critical barrier by the process. We analyse the distributions of catastrophe frequency, severity and first time to hit, not only for single process, but for dual process as well. Based on our first results we could not falsify the Poisson feature of frequency, and long tail feature of severity. Distribution of “first time to hit” requires more sophisticated analysis. At the end of paper we examine advantages of simulation based forecasting, and finally we concluding with the possible, further research directions to be done in the future.

Az árfolyamsávok empirikus modelljei és a devizaárfolyam sávon belüli előrejelezhetetlensége = Empirical models of exchange rate target zones

A sávosan rögzített devizaárfolyamok elméleti és gyakorlati vizsgálatai a nemzetközi közgazdaságtan egyik legnépszerűbb témaköre volt a kilencvenes évek elején. A gyakorlati módszerek közül az alkalmazások és hivatkozások száma tekintetében az úgynevezett eltolódással igazítás módszere emelkedett ki. A módszert alkalmazó szerzők szerint amíg a lebegő árfolyamú devizák előrejelzése céltalan feladatnak tűnik, addig sávos árfolyam esetén az árfolyam sávon belüli helyzetének előrejelzése sikeresen végezhető. E tanulmány bemutatja, hogy az Európai Monetáris Rendszer és az északeurópai államok sávos árfolyamrendszereinél e módszer alkalmazásával adódott eredmények például a lebegő árfolyamú amerikai dollárra és az egységgyökfolyamatok többségére is érvényesek. A tanulmány feltárja e látszólagos ellentmondás okait, és bemutat egy olyan, a sávos árfolyamrendszerek főbb megfigyelt jellemzőire épülő modellt, amelynek keretei között a sávon belüli árfolyam előrejelzése nem feltétlenül lehetséges, mert a leértékelés előtti időszakban a sávon belüli árfolyam alakulása kaotikus lehet. / === / Following the development of the first exchange rate target zone model at the end of the eighties dozens of papers analyzed theoretical and empirical topics of currency bands. This paper reviews different empirical methods to analyze the credibility of the band and lays special emphasis on the most widely used method, the so-called drift-adjustment method. Papers applying that method claim that while forecasting a freely floating currency is hopeless, predicting an exchange rate within the future band is successful. This paper shows that the results achieved by applications to EMS and Nordic currencies are not specific to data of target zone currencies. For example, application to US dollar and even to most unit root processes leads qualitatively to the same. This paper explores the solutions of this puzzle and shows a model of target zones in which the exchange rate within the band is not necessarily predictable since the process might follow chaotic dynamics before devaluation.

The multiple hierarchical legislatures in representative democracy

Multiple hierarchical models of representative democracies in which, for instance, voters elect county representatives, county representatives elect district representatives, district representatives elect state representatives and state representatives a president, reduces the number of electors a representative is answerable for, and therefore, considering each level separately, these models could come closer to direct democracy. In this paper we show that worst case policy bias increases with the number of hierarchical levels. This also means that the opportunities of a gerrymanderer increase in the number of hierarchical levels.

Invariance under type morphisms: the bayesian Nash equilibrium

Ely and Peski (2006) and Friedenberg and Meier (2010) provide examples when changing the type space behind a game, taking a "bigger" type space, induces changes of Bayesian Nash Equilibria, in other words, the Bayesian Nash Equilibrium is not invariant under type morphisms. In this paper we introduce the notion of strong type morphism. Strong type morphisms are stronger than ordinary and conditional type morphisms (Ely and Peski, 2006), and we show that Bayesian Nash Equilibria are not invariant under strong type morphisms either. We present our results in a very simple, finite setting, and conclude that there is no chance to get reasonable assumptions for Bayesian Nash Equilibria to be invariant under any kind of reasonable type morphisms.

The existence of an inverse limit of inverse system of measure spaces - a purely measurable case

The existence of an inverse limit of an inverse system of (probability) measure spaces has been investigated since the very beginning of the birth of the modern probability theory. Results from Kolmogorov [10], Bochner [2], Choksi [5], Metivier [14], Bourbaki [3] among others have paved the way of the deep understanding of the problem under consideration. All the above results, however, call for some topological concepts, or at least ones which are closely related topological ones. In this paper we investigate purely measurable inverse systems of (probability) measure spaces, and give a sucient condition for the existence of a unique inverse limit. An example for the considered purely measurable inverse systems of (probability) measure spaces is also given.