A cardinally convex game with empty core

In this note we present a cardinally convex game (Sharkey, 1981) with empty core. Sharkey assumes that V (N) is convex, we do not do so, hence we do not contradict Sharkey's result.

Ranking in Swiss system chess team tournaments

The paper uses paired comparison-based scoring procedures for ranking the participants of a Swiss system chess team tournament. We present the main challenges of ranking in Swiss system, the features of individual and team competitions as well as the failures of official lexicographical orders. The tournament is represented as a ranking problem, our model is discussed with respect to the properties of the score, generalized row sum and least squares methods. The proposed procedure is illustrated with a detailed analysis of the two recent chess team European championships. Final rankings are compared by their distances and visualized with multidimensional scaling (MDS). Differences to official ranking are revealed by the decomposition of least squares method. Rankings are evaluated by prediction accuracy, retrodictive performance, and stability. The paper argues for the use of least squares method with a results matrix favoring match points.

Measuring centrality by a generalization of degree

Network analysis has emerged as a key technique in communication studies, economics, geography, history and sociology, among others. A fundamental issue is how to identify key nodes in a network, for which purpose a number of centrality measures have been developed. This paper proposes a new parametric family of centrality measures called generalized degree. It is based on the idea that a relationship to a more interconnected node contributes to centrality in a greater extent than a connection to a less central one. Generalized degree improves on degree by redistributing its sum over the network with the consideration of the global structure. Application of the measure is supported by a set of basic properties. A sufficient condition is given for generalized degree to be rank monotonic, excluding counter-intuitive changes in the centrality ranking after certain modifications of the network. The measure has a graph interpretation and can be calculated iteratively. Generalized degree is recommended to apply besides degree since it preserves most favorable attributes of degree, but better reflects the role of the nodes in the network and has an increased ability to distinguish between their importance.

On the completeness of the universal knowledge-belief space: A technical note

Meier (2008) shows that the universal knowledge-belief space exists. However, besides the universality there is an other important property might be imposed on knowledge- belief spaces, inherited also from type spaces, the completeness. In this paper we introduce the notion of complete knowledge-belief space, and demonstrate that the universal knowledge-belief space is not complete, that is, some subjective beliefs (probability measures) on the universal knowledge-belief space are not knowledge-belief types.

Incomplete pairwise comparison matrices and weighting methods

A special class of preferences, given by a directed acyclic graph, is considered. They are represented by incomplete pairwise comparison matrices as only partial information is available: for some pairs no comparison is given in the graph. A weighting method satisfies the property linear order preservation if it always results in a ranking such that an alternative directly preferred to another does not have a lower rank. We study whether two procedures, the Eigenvector Method and the Logarithmic Least Squares Method meet this axiom. Both weighting methods break linear order preservation, moreover, the ranking according to the Eigenvector Method depends on the incomplete pairwise comparison representation chosen.

Between plurality and proportionality: an analysis of vote transfer systems

The paper considers a general model of electoral systems combining district-based elections with a compensatory mechanism in order to implement any outcome between strictly majoritarian and purely proportional seat allocation. It contains vote transfer and allows for the application of three different correction formulas. Analysis in a two-party system shows that a trade-off exists for the dominant party between the expected seat share and the chance of obtaining majority. Vote transfer rules are also investigated by focusing on the possibility of manipulation. The model is applied to the 2014 Hungarian parliamentary election. Hypothetical results reveal that the vote transfer rule cannot be evaluated in itself, only together with the share of constituency seats. With an appropriate choice of the latter, the three mechanisms can be made functionally equivalent.

Egységgyöktesztek alkalmazása szezonalitást is tartalmazó idősorok esetében energiatőzsde-adatok példáján

A szezonalitás megfelelő kezelésének kérdése hosszú és rövid távú idősorok esetén egyaránt érdekes feladat. A döntés a determinisztikus vagy sztochasztikus modellezést, illetve annak következményeit illetően hasonló relevanciájúak, mint a determinisztikus és sztochasztikus trend közötti különbségtétel. A szerző tanulmányában ismerteti, hogy milyen módon lehetséges a sztochasztikus trend és szezonalitás tesztelése abban az esetben, amikor azok egymástól nem függetlenek. Az eredményeket európai energiatőzsdék (villamos energia és földgáz) day-ahead (spot) piaci kereskedési adatain mutatja be.

Young's axiomatization of the Shapley value - a new proof

We give a new proof of Young's characterization of the Shapley value. Moreover, as applications of the new proof, we show that Young's axiomatization of the Shapley value is valid on various well-known subclasses of TU games.

Distance-based accessibility indices

The paper attempts to develop a suitable accessibility index for networks where each link has a value such that a smaller number is preferred like distance, cost, or travel time. A measure called distance sum is characterized by three independent properties: anonymity, an appropriately chosen independence axiom, and dominance preservation, which requires that a node not far to any other is at least as accessible. We argue for the need of eliminating the independence property in certain applications. Therefore generalized distance sum, a family of accessibility indices, will be suggested. It is linear, considers the accessibility of vertices besides their distances and depends on a parameter in order to control its deviation from distance sum. Generalized distance sum is anonymous and satisfies dominance preservation if its parameter meets a sufficient condition. Two detailed examples demonstrate its ability to reflect the vulnerability of accessibility to link disruptions.

Assignment Games with Externalities

We examine assignment games, wherematched pairs of firms and workers create some monetary value to distribute among themselves and the agents aim to maximize their payoff. In the majority of this literature, externalities - in the sense that a pair’s value depends on the pairing of the others - have been neglected. However, inmost applications a firm’s success depends on, say, the success of its rivals and suppliers. Thus, it is natural to ask how the classical results on assignment games are affected by the introduction of externalities? The answer is – dramatically. We find that (i) a problem may have no stable outcome, (ii) stable outcomes can be inefficient (not maximize total value), (iii) efficient outcomes can be unstable, and (iv) the set of stable outcomes may not form a lattice. We show that stable outcomes always exist if agents are "pessimistic." This is a knife-edge result: there are problems in which the slightest optimism by a single pair erases all stable outcomes.

Some fairytales about risk management

When I started writing this paper, I thought I would only be writing about the parallel between the mathematical theory of inventory and production – as a familiar model of operations research – and liquidity management. And then during the writing process, predictably enough I must say, the scandals surrounding the Buda-Cash and Quaestor brokerages erupted. Likewise in this period, the debate about foreign currency lending gained fresh impetus; about who made which mistakes when, or whether there was anyone who didn’t make mistakes. The most surprising twist revealed in the Buda-Cash and Quaestor cases – beyond alleged losses running into several hundreds of billions of forints – was that all this could be accumulated in 15 years of selfless effort. And even if this information proves to be comment born of initial over-excitement, it still demands an explanation one way or another. If it’s true, then how can this be? And if it isn’t, then what made it appear as if this is what happened? The questions and contradictions are obvious. But the main questions are these: What do risk managers actually do? What do we pay them for? And how far can we trust them?

Esti mesék a kockázatról

Amikor ezt a dolgozatot elkezdtem, még arra gondoltam, hogy csak az operációkutatás közismert modellje, a raktárkészletezés matematikai elmélete és a likviditáskezelés közötti párhuzamról fogok írni. A dolgozat írása közben törtek ki a Buda-Cash és a Quaestor körüli, azt kell mondanom, ügyeletes botrányok. Ugyancsak ebben az időszakban kapott újabb lendületet a devizahitelezéssel kapcsolatos vita: ki mikor mit hibázott, illetve volt-e bárki, aki ne hibázott volna? A Buda-Cash- és a Quaestor-ügyben felmerülő, legmeglepőbb fordulat az állítólagos több százmilliárd forint veszteségen túl az volt, hogy mindezt tizenöt év áldozatos munkájával sikerült összehozni. Még ha ezek az információk első felindulásból született megjegyzések, akkor is magyarázatra szorulnak. Így vagy úgy. Ha igaz, akkor hogyan képzelhető ez el, ha nem igaz, akkor miből ered az a látszat, hogy ez így történt? A felmerülő kérdések és az ellentmondások nyilvánvalóak. A legfőbb kérdés azonban a következő: mit is csinálnak a kockázatkezelők? Miért is fizetjük őket? Mennyire bízhatunk bennük?

Összefüggő biztosítási kockázatok modellezése

A biztosítási és pénzügyi gyakorlatban előforduló kockázatok jó része nem tekinthető egymástól függetlennek, hagyományosan legtöbbször mégis megelégedtek az alkalmazók a függetlenség feltételezésével vagy jobb esetben a lineáris korrelációs együttható kiszámításával, a matematikai kezelhetőség kedvéért. Az elmúlt másfél évtized azonban paradigmaváltással járt e téren: akadémiai körökben csakúgy, mint az aktuáriusok, kockázatkezelők könyvespolcain is megjelentek és gyorsan teret hódítottak maguknak a kopulákról szóló cikkek és tanulmányok, így a kopulák mára az összefüggő kockázatok modellezésének standard eszközévé váltak. Jelen tanulmány a kopulák biztosítási alkalmazási lehetőségeit tekinti át.

Improved stochastic optimization of railway timetables

We present a general model to find the best allocation of a limited amount of supplements (extra minutes added to a timetable in order to reduce delays) on a set of interfering railway lines. By the best allocation, we mean the solution under which the weighted sum of expected delays is minimal. Our aim is to finely adjust an already existing and well-functioning timetable. We model this inherently stochastic optimization problem by using two-stage recourse models from stochastic programming, building upon earlier research from the literature. We present an improved formulation, allowing for an efficient solution using a standard algorithm for recourse models. We show that our model may be solved using any of the following theoretical frameworks: linear programming, stochastic programming and convex non-linear programming, and present a comparison of these approaches based on a real-life case study. Finally, we introduce stochastic dependency into the model, and present a statistical technique to estimate the model parameters from empirical data.

An asymptotic test for the Conditional Value-at-Risk

Conditional Value-at-Risk (equivalent to the Expected Shortfall, Tail Value-at-Risk and Tail Conditional Expectation in the case of continuous probability distributions) is an increasingly popular risk measure in the fields of actuarial science, banking and finance, and arguably a more suitable alternative to the currently widespread Value-at-Risk. In my paper, I present a brief literature survey, and propose a statistical test of the location of the CVaR, which may be applied by practising actuaries to test whether CVaR-based capital levels are in line with observed data. Finally, I conclude with numerical experiments and some questions for future research.