Hamiltonian trajectories and saddle points in mathematical economics
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R. Rockafellar (2009)
Control and Cybernetics
Hong Qiu, Jiongmin Yong (2013)
ESAIM: Control, Optimisation and Calculus of Variations
A two-person zero-sum differential game with unbounded controls is considered. Under proper coercivity conditions, the upper and lower value functions are characterized as the unique viscosity solutions to the corresponding upper and lower Hamilton–Jacobi–Isaacs equations, respectively. Consequently, when the Isaacs’ condition is satisfied, the upper and lower value functions coincide, leading to the existence of the value function of the differential game. Due to the unboundedness of the controls,...
César U. S. Solis, Julio B. Clempner, Alexander S. Poznyak (2019)
Kybernetika
This paper presents a new model for computing optimal randomized security policies in non-cooperative Stackelberg Security Games (SSGs) for multiple players. Our framework rests upon the extraproximal method and its extension to Markov chains, within which we explicitly compute the unique Stackelberg/Nash equilibrium of the game by employing the Lagrange method and introducing the Tikhonov regularization method. We also consider a game-theory realization of the problem that involves defenders and...
Jean-Pierre Aubin, Halina Frankowska (1985)
Annales de l'I.H.P. Analyse non linéaire
Youssef El-Khatib, Nicolas Privault (2003)
Applicationes Mathematicae
This paper aims at a unified treatment of hedging in market models driven by martingales with deterministic bracket , including Brownian motion and the Poisson process as particular cases. Replicating hedging strategies for European, Asian and Lookback options are explicitly computed using either the Clark-Ocone formula or an extension of the delta hedging method, depending on which is most appropriate.
Marek Andrzej Kociński (2010)
Applicationes Mathematicae
Hedging of the European option in a discrete time financial market with proportional transaction costs is considered. It is shown that for a certain class of options the set of portfolios which allow the seller to pay the claim of the buyer in quite a general discrete time market model is the same as the set of such portfolios under the assumption that the stock price movement is given by a suitable CRR model.
Martin Loebl (1988)
Commentationes Mathematicae Universitatis Carolinae
Martin Loebl (1985)
Commentationes Mathematicae Universitatis Carolinae
Jiří Matoušek, Martin Loebl (1991)
Commentationes Mathematicae Universitatis Carolinae
L. Kirby and J. Paris introduced the Hercules and Hydra game on rooted trees as a natural example of an undecidable statement in Peano Arithmetic. One can show that Hercules has a “short” strategy (he wins in a primitively recursive number of moves) and also a “long” strategy (the finiteness of the game cannot be proved in Peano Arithmetic). We investigate the conflict of the “short” and “long” intentions (a problem suggested by J. Nešetřil). After each move of Hercules (trying to kill Hydra fast)...
Chang, Mou-Hsiung (2007)
Journal of Applied Mathematics and Stochastic Analysis
Chang, Mou-Hsiung (2007)
Journal of Applied Mathematics and Stochastic Analysis
Westerhoff, Frank H. (2005)
Discrete Dynamics in Nature and Society
Jaroslav Doležal (1976)
Kybernetika
Alain Guénoche (1993)
Mathématiques et Sciences Humaines
En classification conceptuelle d'un ensemble d'objets décrits dans un espace de représentation, on cherche à construire une partition des objets en classes disjointes et simultanément une caractérisation de chaque classe dans les termes de l'espace de représentation. Dans le cas, très courant, où cet espace est engendré par des données binaires nous présentons deux algorithmes, dérivés des méthodes ascendantes et descendantes en classification qui maximisent localement un indice de cohésion des...
Sedlačíková, Blanka (2012)
Cai, Jianping (2005)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Anuradha, V., Jain, Chinmay, Snoeyink, Jack, Szabó, Tibor (2008)
The Electronic Journal of Combinatorics [electronic only]
Boštan Brešar, Paul Dorbec, Sandi Klavžar, Gašpar Košmrlj (2017)
Discussiones Mathematicae Graph Theory
The domination game is played on an arbitrary graph G by two players, Dominator and Staller. The game is called Game 1 when Dominator starts it, and Game 2 otherwise. In this paper bluff graphs are introduced as the graphs in which every vertex is an optimal start vertex in Game 1 as well as in Game 2. It is proved that every minus graph (a graph in which Game 2 finishes faster than Game 1) is a bluff graph. A non-trivial infinite family of minus (and hence bluff) graphs is established. minus graphs...
Jürgen W. Sander (2007)
Mathematica Slovaca
Lassana Samassi, Rabah Tahraoui (2008)
ESAIM: Control, Optimisation and Calculus of Variations
The aim of this paper is to give a general idea to state optimality conditions of control problems in the following form: , (1) where is a set of admissible controls and is the solution of the following equation: ; . (2). The results are nonlocal and new.
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