ESTIMATION A PRIORI DES ERREURS DANS LA RESOLUTION NUMERIQUE D'EQUATIONS DIFFERENTIELLES STOCHASTIQUES PDF Download
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Author: Pierre-Yves Glorennec
Publisher:
ISBN:
Category :
Languages : fr
Pages : 144
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Book Description
GENERALITES. DISCRETISATION A INTERVALLES CONSTANTS, CAS "AVEC MEMOIRE". DISCRETISATION ADAPTEE. DISCRETISATION AU 2EME ORDRE. CONVERGENCE EN LOI. ETUDE NUMERIQUE PAR DES METHODES DE SIMULATION
Author: Pierre-Yves Glorennec
Publisher:
ISBN:
Category :
Languages : fr
Pages : 144
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Book Description
GENERALITES. DISCRETISATION A INTERVALLES CONSTANTS, CAS "AVEC MEMOIRE". DISCRETISATION ADAPTEE. DISCRETISATION AU 2EME ORDRE. CONVERGENCE EN LOI. ETUDE NUMERIQUE PAR DES METHODES DE SIMULATION
Author: Peter E. Kloeden
Publisher: Springer Science & Business Media
ISBN: 3662126168
Category : Mathematics
Languages : en
Pages : 666
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Book Description
The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations. From the reviews: "The authors draw upon their own research and experiences in obviously many disciplines... considerable time has obviously been spent writing this in the simplest language possible." --ZAMP
Author: Eckhard Platen
Publisher: Springer Science & Business Media
ISBN: 364213694X
Category : Mathematics
Languages : en
Pages : 868
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Book Description
In financial and actuarial modeling and other areas of application, stochastic differential equations with jumps have been employed to describe the dynamics of various state variables. The numerical solution of such equations is more complex than that of those only driven by Wiener processes, described in Kloeden & Platen: Numerical Solution of Stochastic Differential Equations (1992). The present monograph builds on the above-mentioned work and provides an introduction to stochastic differential equations with jumps, in both theory and application, emphasizing the numerical methods needed to solve such equations. It presents many new results on higher-order methods for scenario and Monte Carlo simulation, including implicit, predictor corrector, extrapolation, Markov chain and variance reduction methods, stressing the importance of their numerical stability. Furthermore, it includes chapters on exact simulation, estimation and filtering. Besides serving as a basic text on quantitative methods, it offers ready access to a large number of potential research problems in an area that is widely applicable and rapidly expanding. Finance is chosen as the area of application because much of the recent research on stochastic numerical methods has been driven by challenges in quantitative finance. Moreover, the volume introduces readers to the modern benchmark approach that provides a general framework for modeling in finance and insurance beyond the standard risk-neutral approach. It requires undergraduate background in mathematical or quantitative methods, is accessible to a broad readership, including those who are only seeking numerical recipes, and includes exercises that help the reader develop a deeper understanding of the underlying mathematics.
Author: D. Kannan
Publisher: CRC Press
ISBN: 9780824706609
Category : Mathematics
Languages : en
Pages : 800
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Book Description
An introduction to general theories of stochastic processes and modern martingale theory. The volume focuses on consistency, stability and contractivity under geometric invariance in numerical analysis, and discusses problems related to implementation, simulation, variable step size algorithms, and random number generation.
Author: David Chevance
Publisher:
ISBN:
Category :
Languages : fr
Pages : 134
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Book Description
LA PREMIERE PARTIE DE CETTE THESE A POUR OBJET LA CONSTRUCTION D'UN ALGORITHME PROBABILISTE POUR RESOUDRE NUMERIQUEMENT DES EQUATIONS DIFFERENTIELLES STOCHASTIQUES RETROGRADES (EDSR) DANS LE CAS MARKOVIEN, OU L'EQUATION EST ASSOCIEE A UN PROCESSUS FORWARD SOLUTION D'UNE EDS. NOUS DECRIVONS UN PREMIER ALGORITHME QUI REPOSE SUR UNE DOUBLE DISCRETISATION DE L'EQUATION, EN TEMPS ET EN ESPACE, ET UTILISE DES SIMULATIONS DE TRAJECTOIRES DU PROCESSUS FORWARD. LA DISCRETISATION EN TEMPS EST UNE EXTENSION DU SCHEMA D'EULER POUR LES EDS, OU L'ON A REMPLACE LE MOUVEMENT BROWNIEN PAR UNE MARCHE ALEATOIRE. ON INTRODUIT ENSUITE UNE APPROXIMATION SUPPLEMENTAIRE EN PROJETANT A CHAQUE INSTANT DE DISCRETISATION LE PROCESSUS FORWARD SUR L'ENSEMBLE DES TRAJECTOIRES SIMULEES. ON EVITE AINSI UNE COMPLEXITE ALGORITHMIQUE QUI SERAIT EXPONENTIELLE. NOUS MONTRONS UNE VITESSE DE CONVERGENCE POUR CET ALGORITHME DANS LE CADRE DE LA DIMENSION 1. NOUS PRESENTONS AUSSI UNE VARIANTE DE CE ALGORITHME, ADAPTEE A DES EDSR DONT LES PARAMETRES SONT MOINS REGULIERS, EN REMPLACANT NOTAMMENT LE SCHEMA D'EULER DANS LA DISCRETISATION DU PROCESSUS FORWARD PAR LE SCHEMA DE MILSHTEIN. CELA NOUS PERMET ENSUITE D'ECRIRE UN ALGORITHME DE DISCRETISATION D'EDSR REFLECHIES. DANS UNE SECONDE PARTIE, NOUS ANALYSONS L'APPROXIMATION DE MACMILLAN, ET BARONE-ADESI ET WHALEY, UTILISEE EN FINANCE POUR ESTIMER LE PRIX D'UNE OPTION AMERICAINE. EN ECRIVANT LE PRIX DE L'OPTION AMERICAINE COMME LA SOLUTION D'UNE CERTAINE EQUATION DIFFERENTIELLE STOCHASTIQUE RETROGRADE REFLECHIE, NOUS OBTENONS UNE BORNE GENERALE POUR L'ERREUR DE L'APPROXIMATION ET NOUS MONTRONS QUE L'APPROXIMATION CONVERGE VERS LE PRIX EXACT QUAND LA VOLATILITE DU SOUS-JACENT TEND VERS ZERO. NOUS PROPOSONS ENSUITE UNE DEUXIEME DEMONSTRATION, PLUS ELEMENTAIRE, DE CE RESULTAT ASYMPTOTIQUE, EN FAISANT INTERVENIR LE PRIX D'UN PUT PERPETUEL.
Author:
Publisher:
ISBN:
Category : Mathematical statistics
Languages : en
Pages : 380
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Book Description
Author: Wilfried Grossmann
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 340
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Book Description
Proceedings of the 4th Pannonian Symposium on Mathematical Statistics, Bad Tatzmannsdorf, Austria, 4-10 September 1983, Volume B.
Author:
Publisher:
ISBN:
Category : Computer science
Languages : en
Pages : 438
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Author: Veronika Czellàr
Publisher:
ISBN:
Category :
Languages : fr
Pages : 64
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Book Description
Author: David Chevance
Publisher:
ISBN:
Category :
Languages : fr
Pages : 0
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