Nonlinear dynamics in psychology.
Nonlinear elliptic systems in stochastic game theory.
Nonlinear Fokker-Planck equation in the model of asset returns.
Nonlinear variational inequalities and the existence of equilibrium in economies with a Riesz space of commodities
Nonlinearity in social dynamics -- order versus chaos.
Nonparametric statistical methods and the pricing of derivative securities.
Nonsmooth analysis approach to Isaac's equation.
Nonstandard Finite Difference Schemes with Application to Finance: Option Pricing
2000 Mathematics Subject Classification: 65M06, 65M12.The paper is devoted to pricing options characterized by discontinuities in the initial conditions of the respective Black-Scholes partial differential equation. Finite difference schemes are examined to highlight how discontinuities can generate numerical drawbacks such as spurious oscillations. We analyze the drawbacks of the Crank-Nicolson scheme that is most frequently used numerical method in Finance because of its second order accuracy....
Non-terminating stochastic ratio game
Nonzero-sum semi-Markov games with countable state spaces
We consider nonzero-sum semi-Markov games with a countable state space and compact metric action spaces. We assume that the payoff, mean holding time and transition probability functions are continuous on the action spaces. The main results concern the existence of Nash equilibria for nonzero-sum discounted semi-Markov games and a class of ergodic semi-Markov games with the expected average payoff criterion.
Normalisation Affects The Results of MADM Methods
Normality assumption for the log-return of the stock prices
The normality of the log-returns for the price of the stocks is one of the most important assumptions in mathematical finance. Usually is assumed that the price dynamics of the stocks are driven by geometric Brownian motion and, in that case, the log-return of the prices are independent and normally distributed. For instance, for the Black-Scholes model and for the Black-Scholes pricing formula [4] this is one of the main assumptions. In this paper we will investigate if this assumption is verified...
Normalization of general coalition-games
Note On The Game Colouring Number Of Powers Of Graphs
We generalize the methods of Esperet and Zhu [6] providing an upper bound for the game colouring number of squares of graphs to obtain upper bounds for the game colouring number of m-th powers of graphs, m ≥ 3, which rely on the maximum degree and the game colouring number of the underlying graph. Furthermore, we improve these bounds in case the underlying graph is a forest.
Note sur la théorie mathématique des assurances contre l'invalidité
Note sur le calcul de la probabilité des paradoxes du vote
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.
Note sur un problème fondamental de la théorie de l'équilibre économique
Note sur une caractérisation des graphes dont le degré de déséquilibre est maximal
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.
Note: The Smallest Nonevasive Graph Property
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...
Notes on free lunch in the limit and pricing by conjugate duality theory
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...