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# Documents  93E20 | enregistrements trouvés : 51

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## Approximation and calibration of laws of solutions to stochastic differential equations Bion-Nadal, Jocelyne | CIRM H

Post-edited

Research talks;Probability and Statistics

In many situations where stochastic modeling is used, one desires to choose the coefficients of a stochastic differential equation which represents the reality as simply as possible. For example one desires to approximate a diffusion model
with high complexity coefficients by a model within a class of simple diffusion models. To achieve this goal, we introduce a new Wasserstein type distance on the set of laws of solutions to d-dimensional stochastic differential equations.
This new distance $\widetilde{W}^{2}$ is defined similarly to the classical Wasserstein distance $\widetilde{W}^{2}$ but the set of couplings is restricted to the set of laws of solutions of 2$d$-dimensional stochastic differential equations. We prove that this new distance $\widetilde{W}^{2}$ metrizes the weak topology. Furthermore this distance $\widetilde{W}^{2}$ is characterized in terms of a stochastic control problem. In the case d = 1 we can construct an explicit solution. The multi-dimensional case, is more tricky and classical results do not apply to solve the HJB equation because of the degeneracy of the differential operator. Nevertheless, we prove that this HJB equation admits a regular solution.
In many situations where stochastic modeling is used, one desires to choose the coefficients of a stochastic differential equation which represents the reality as simply as possible. For example one desires to approximate a diffusion model
with high complexity coefficients by a model within a class of simple diffusion models. To achieve this goal, we introduce a new Wasserstein type distance on the set of laws of solutions to d-dimensional ...

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## Graphon mean field games and the GMFG equations Caines, Peter E. | CIRM H

Post-edited

Research talks;Combinatorics;Control Theory and Optimization;Partial Differential Equations;Probability and Statistics

Very large networks linking dynamical agents are now ubiquitous and there is significant interest in their analysis, design and control. The emergence of the graphon theory of large networks and their infinite limits has recently enabled the formulation of a theory of the centralized control of dynamical systems distributed on asymptotically infinite networks [Gao and Caines, IEEE CDC 2017, 2018]. Furthermore, the study of the decentralized control of such systems has been initiated in [Caines and Huang, IEEE CDC 2018] where Graphon Mean Field Games (GMFG) and the GMFG equations are formulated for the analysis of non-cooperative dynamical games on unbounded networks. In this talk the GMFG framework will be first be presented followed by the basic existence and uniqueness results for the GMFG equations, together with an epsilon-Nash theorem relating the infinite population equilibria on infinite networks to that of finite population equilibria on finite networks. Very large networks linking dynamical agents are now ubiquitous and there is significant interest in their analysis, design and control. The emergence of the graphon theory of large networks and their infinite limits has recently enabled the formulation of a theory of the centralized control of dynamical systems distributed on asymptotically infinite networks [Gao and Caines, IEEE CDC 2017, 2018]. Furthermore, the study of the decentralized ...

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## Filtering and control of random processesproceedings of the e.n.s.t.,c.n.e.t.,colloquium held in paris,france,feb. 23-24,1983 Korezlioglu, H. ; Mazziotto, G. ; Szpirglas, J. | Springer-Verlag 1984

Congrès

ISBN 978-0-387-13270-9

Lecture notes in control and information sciences , 0061

Localisation : Colloque 1er étage (PARI)

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## Singular Perturbations in Systems and Control Ardema, M.D. | CISM;Springer-Verlag 1983

Congrès

- 337 p.
ISBN 978-3-211-81751-3

C.I.S.M. course and lectures , 0280

Localisation : Colloque 1er étage (UDIN)

chaine de Markov perturbée # controle en retour stable # controle optimal # controle optimal non linéaire # controle par retour composite # couche de transition # couche interne # diffusion # # découplage rapide/ lent # estimation gaussienne quadratique linéaire # perturbation régulière # perturbation singulière # problème aux valeurs propres non linéaire perturbé singulièr # solution limitante angulaire # synthèse de controle en retour à haut gain # système non linéaire # système à paramètres distribués chaine de Markov perturbée # controle en retour stable # controle optimal # controle optimal non linéaire # controle par retour composite # couche de transition # couche interne # diffusion # # découplage rapide/ lent # estimation gaussienne quadratique linéaire # perturbation régulière # perturbation singulière # problème aux valeurs propres non linéaire perturbé singulièr # solution limitante angulaire # synthèse de controle en retour à haut ...

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## Mathematical financeproceedings of the period of a workshop of the 1992-93 IMA program on control theory Davis, Mark H. A. ; Duffie, Darrell ; Fleming, Wendell H. ; Shreve, Steven E. | Springer 1995

Congrès

ISBN 978-0-387-94439-5

The IMA volumes in mathematics and its applications , 0065

Localisation : Colloque 1er étage (MINN)

arbitrage et lunch libre # compétition imparfaite # conmmerce continu # contrainte descendue # contrôle stochastique sensible du risque # coût de transaction # droit de transaction # entretien # fixation du prix de l'actif # information asymétrique # mathématique de la finance # mise à prix de l'actif du capital # modèle d'investissement optimal # modèle de marché financier général # optimisation de portefeuille # option américaine # portefeuille contraint # prime de liquidité # problème d'arrêt optimal pour une option de mise américaine # valuation de réclamation contingente arbitrage et lunch libre # compétition imparfaite # conmmerce continu # contrainte descendue # contrôle stochastique sensible du risque # coût de transaction # droit de transaction # entretien # fixation du prix de l'actif # information asymétrique # mathématique de la finance # mise à prix de l'actif du capital # modèle d'investissement optimal # modèle de marché financier général # optimisation de portefeuille # option américaine # po...

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## Introduction to mathematical finance :American Mathematical Society short course#Jan. 6-7 Heath, David C. ; Swindle, Glen | American Mathematical Society 1999

Congrès

- 167 p.
ISBN 978-0-8218-0751-4

Proceedings of symposia in applied mathematics , 0057

Localisation : Collection 1er étage

mathématiques de l'économie # mathématiques appliquées # investissement # modèle mathématique # gestion de portefeuille # finance # analyse stochastique # théorie mathématique du risque # coût # prix # contrôle optimal stochastique

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## Stochastic analysis and related topics VIII :8th gazimagusa (Famagusta) (North Cyprus) workshop on...#Sept. 18-27 Capar, Ulug ; Ustünel, Ali Süleyman | Birkhäuser Verlag 2003

Congrès

- 205 p.
ISBN 978-3-7643-6998-9

Progress in probability , 0053

Localisation : Colloque 1er étage (SILI)

analyse stochastique # processus stochastique # contrôle stochastique optimal # application à la biologie # théorie des jeux # jeu stochatique # processus tangent # mesure de Levy # système linéaire stochaqtique # processus de Levy

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## Mathematics of finance :proceedings of an AMS-IMS-SIAM joint summer research conference on ...#June 22-26 Yin, G. George ; Zhang, Qing | American Mathematical Society 2004

Congrès

- 398 p.
ISBN 978-0-8218-3412-1

Contemporary mathematics , 0351

Localisation : Collection 1er étage

finance # mathématiques financières # équation différentielle stochastique # analyse stochastique # application # théorie de l'utilité # modèle de marché # processus gaussien # chaîne de Markov # processus de diffusion # contrôle stochastique optimal

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## Stochastic methods in finance :lectures given at the C.I.M.E.-E.M.S. summer school held in Bressanone#July 6-12 Back, K. ; Bielecki, T. R. ; Hippel, Arthur ; Peng, S. ; Schachermayer, W. ; Frittelli, Marco ; Runggaldier, Wolfgang | Springer 2004

Congrès

- 306 p.
ISBN 978-3-540-22953-7

Lecture notes in mathematics , 1856

Localisation : Collection 1er étage

contrôle stochastique # équation différentielle stochastique retrograde # finance # marché financier # risque # banqueroute

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## Seminar on stochastic analysis, random fields and applications V#May 30 - June 3 Dozzi, Marco ; Russo, Francesco ; Dalang, Robert C. | Springer 2008

Congrès

- 519 p.
ISBN 978-3-7643-8457-9

Progress in probability , 0059

Localisation : Colloque 1er étage (ASCO)

EDP stochastique # système dynamique # analyse fonctionnelle infinie dimensionnelle # méthode probabiliste dans la théorie des espaces de Banach # approximation # ingénierie financière

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## Variational and optimal control problems on unbounded domains.A workshop in memory of Arie LeizarowitzHaifa # January 9-12, 2012 Wolansky, Gershon ; Zaslavski, Alexander J. | American Mathematical Society;Bar-Ilan University 2014

Congrès

- xvi; 247 p.
ISBN 978-1-4704-1077-3

Contemporary mathematics , 0619

Localisation : Collection 1er étage

équations différentielles # optimisation mathématique # solution optimale # stabilité des systèmes # processus de diffusion

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## Mean field games with major and minor players Carmona, René | CIRM H

Multi angle

Research School;Control Theory and Optimization;Probability and Statistics

We introduce a new strategy for the solution of Mean Field Games in the presence of major and minor players. This approach is based on a formulation of the fixed point step in spaces of controls. We use it to highlight the differences between open and closed loop problems. We illustrate the implementation of this approach for linear quadratic and finite state space games, and we provide numerical results motivated by applications in biology and cyber-security. We introduce a new strategy for the solution of Mean Field Games in the presence of major and minor players. This approach is based on a formulation of the fixed point step in spaces of controls. We use it to highlight the differences between open and closed loop problems. We illustrate the implementation of this approach for linear quadratic and finite state space games, and we provide numerical results motivated by applications in biology and ...

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## Capacity expansion games with application to competition in power generation investments Aïd, René | CIRM H

Multi angle

Research School;Control Theory and Optimization;Mathematics in Science and Technology

We consider competitive capacity investment for a duopoly of two distinct producers. The producers are exposed to stochastically fluctuating costs and interact through aggregate supply. Capacity expansion is irreversible and modeled in terms of timing strategies characterized through threshold rules. Because the impact of changing costs on the producers is asymmetric, we are led to a nonzero-sum timing game describing the transitions among the discrete investment stages. Working in a continuous-time diffusion framework, we characterize and analyze the resulting Nash equilibrium and game values. Our analysis quantifies the dynamic competition effects and yields insight into dynamic preemption and over-investment in a general asymmetric setting. A case-study considering the impact of fluctuating emission costs on power producers investing in nuclear and coal-fired plants is also presented. We consider competitive capacity investment for a duopoly of two distinct producers. The producers are exposed to stochastically fluctuating costs and interact through aggregate supply. Capacity expansion is irreversible and modeled in terms of timing strategies characterized through threshold rules. Because the impact of changing costs on the producers is asymmetric, we are led to a nonzero-sum timing game describing the transitions among the ...

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## Some asymptotic results about American options and volativity De Marco, Stefano | CIRM H

Multi angle

Research talks;Control Theory and Optimization;Numerical Analysis and Scientific Computing

The valuation of American options (a widespread type of financial contract) requires the numerical solution of an optimal stopping problem. Numerical methods for such problems have been widely investigated. Monte-Carlo methods are based on the implementation of dynamic programming principles coupled with regression techniques. In lower dimension, one can choose to tackle the related free boundary PDE with deterministic schemes.
Pricing of American options will therefore be inevitably heavier than the one of European options, which only requires the computation of a (linear) expectation. The calibration (fitting) of a stochastic model to market quotes for American options is therefore an a priori demanding task. Yet, often this cannot be avoided: on exchange markets one is typically provided only with market quotes for American options on single stocks (as opposed to large stock indexes - e.g. S&P500 - for which large amounts of liquid European options are typically available).
In this talk, we show how one can derive (approximate, but accurate enough) explicit formulas - therefore replacing other numerical methods, at least in a low-dimensional case - based on asymptotic calculus for diffusions.
More precisely: based on a suitable representation of the PDE free boundary, we derive an approximation of this boundary close to final time that refines the expansions known so far in the literature. Via the early premium formula, this allows to derive semi-closed expressions for the price of the American put/call. The final product is a calibration recipe of a Dupire's local volatility to American option data.
Based on joint work with Pierre Henry-Labordère.
The valuation of American options (a widespread type of financial contract) requires the numerical solution of an optimal stopping problem. Numerical methods for such problems have been widely investigated. Monte-Carlo methods are based on the implementation of dynamic programming principles coupled with regression techniques. In lower dimension, one can choose to tackle the related free boundary PDE with deterministic schemes.
Pricing of ...

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## The computation and theory of optimal control Dyer, Peter ; Mcreynolds, Stephen R. | Academic Press 1970

Ouvrage

- 242 p.
ISBN 978-0-12-226250-0

Mathematics in science and engineering , 0065

Localisation : Ouvrage RdC (DYER)

analyse numérique # général # contrôle optimal

93E20

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## Oscillation theory of optimal processes Smirnov, George M. ; Silverman, Robert H. | John Wiley And Sons 1984

Ouvrage

- 154 p.
ISBN 978-0-471-89399-8

Localisation : Ouvrage RdC (SMIR)

calcul des variations et de la commande optimale # optimisation

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## Theorie probabiliste du controle des diffusions Bismut, Jean-Michel | American Mathematical Society 1976

Ouvrage

ISBN 978-0-8218-1867-1

Memoirs of the american mathematical society , 0167

Localisation : Collection 1er étage

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## Characterization of optimal strategies in dynamic games Groenewegen, L. P. J. | Mathematisch Centrum 1985

Ouvrage

- 110 p.
ISBN 978-90-6196-156-7

Mathematical centre tracts , 0090

Localisation : Collection 1er étage

controle optimal # controle stochastique # théorie des jeux # théorie de la distribution invariante controlée

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## Deterministic and stochastic optimal control Fleming, Wendell H. ; Rishel, Raymond W. | Springer-Verlag 1975

Ouvrage

- 222 p.
ISBN 978-3-540-90155-6

Applications of mathematics , 0001

Localisation : Ouvrage RdC (FLEM)

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## Stochastic games with finite state and action spaces Vrieze, O. J. | Centre For Mathematics And Computer Science 1987

Ouvrage

- 221 p.
ISBN 978-90-6196-313-4

CWI tract , 0033

Localisation : Collection 1er étage

controle stochastique optimal # jeux a plusieurs pas # théorie des jeux stochastique

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