Représentation des solutions et contrôle d'équations différentielles stochastiques PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Représentation des solutions et contrôle d'équations différentielles stochastiques PDF full book. Access full book title Représentation des solutions et contrôle d'équations différentielles stochastiques by Claude Bernier. Download full books in PDF and EPUB format.
Author: Claude Bernier
Publisher:
ISBN:
Category :
Languages : fr
Pages :
Get Book Here
Book Description
Author: Claude Bernier
Publisher:
ISBN:
Category :
Languages : fr
Pages :
Get Book Here
Book Description
Author: Imre Csiszar
Publisher: Springer Science & Business Media
ISBN: 1461219809
Category : Mathematics
Languages : en
Pages : 358
Get Book Here
Book Description
Author: Sébastien Choukroun
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Get Book Here
Book Description
This thesis is divided into two parts that may be read independently. In the first part, three uses of backward stochastic differential equations are presented. The first chapter is an application of these equations to the mean-variance hedging problem in an incomplete market where multiple defaults can occur. We make a conditional density hypothesis on the default times. We then decompose the value function into a sequence of value functions between consecutive default times and we prove that each of them admits a quadratic form. Finally, we illustrate our results for a specific case where 2 default times follow independent exponential laws. The two following applications are extensions of the paper [75]. The second chapter is the study of a class of backward stochastic differential equations with nonpositive jumps and upper barrier. Existence and uniqueness of a minimal solution are proved by a double penalization approach under regularity assumptions on the obstacle. This method allows us to solve the case where the diffusion coefficient is degenerate. We also show, in a suitable markovian framework, the connection between our class of backward stochastic differential equations and fully nonlinear variational inequalities. In particular, our backward equation representation provides a Feynman-Kac type formula for PDEs associated to general zero-sum stochastic differential controller-and-stopper games, where control affects both drift and diffusion term, and the diffusion coefficient can be degenerate. Moreover, we state a dual game formula of this backward equation minimal solution, which gives a new representation for zero-sum stochastic differential controller-and-stopper games The third chapter is linked to model uncertainty, where the uncertainty affects both volatility and intensity. This kind of stochastic control problems is associated to a fully nonlinear integro-partial differential equation, such that the measure lambda(a,.) characterizing the jump part depends on a parameter a. We do not assume that the family lambda(a,.) is dominated. We obtain a nonlinear Feynman-Kac formula for the value function associated to these control problems. To this aim, we introduce a class of backward stochastic differential equations with jumps and partially constrained diffusive part. Here the case where the diffusion coefficient is degenerate is solved as well. In the second part, a conditional asset liability management problem is solved. We first derive the proper domain of definition of the value function associated to the problem by identifying the minimal wealth for which there exists an admissible investment strategy allowing to satisfy the constraint at maturity. This minimal wealth is identified as a solution of viscosity of a PDE. We also show that its Fenschel-Legendre transform is a solution of viscosity of another PDE, which allows to obtain a scheme with a faste convergence. We then identify the value function linked to the problem of interest as a solution of viscosity of a PDE on its domain of definition. Finally, we solve numerically the problem and we provide graphs of the minimal wealth, of the value function of the problem and of the optimal strategy.
Author: Gérard Ben Arous
Publisher:
ISBN:
Category :
Languages : fr
Pages : 144
Get Book Here
Book Description
EQUATIONS STOCHASTIQUES A COEFFICIENTS ANALYTIQUES. EQUATIONS STOCHASTIQUES INVARIANTES SUR UN GROUPE DE LIE. REPRESENTATION EXPLICITE DE LA SOLUTION DE CERTAINES EQUATIONS STOCHASTIQUES SUR UNE VARIETE
Author: Jin Ma
Publisher: Springer
ISBN: 3540488316
Category : Mathematics
Languages : en
Pages : 285
Get Book Here
Book Description
This volume is a survey/monograph on the recently developed theory of forward-backward stochastic differential equations (FBSDEs). Basic techniques such as the method of optimal control, the 'Four Step Scheme', and the method of continuation are presented in full. Related topics such as backward stochastic PDEs and many applications of FBSDEs are also discussed in detail. The volume is suitable for readers with basic knowledge of stochastic differential equations, and some exposure to the stochastic control theory and PDEs. It can be used for researchers and/or senior graduate students in the areas of probability, control theory, mathematical finance, and other related fields.
Author: Nizar Touzi
Publisher: Springer Science & Business Media
ISBN: 1461442850
Category : Mathematics
Languages : en
Pages : 219
Get Book Here
Book Description
This book collects some recent developments in stochastic control theory with applications to financial mathematics. We first address standard stochastic control problems from the viewpoint of the recently developed weak dynamic programming principle. A special emphasis is put on the regularity issues and, in particular, on the behavior of the value function near the boundary. We then provide a quick review of the main tools from viscosity solutions which allow to overcome all regularity problems. We next address the class of stochastic target problems which extends in a nontrivial way the standard stochastic control problems. Here the theory of viscosity solutions plays a crucial role in the derivation of the dynamic programming equation as the infinitesimal counterpart of the corresponding geometric dynamic programming equation. The various developments of this theory have been stimulated by applications in finance and by relevant connections with geometric flows. Namely, the second order extension was motivated by illiquidity modeling, and the controlled loss version was introduced following the problem of quantile hedging. The third part specializes to an overview of Backward stochastic differential equations, and their extensions to the quadratic case.
Author: Rong SITU
Publisher: Springer Science & Business Media
ISBN: 0387251758
Category : Technology & Engineering
Languages : en
Pages : 444
Get Book Here
Book Description
Stochastic differential equations (SDEs) are a powerful tool in science, mathematics, economics and finance. This book will help the reader to master the basic theory and learn some applications of SDEs. In particular, the reader will be provided with the backward SDE technique for use in research when considering financial problems in the market, and with the reflecting SDE technique to enable study of optimal stochastic population control problems. These two techniques are powerful and efficient, and can also be applied to research in many other problems in nature, science and elsewhere.
Author: Grigorij Kulinich
Publisher: Springer Nature
ISBN: 3030412911
Category : Mathematics
Languages : en
Pages : 240
Get Book Here
Book Description
This book is devoted to unstable solutions of stochastic differential equations (SDEs). Despite the huge interest in the theory of SDEs, this book is the first to present a systematic study of the instability and asymptotic behavior of the corresponding unstable stochastic systems. The limit theorems contained in the book are not merely of purely mathematical value; rather, they also have practical value. Instability or violations of stability are noted in many phenomena, and the authors attempt to apply mathematical and stochastic methods to deal with them. The main goals include exploration of Brownian motion in environments with anomalies and study of the motion of the Brownian particle in layered media. A fairly wide class of continuous Markov processes is obtained in the limit. It includes Markov processes with discontinuous transition densities, processes that are not solutions of any Itô's SDEs, and the Bessel diffusion process. The book is self-contained, with presentation of definitions and auxiliary results in an Appendix. It will be of value for specialists in stochastic analysis and SDEs, as well as for researchers in other fields who deal with unstable systems and practitioners who apply stochastic models to describe phenomena of instability.
Author: Tijana Levajković
Publisher: Springer
ISBN: 3319656783
Category : Mathematics
Languages : en
Pages : 139
Get Book Here
Book Description
This book provides a comprehensive and unified introduction to stochastic differential equations and related optimal control problems. The material is new and the presentation is reader-friendly. A major contribution of the book is the development of generalized Malliavin calculus in the framework of white noise analysis, based on chaos expansion representation of stochastic processes and its application for solving several classes of stochastic differential equations with singular data involving the main operators of Malliavin calculus. In addition, applications in optimal control and numerical approximations are discussed. The book is divided into four chapters. The first, entitled White Noise Analysis and Chaos Expansions, includes notation and provides the reader with the theoretical background needed to understand the subsequent chapters. In Chapter 2, Generalized Operators of Malliavin Calculus, the Malliavin derivative operator, the Skorokhod integral and the Ornstein-Uhlenbeck operator are introduced in terms of chaos expansions. The main properties of the operators, which are known in the literature for the square integrable processes, are proven using the chaos expansion approach and extended for generalized and test stochastic processes. Chapter 3, Equations involving Malliavin Calculus operators, is devoted to the study of several types of stochastic differential equations that involve the operators of Malliavin calculus, introduced in the previous chapter. Fractional versions of these operators are also discussed. Finally, in Chapter 4, Applications and Numerical Approximations are discussed. Specifically, we consider the stochastic linear quadratic optimal control problem with different forms of noise disturbances, operator differential algebraic equations arising in fluid dynamics, stationary equations and fractional versions of the equations studied – applications never covered in the extant literature. Moreover, numerical validations of the method are provided for specific problems."
Author:
Publisher:
ISBN:
Category : Dissertations, Academic
Languages : en
Pages : 950
Get Book Here
Book Description
