De nombreux travaux se sont efforcés au cours des années récentes de calculer la probabilité des paradoxes ou des difficultés que la théorie des choix collectifs a mis en évidence. On passe en revue dans cette note les principaux modèles de calcul utilisés dans ces travaux. On applique en outre l'un des modèles présentés au calcul de la probabilité de quelques paradoxes bien connus de la théorie du vote.
Dans cette note on démontre la conjecture d'Abelson et Rosenberg sur le degré maximal de déséquilibre d'un graphe à n sommets et on caractérise ces graphes maximaux.
A property of n-vertex graphs is called evasive if every algorithm testing this property by asking questions of the form “is there an edge between vertices u and v” requires, in the worst case, to ask about all pairs of vertices. Most “natural” graph properties are either evasive or conjectured to be such, and of the few examples of nontrivial nonevasive properties scattered in the literature the smallest one has n = 6. We exhibit a nontrivial, nonevasive property of 5-vertex graphs and show that...
King and Korf [KingKorf01] introduced, in the framework of a discrete- time dynamic market model on a general probability space, a new concept of arbitrage called free lunch in the limit which is slightly weaker than the common free lunch. The definition was motivated by the attempt at proposing the pricing theory based on the theory of conjugate duality in optimization. We show that this concept of arbitrage fails to have a basic property of other common concepts used in pricing theory – it depends...
This paper deals with the construction of numerical solution of the Black-Scholes (B-S) type equation modeling option pricing with variable yield discrete dividend payment at time . Firstly the shifted delta generalized function appearing in the B-S equation is approximated by an appropriate sequence of nice ordinary functions. Then a semidiscretization technique applied on the underlying asset is used to construct a numerical solution. The limit of this numerical solution is independent of the...
We consider a model for the control of a linear network flow system with unknown but bounded demand and polytopic bounds on controlled flows. We are interested in the problem of finding a suitable objective function that makes robust optimal the policy represented by the so-called linear saturated feedback control. We regard the problem as a suitable differential game with switching cost and study it in the framework of the viscosity solutions theory for Bellman and Isaacs equations.
We consider a model for the control of a linear network flow system with unknown but bounded demand and polytopic bounds on controlled flows. We are interested in the problem of finding a suitable objective function that makes robust optimal the policy represented by the so-called linear saturated feedback control. We regard the problem as a suitable differential game with switching cost and study it in the framework of the viscosity solutions theory for Bellman and Isaacs equations.