Equations différentielles stochastiques rétrogrades avec condition finale singulière PDF Download
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Author: Alexandre Popier (François, Roland)
Publisher:
ISBN:
Category :
Languages : fr
Pages : 130
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Author: Alexandre Popier (François, Roland)
Publisher:
ISBN:
Category :
Languages : fr
Pages : 130
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Author: Anis Matoussi
Publisher:
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Category :
Languages : fr
Pages : 0
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Author: Michèle Breton
Publisher: Springer Science & Business Media
ISBN: 0387251189
Category : Business & Economics
Languages : en
Pages : 268
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GERAD celebrates this year its 25th anniversary. The Center was created in 1980 by a small group of professors and researchers of HEC Montreal, McGill University and of the Ecole Polytechnique de Montreal. GERAD's activities achieved sufficient scope to justify its conversion in June 1988 into a Joint Research Centre of HEC Montreal, the Ecole Polytechnique de Montreal and McGill University. In 1996, the U- versite du Quebec a Montreal joined these three institutions. GERAD has fifty members (professors), more than twenty research associates and post doctoral students and more than two hundreds master and Ph.D. students. GERAD is a multi-university center and a vital forum for the devel- ment of operations research. Its mission is defined around the following four complementarily objectives: • The original and expert contribution to all research fields in GERAD's area of expertise; • The dissemination of research results in the best scientific outlets as well as in the society in general; • The training of graduate students and post doctoral researchers; • The contribution to the economic community by solving important problems and providing transferable tools.
Author: Philippe Briand (mathématicien).)
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Languages : fr
Pages : 0
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Author: David Chevance
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Languages : fr
Pages : 0
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Author: Ibtissam Hdhiri
Publisher:
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Category :
Languages : en
Pages : 153
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This thesis deals with the Backward stochastic differential equations (BSDEs for short) and their applications. The first part is devoted to the double barrier refiected BSDEs. We show the existence of a solution for su ch equations when the barriers are completely separate and the generator is continuous with quadratic growth. As an application we solve the risk-sensitive mixed zero-sum stochastic differential game. ln addition we deal with recallable options under K nightian uncertainty.ln the second part, we focus on a real option problem namely the starting and stopping problem when the noise is driven by a Brownian motion and an independent Poisson process. This problem is tackled in using the notion of Snell envelope and BSDEs with jumps. We de rive a stochastic verification theorem which we show later that is satisfied. lVhen the random noise stems from a standard SDE with jumps we show that the problem is related to a system of two variational inequalities, hence we give a deterministic verification result. Finally, we deal with the problem with exponential utilities.
Author: Anis Matoussi
Publisher:
ISBN:
Category :
Languages : fr
Pages : 204
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Cette thèse a pour objet, d'une part, l'étude des équations différentielles stochastiques rétrogrades réfléchies (EDDSR) et d'autre part, la preuve de l'existence et l'unicité des solutions d'équations aux dérivées partielles stochastiques quasi-linéaires (EDPS), formulées dans un sens faible ; en utilisant des solutions généralisées des équations différentielles doublement stochastiques rétrogrades (EDDSR). dans la première partie, on s'attache à montrer l'existence d'une solution pour l'EDSR réfléchie sur une ou deux barrières à coefficient non Lipschitz. on s'interroge en effet sur les hypothèses minimales à inclure pour obtenir ce résultat. dans la seconde partie, on s'intéresse à l'EDPS quasi-lineaire suivante : U/T = LU (T, X) + F(T, X, U(T, X), (*U)(T, X))DT + H(T, X, U(T, X), (*U)(T, X))B/T(T), U(T, X) = G(X) ou G est une distribution. Compte tenu des résultats déjà connus sur ce sujet, nous répondons aux questions suivantes: - dans le cas ou les coefficients F(S, X, Y, Z) et H(S, X, Y, Z) sont linéaires en (Y, Z) et appartiennent à un espace de type Sobolev en X, existe-t-il une formulation faible des EDDSR pour donner une formule de Feynman-Kac pour la solution d'EDPS ? - dans le cas ou les coefficients sont non-linéaires, peut-on montrer l'existence et l'unicite d'une solution de l'EDPS et ainsi généraliser les résultats obtenus par Barles et Lesigne (1997) dans le cadre des EDP standards ?
Author: Sébastien Choukroun
Publisher:
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Category :
Languages : en
Pages : 0
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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: Anne Gégout-Petit
Publisher:
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Languages : fr
Pages : 0
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Author: Hao Wang
Publisher:
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Category :
Languages : en
Pages : 153
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The main objective of the thesis is to study the existence and uniqueness of solutions of reflected backward stochastic differential equations and to relate this notion to the study of the problems such as the reversible investment or so-called optimal switching problem, the mixed zero-sum stochastic differential games and the probabilistic interpretation of the weak solution of partial differential equations, either in viscosity sense or in Sobolev space under different framework.
