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Author: Arij Manai Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
This thesis is dedicated to the study of backward stochastic differential equations (BSDEs) and their applications. In chapter 1, we study the problem of maximizing the utility from terminal wealth where the stock price may jump and there are investment constraints on the agent 's strategies. We focus on the BSDE whose solution represents the maximal utility, which allows transferring results on quadratic BSDEs, in particular the stability results, to the problem of utility maximisation. In chapter 2, we consider the problem of pricing American options from theoretical and numerical sides based upon an alternative representation of the value of the option in the form of a viscosity solution of a parabolic equation with a nonlinear reaction term. We extend the viscosity solution characterization proved in [Benth, Karlsen and Reikvam 2003] for call/put American option prices to the case of a general payoff function in a multi-dimensional setting. We address two new numerical schemes inspired by the branching processes. Our numerical experiments show that approximating the discontinuous driver of the associated reaction/diffusion PDE by local polynomials is not efficient, while a simple randomization procedure provides very good results. In chapter 3, we prove existence and uniqueness results for a general class of coupled mean-field forward-backward SDEs with jumps under weak monotonicity conditions and without the non-degeneracy assumption on the forward equation and we give an application in the field of storage in smart grids in the case where the production of electricity is unpredictable.
Author: Arij Manai Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
This thesis is dedicated to the study of backward stochastic differential equations (BSDEs) and their applications. In chapter 1, we study the problem of maximizing the utility from terminal wealth where the stock price may jump and there are investment constraints on the agent 's strategies. We focus on the BSDE whose solution represents the maximal utility, which allows transferring results on quadratic BSDEs, in particular the stability results, to the problem of utility maximisation. In chapter 2, we consider the problem of pricing American options from theoretical and numerical sides based upon an alternative representation of the value of the option in the form of a viscosity solution of a parabolic equation with a nonlinear reaction term. We extend the viscosity solution characterization proved in [Benth, Karlsen and Reikvam 2003] for call/put American option prices to the case of a general payoff function in a multi-dimensional setting. We address two new numerical schemes inspired by the branching processes. Our numerical experiments show that approximating the discontinuous driver of the associated reaction/diffusion PDE by local polynomials is not efficient, while a simple randomization procedure provides very good results. In chapter 3, we prove existence and uniqueness results for a general class of coupled mean-field forward-backward SDEs with jumps under weak monotonicity conditions and without the non-degeneracy assumption on the forward equation and we give an application in the field of storage in smart grids in the case where the production of electricity is unpredictable.
Author: Jin Ma Publisher: Springer ISBN: 3540488316 Category : Mathematics Languages : en Pages : 285
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: N El Karoui Publisher: CRC Press ISBN: 9780582307339 Category : Mathematics Languages : en Pages : 236
Book Description
This book presents the texts of seminars presented during the years 1995 and 1996 at the Université Paris VI and is the first attempt to present a survey on this subject. Starting from the classical conditions for existence and unicity of a solution in the most simple case-which requires more than basic stochartic calculus-several refinements on the hypotheses are introduced to obtain more general results.
Author: Rym Salhi Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
This thesis focuses on backward stochastic differential equation with jumps and their applications. In the first chapter, we study a backward stochastic differential equation (BSDE for short) driven jointly by a Brownian motion and an integer valued random measure that may have infinite activity with compensator being possibly time inhomogeneous. In particular, we are concerned with the case where the driver has quadratic growth and unbounded terminal condition. The existence and uniqueness of the solution are proven by combining a monotone approximation technics and a forward approach. Chapter 2 is devoted to the well-posedness of generalized doubly reflected BSDEs (GDRBSDE for short) with jumps under weaker assumptions on the data. In particular, we study the existence of a solution for a one-dimensional GDRBSDE with jumps when the terminal condition is only measurable with respect to the related filtration and when the coefficient has general stochastic quadratic growth. We also show, in a suitable framework, the connection between our class of backward stochastic differential equations and risk sensitive zero-sum game. In chapter 3, we investigate a general class of fully coupled mean field forward-backward under weak monotonicity conditions without assuming any non-degeneracy assumption on the forward equation. We derive existence and uniqueness results under two different sets of conditions based on proximation schema weither on the forward or the backward equation. Later, we give an application for storage in smart grids.
Author: Samuel N. Cohen Publisher: Springer Nature ISBN: 3030222853 Category : Mathematics Languages : en Pages : 300
Book Description
This collection of selected, revised and extended contributions resulted from a Workshop on BSDEs, SPDEs and their Applications that took place in Edinburgh, Scotland, July 2017 and included the 8th World Symposium on BSDEs. The volume addresses recent advances involving backward stochastic differential equations (BSDEs) and stochastic partial differential equations (SPDEs). These equations are of fundamental importance in modelling of biological, physical and economic systems, and underpin many problems in control of random systems, mathematical finance, stochastic filtering and data assimilation. The papers in this volume seek to understand these equations, and to use them to build our understanding in other areas of mathematics. This volume will be of interest to those working at the forefront of modern probability theory, both established researchers and graduate students.
Author: Samuel N. Cohen Publisher: ISBN: 9783030222864 Category : Computer science Languages : en Pages : 300
Book Description
This collection of selected, revised and extended contributions resulted from a Workshop on BSDEs, SPDEs and their Applications that took place in Edinburgh, Scotland, July 2017 and included the 8th World Symposium on BSDEs. The volume addresses recent advances involving backward stochastic differential equations (BSDEs) and stochastic partial differential equations (SPDEs). These equations are of fundamental importance in modelling of biological, physical and economic systems, and underpin many problems in control of random systems, mathematical finance, stochastic filtering and data assimilation. The papers in this volume seek to understand these equations, and to use them to build our understanding in other areas of mathematics. This volume will be of interest to those working at the forefront of modern probability theory, both established researchers and graduate students.
Author: Tony G. Deangelo Publisher: Nova Science Publishers ISBN: 9781536138092 Category : Stochastic differential equations Languages : en Pages : 0
Book Description
"In this collection, the authors begin by introducing a methodology for examining continuous-time Ornstein-Uhlenbech family processes defined by stochastic differential equations (SDEs). Additionally, a study is presented introducing the mathematics of mixed effect parameters in univariate and bivariate SDEs and describing how such a model can be used to aid our understanding of growth processes using real world datasets. Results and experience from applying the concepts and techniques in an extensive individual tree and stand growth modeling program in Lithuania are described as examples. Next, the authors present a review paper on J-calculus, as well as a contributed paper which displays some new results on the topic and deepens some special properties in relation with non-differentiability of functions. Following this, this book develops the general framework to be used in our papers [2, 9, 8]. The starting point for the discussion will be the standard risk-sensitive structures, and how constructions of this kind can be given a rigorous treatment. The risk-sensitive optimal control is also investigated by using the extending part of this of problem of backward stochastic equation. In the closing article, the authors note that the square of an O-U process is the Cox-Ingersoll-Ross process used as a model for volatility in finance. The filtered form of the original hazard rate based on this new observation is also studied. If the difference between the original hazard rate and the filtered one is not significant, then the person is not affected by the new frailty"--
Author: Arij Manai
Author: Arij Manai
Author: Jin Ma
Author: N El Karoui
Author: Rym Salhi
Author: Samuel N. Cohen
Author: Yuhan Yao
Author: Simo Särkkä
Author: Samuel N. Cohen
Author: Rong Situ
Author: Tony G. Deangelo