Relevant bibliographies by topics / Forward Backward Stochastic Differential Equations (FBSDE)

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  1. Journal articles
  2. Dissertations / Theses
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  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Forward Backward Stochastic Differential Equations (FBSDE)'

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Published: 1 February 2025

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Journal articles on the topic "Forward Backward Stochastic Differential Equations (FBSDE)"

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Zhang, Kevin, Junhao Zhu, Dehan Kong, and Zhaolei Zhang. "Modeling single cell trajectory using forward-backward stochastic differential equations." PLOS Computational Biology 20, no. 4 (2024): e1012015. http://dx.doi.org/10.1371/journal.pcbi.1012015.

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Recent advances in single-cell sequencing technology have provided opportunities for mathematical modeling of dynamic developmental processes at the single-cell level, such as inferring developmental trajectories. Optimal transport has emerged as a promising theoretical framework for this task by computing pairings between cells from different time points. However, optimal transport methods have limitations in capturing nonlinear trajectories, as they are static and can only infer linear paths between endpoints. In contrast, stochastic differential equations (SDEs) offer a dynamic and flexible approach that can model non-linear trajectories, including the shape of the path. Nevertheless, existing SDE methods often rely on numerical approximations that can lead to inaccurate inferences, deviating from true trajectories. To address this challenge, we propose a novel approach combining forward-backward stochastic differential equations (FBSDE) with a refined approximation procedure. Our FBSDE model integrates the forward and backward movements of two SDEs in time, aiming to capture the underlying dynamics of single-cell developmental trajectories. Through comprehensive benchmarking on multiple scRNA-seq datasets, we demonstrate the superior performance of FBSDE compared to other methods, highlighting its efficacy in accurately inferring developmental trajectories.
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Takahashi, Akihiko, and Toshihiro Yamada. "An asymptotic expansion of forward-backward SDEs with a perturbed driver." International Journal of Financial Engineering 02, no. 02 (2015): 1550020. http://dx.doi.org/10.1142/s2424786315500206.

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Motivated by nonlinear pricing in finance, this paper presents a mathematical validity of an asymptotic expansion scheme for a system of forward-backward stochastic differential equations (FBSDEs) in terms of a perturbed driver in the BSDE and a small diffusion in the FSDE. In particular, we represent the coefficients of the expansion of the FBSDE up to an arbitrary order, and obtain the error estimate of the expansion with respect to the driver and the small noise perturbation.
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Yang, Jie, and Weidong Zhao. "Convergence of Recent Multistep Schemes for a Forward-Backward Stochastic Differential Equation." East Asian Journal on Applied Mathematics 5, no. 4 (2015): 387–404. http://dx.doi.org/10.4208/eajam.280515.211015a.

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AbstractConvergence analysis is presented for recently proposed multistep schemes, when applied to a special type of forward-backward stochastic differential equations (FB-SDEs) that arises in finance and stochastic control. The corresponding k-step scheme admits a k-order convergence rate in time, when the exact solution of the forward stochastic differential equation (SDE) is given. Our analysis assumes that the terminal conditions and the FBSDE coefficients are sufficiently regular.
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Geiss, Christel, Céline Labart, and Antti Luoto. "Mean square rate of convergence for random walk approximation of forward-backward SDEs." Advances in Applied Probability 52, no. 3 (2020): 735–71. http://dx.doi.org/10.1017/apr.2020.17.

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AbstractLet (Y, Z) denote the solution to a forward-backward stochastic differential equation (FBSDE). If one constructs a random walk $B^n$ from the underlying Brownian motion B by Skorokhod embedding, one can show $L_2$-convergence of the corresponding solutions $(Y^n,Z^n)$ to $(Y, Z).$ We estimate the rate of convergence based on smoothness properties, especially for a terminal condition function in $C^{2,\alpha}$. The proof relies on an approximative representation of $Z^n$ and uses the concept of discretized Malliavin calculus. Moreover, we use growth and smoothness properties of the partial differential equation associated to the FBSDE, as well as of the finite difference equations associated to the approximating stochastic equations. We derive these properties by probabilistic methods.
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Ji, Shaolin, Chuanfeng Sun, and Qingmeng Wei. "The Dynamic Programming Method of Stochastic Differential Game for Functional Forward-Backward Stochastic System." Mathematical Problems in Engineering 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/958920.

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This paper is devoted to a stochastic differential game (SDG) of decoupled functional forward-backward stochastic differential equation (FBSDE). For our SDG, the associated upper and lower value functions of the SDG are defined through the solution of controlled functional backward stochastic differential equations (BSDEs). Applying the Girsanov transformation method introduced by Buckdahn and Li (2008), the upper and the lower value functions are shown to be deterministic. We also generalize the Hamilton-Jacobi-Bellman-Isaacs (HJBI) equations to the path-dependent ones. By establishing the dynamic programming principal (DPP), we derive that the upper and the lower value functions are the viscosity solutions of the corresponding upper and the lower path-dependent HJBI equations, respectively.
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Song, Yunquan. "Terminal-Dependent Statistical Inference for the FBSDEs Models." Mathematical Problems in Engineering 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/365240.

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The original stochastic differential equations (OSDEs) and forward-backward stochastic differential equations (FBSDEs) are often used to model complex dynamic process that arise in financial, ecological, and many other areas. The main difference between OSDEs and FBSDEs is that the latter is designed to depend on a terminal condition, which is a key factor in some financial and ecological circumstances. It is interesting but challenging to estimate FBSDE parameters from noisy data and the terminal condition. However, to the best of our knowledge, the terminal-dependent statistical inference for such a model has not been explored in the existing literature. We proposed a nonparametric terminal control variables estimation method to address this problem. The reason why we use the terminal control variables is that the newly proposed inference procedures inherit the terminal-dependent characteristic. Through this new proposed method, the estimators of the functional coefficients of the FBSDEs model are obtained. The asymptotic properties of the estimators are also discussed. Simulation studies show that the proposed method gives satisfying estimates for the FBSDE parameters from noisy data and the terminal condition. A simulation is performed to test the feasibility of our method.
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DOS REIS, GONÇALO, and RICARDO J. N. DOS REIS. "A NOTE ON COMONOTONICITY AND POSITIVITY OF THE CONTROL COMPONENTS OF DECOUPLED QUADRATIC FBSDE." Stochastics and Dynamics 13, no. 04 (2013): 1350005. http://dx.doi.org/10.1142/s0219493713500056.

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In this note we are concerned with the solution of Forward–Backward Stochastic Differential Equations (FBSDE) with drivers that grow quadratically in the control component (quadratic growth FBSDE or qgFBSDE). The main theorem is a comparison result that allows comparing componentwise the signs of the control processes of two different qgFBSDE. As a by-product one obtains conditions that allow establishing the positivity of the control process.
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Wang, Mingcan, and Xiangjun Wang. "Hybrid Neural Networks for Solving Fully Coupled, High-Dimensional Forward–Backward Stochastic Differential Equations." Mathematics 12, no. 7 (2024): 1081. http://dx.doi.org/10.3390/math12071081.

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The theory of forward–backward stochastic differential equations occupies an important position in stochastic analysis and practical applications. However, the numerical solution of forward–backward stochastic differential equations, especially for high-dimensional cases, has stagnated. The development of deep learning provides ideas for its high-dimensional solution. In this paper, our focus lies on the fully coupled forward–backward stochastic differential equation. We design a neural network structure tailored to the characteristics of the equation and develop a hybrid BiGRU model for solving it. We introduce the time dimension based on the sequence nature after discretizing the FBSDE. By considering the interactions between preceding and succeeding time steps, we construct the BiGRU hybrid model. This enables us to effectively capture both long- and short-term dependencies, thus mitigating issues such as gradient vanishing and explosion. Residual learning is introduced within the neural network at each time step; the structure of the loss function is adjusted according to the properties of the equation. The model established above can effectively solve fully coupled forward–backward stochastic differential equations, effectively avoiding the effects of dimensional catastrophe, gradient vanishing, and gradient explosion problems, with higher accuracy, stronger stability, and stronger model interpretability.
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Wu, Zhen. "Fully coupled FBSDE with Brownian motion and Poisson process in stopping time duration." Journal of the Australian Mathematical Society 74, no. 2 (2003): 249–66. http://dx.doi.org/10.1017/s1446788700003281.

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AbstractWe first give the existence and uniqueness result and a comparison theorem for backward stochastic differential equations with Brownian motion and Poisson process as the noise source in stopping time (unbounded) duration. Then we obtain the existence and uniqueness result for fully coupled forward-backward stochastic differential equation with Brownian motion and Poisson process in stopping time (unbounded) duration. We also proved a comparison theorem for this kind of equation.
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Wei, Qingmeng, Jiongmin Yong, and Zhiyong Yu. "Linear quadratic stochastic optimal control problems with operator coefficients: open-loop solutions." ESAIM: Control, Optimisation and Calculus of Variations 25 (2019): 17. http://dx.doi.org/10.1051/cocv/2018013.

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An optimal control problem is considered for linear stochastic differential equations with quadratic cost functional. The coefficients of the state equation and the weights in the cost functional are bounded operators on the spaces of square integrable random variables. The main motivation of our study is linear quadratic (LQ, for short) optimal control problems for mean-field stochastic differential equations. Open-loop solvability of the problem is characterized as the solvability of a system of linear coupled forward-backward stochastic differential equations (FBSDE, for short) with operator coefficients, together with a convexity condition for the cost functional. Under proper conditions, the well-posedness of such an FBSDE, which leads to the existence of an open-loop optimal control, is established. Finally, as applications of our main results, a general mean-field LQ control problem and a concrete mean-variance portfolio selection problem in the open-loop case are solved.
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Dissertations / Theses on the topic "Forward Backward Stochastic Differential Equations (FBSDE)"

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Fromm, Alexander. "Theory and applications of decoupling fields for forward-backward stochastic differential equations." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2015. http://dx.doi.org/10.18452/17115.

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Diese Arbeit beschäftigt sich mit der Theorie der sogenannten stochastischen Vorwärts-Rückwärts-Differentialgleichungen (FBSDE), welche als ein stochastisches Anologon und in gewisser Weise als eine Verallgemeinerung von parabolischen quasi-linearen partiellen Differentialgleichungen betrachtet werden können. Die Dissertation besteht aus zwei Teilen: In dem ersten entwicklen wir die Theorie der sogenannten Entkopplungsfelder für allgemeine mehrdimensionale stark gekoppelte FBSDE. Diese Theorie besteht aus Existenz- sowie Eindeutigkeitsresultaten basierend auf dem Konzept des maximalen Intervalls. Es beinhaltet darüberhinaus Werkzeuge um Regularität von konkreten Problemen zu untersuchen. Insgesamt wird die Theorie für drei Klassen von Problemen entwickelt: In dem ersten Fall werden Lipschitz-Bedingungen an die Parameter des Problems vorausgesetzt, welche zugleich vom Zufall abhängen dürfen. Die Untersuchung der beiden anderen Klassen basiert auf dem ersten. In diesen werden die Parameter als deterministisch vorausgesetzt. Gleichwohl wird die Lipschitz-Stetigkeit durch zwei verschiedene Formen der lokalen Lipschitz-Stetigkeit abgeschwächt. In dem zweiten Teil werden diese abstrakten Resultate auf drei konkrete Probleme angewendet: In der ersten Anwendung wird gezeigt wie globale Lösbarkeit von FBSDE in dem sogenannten nicht-degenerierten Fall untersucht werden kann. In der zweiten Anwendung wird die Lösbarkeit eines gekoppelten Systems gezeigt, welches eine Lösung zu dem Skorokhod''schen Einbettungproblem liefert. Die Lösung wird für den Fall einer allgemeinen nicht-linearen Drift konstruiert. Die dritte Anwendung führt auf Lösbarkeit eines komplexen gekoppelten Vorwärt-Rückwärts-Systems, aus welchem optimale Strategien für das Problem der Nutzenmaximierung in unvollständingen Märkten konstruiert werden. Das System wird in einem verhältnismäßig allgmeinen Rahmen gelöst, d.h. für eine verhältnismäßig allgemeine Klasse von Nutzenfunktion auf den reellen Zahlen.<br>This thesis deals with the theory of so called forward-backward stochastic differential equations (FBSDE) which can be seen as a stochastic formulation and in some sense generalization of parabolic quasi-linear partial differential equations. The thesis consist of two parts: In the first we develop the theory of so called decoupling fields for general multidimensional fully coupled FBSDE in a Brownian setting. The theory consists of uniqueness and existence results for decoupling fields on the so called the maximal interval. It also provides tools to investigate well-posedness and regularity for particular problems. In total the theory is developed for three different classes of FBSDE: In the first Lipschitz continuity of the parameter functions is required, which at the same time are allowed to be random. The other two classes we investigate are based on the theory developed for the first one. In both of them all parameter functions have to be deterministic. However, two different types of local Lipschitz continuity replace the more restrictive Lipschitz continuity of the first class. In the second part we apply these techniques to three different problems: In the first application we demonstrate how well-posedness of FBSDE in the so called non-degenerate case can be investigated. As a second application we demonstrate the solvability of a system, which provides a solution to the so called Skorokhod embedding problem (SEP) via FBSDE. The solution to the SEP is provided for the case of general non-linear drift. The third application provides solutions to a complex FBSDE from which optimal trading strategies for a problem of utility maximization in incomplete markets are constructed. The FBSDE is solved in a relatively general setting, i.e. for a relatively general class of utility functions on the real line.
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Wang, Xince. "Quasilinear PDEs and forward-backward stochastic differential equations." Thesis, Loughborough University, 2015. https://dspace.lboro.ac.uk/2134/17383.

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In this thesis, first we study the unique classical solution of quasi-linear second order parabolic partial differential equations (PDEs). For this, we study the existence and uniqueness of the $L^2_{\rho}( \mathbb{R}^{d}; \mathbb{R}^{d}) \otimes L^2_{\rho}( \mathbb{R}^{d}; \mathbb{R}^{k})\otimes L^2_{\rho}( \mathbb{R}^{d}; \mathbb{R}^{k\times d})$ valued solution of forward backward stochastic differential equations (FBSDEs) with finite horizon, the regularity property of the solution of FBSDEs and the connection between the solution of FBSDEs and the solution of quasi-linear parabolic PDEs. Then we establish their connection in the Sobolev weak sense, in order to give the weak solution of the quasi-linear parabolic PDEs. Finally, we study the unique weak solution of quasi-linear second order elliptic PDEs through the stationary solution of the FBSDEs with infinite horizon.
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Nie, Tianyang. "Stochastic differential equations with constraints on the state : backward stochastic differential equations, variational inequalities and fractional viability." Thesis, Brest, 2012. http://www.theses.fr/2012BRES0047.

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Le travail de thèse est composé de trois thèmes principaux : le premier étudie l'existence et l'unicité pour des équations différentielles stochastiques (EDS) progressives-rétrogrades fortement couplées avec des opérateurs sous-différentiels dans les deux équations, dans l’équation progressive ainsi que l’équation rétrograde, et il discute également un nouveau type des inégalités variationnelles partielles paraboliques associées, avec deux opérateurs sous-différentiels, l’un agissant sur le domaine de l’état, l’autre sur le co-domaine. Le second thème est celui des EDS rétrogrades sans ainsi qu’avec opérateurs sous-différentiels, régies par un mouvement brownien fractionnaire avec paramètre de Hurst H&gt; ½. Il étend de manière rigoureuse les résultats de Hu et Peng (SICON, 2009) aux inégalités variationnelles stochastiques rétrogrades. Enfin, le troisième thème met l’accent sur la caractérisation déterministe de la viabilité pour les EDS régies par un mouvement brownien fractionnaire. Ces trois thèmes de recherche mentionnés ci-dessus ont en commun d’étudier des EDS avec contraintes sur le processus d’état. Chacun des trois sujets est basé sur une publication et des manuscrits soumis pour publication, respectivement<br>This PhD thesis is composed of three main topics: The first one studies the existence and the uniqueness for fully coupled forward-backward stochastic differential equations (SDEs) with subdifferential operators in both the forward and the backward equations, and it discusses also a new type of associated parabolic partial variational inequalities with two subdifferential operators, one acting over the state domain and the other over the co-domain. The second topic concerns the investigation of backward SDEs without as well as with subdifferential operator, both driven by a fractional Brownian motion with Hurst parameter H&gt; 1/2. It extends in a rigorous manner the results of Hu and Peng (SICON, 2009) to backward stochastic variational inequalities. Finally, the third topic focuses on a deterministic characterisation of the viability for SDEs driven by a fractional Brownian motion. The three research topics mentioned above have in common to study SDEs with state constraints. The discussion of each of the three topics is based on a publication and on submitted manuscripts, respectively
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Manai, Arij. "Some contributions to backward stochastic differential equations and applications." Thesis, Le Mans, 2019. http://www.theses.fr/2019LEMA1022.

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Cette thèse est consacrée à l'étude des équations différentielles stochastiques rétrogrades (EDSR) et leurs applications. Dans le chapitre 1, on étudie le problème de maximisation de l'utilité de la richesse terminale où le prix de l'actif peut être discontinue sous des contraintes sur les stratégies de l'agent. Nous nous concentrons sur l'EDSR dont la solution représente l'utilité maximale, ce qui permet de transférer des résultats sur les EDSR quadratiques, en particulier les résultats de stabilité, au problème de maximisation d'utilité. Dans le chapitre 2, nous considèrons le problème de valorisation d'options Américaines des points de vue théorique et numérique en s'appuyant sur la représentation du prix de l'option comme solution de viscosité d'une équation parabolique non linéaire. Nous étendons le résultat prouvé dans [Benth, Karlsen and Reikvam 2003] pour un put ou call Américain à un cas plus général dans un cadre multidimensionnel. Nous proposons deux schémas numériques inspirés par les processus de branchement. Nos expériences numériques montrent que l'approximation du générateur discontinu, associé à l'EDP, par des polynômes locaux n'est pas efficace tandis qu'une simple procédure de randomisation donne de très bon résultats. Dans le chapitre 3, nous prouvons des résultats d'existence et d'unicité pour une classe générale d'équations progressives-rétrogrades à champs moyen sous une condition de monotonicité faible et une hypothèse non-dégénérescence sur l'équation progressive et nous donnons une application dans le domaine de stockage d'énergie dans le cas où la production d'électricité est imprévisible<br>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
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Salhi, Rym. "Contributions to quadratic backward stochastic differential equations with jumps and applications." Thesis, Le Mans, 2019. http://www.theses.fr/2019LEMA1023.

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Cette thèse porte sur l'étude des équations différentielles stochastiques rétrogrades (EDSR) avec sauts et leurs applications.Dans le chapitre 1, nous étudions une classe d'EDSR lorsque le bruit provient d'un mouvement Brownien et d'une mesure aléatoire de saut indépendante à activité infinie. Plus précisément, nous traitons le cas où le générateur est à croissance quadratique et la condition terminale est non bornée. L'existence et l'unicité de la solution sont prouvées en combinant à la fois la procédure d'approximation monotone et une approche progressive. Cette méthode permet de résoudre le cas où la condition terminale est non bornée.Le chapitre 2 est consacré aux EDSR avec sauts généralisées doublement réfléchies sous des hypothèses d’intégrabilités faibles. Plus précisément, on montre l'existence d'une solution pour un générateur à croissance quadratique stochastique et une condition terminale non bornée. Nous montrons également, dans un cadre approprié, la connexion entre notre classe d’équations différentielles stochastiques rétrogrades et les jeu à somme nuls.Dans le chapitre 3, nous considérons une classe générale d'EDSR progressive-rétrograde couplée avec sauts de type Mackean Vlasov sous une condition faible de monotonicité. Les résultats d'existence et d'unicité sont établis sous deux classes d'hypothèses en se basant sur des schémas de perturbations soit de l’équation différentielle stochastique progressive, soit de l’équation différentielle stochastique rétrograde. On conclut le chapitre par un problème de stockage optimal d’énergie dans un parc électrique de type champs moyen<br>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
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Fromm, Alexander [Verfasser], Peter [Akademischer Betreuer] Imkeller, Stefan [Akademischer Betreuer] Ankirchner, and Anthony [Akademischer Betreuer] Réveillac. "Theory and applications of decoupling fields for forward-backward stochastic differential equations / Alexander Fromm. Gutachter: Peter Imkeller ; Stefan Ankirchner ; Anthony Réveillac." Berlin : Humboldt Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2015. http://d-nb.info/1065723083/34.

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Ouknine, Anas. "Μοdèles affines généralisées et symétries d'équatiοns aux dérivés partielles". Electronic Thesis or Diss., Normandie, 2024. http://www.theses.fr/2024NORMR085.

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Cette thèse se consacre à étudier les symétries de Lie d'une classe particulière d'équations différentielles partielles (EDP), désignée sous le nom d'équation de Kolmogorov rétrograde. Cette équation joue un rôle essentiel dans le cadre des modèles financiers, notamment en lien avec le modèle de Longstaff-Schwartz, qui est largement utilisé pour la valorisation des options et des produits dérivés.Dans un contexte plus générale, notre étude s'oriente vers l'analyse des symétries de Lie de l'équation de Kolmogorov rétrograde, en introduisant un terme non linéaire. Cette généralisation est significative, car l'équation ainsi modifiée est liée à une équation différentielle stochastique rétrograde et progressive (EDSRP) via la formule de Feynman-Kac généralisée (non linéaire). Nous nous intéressons également à l'exploration des symétries de cette équation stochastique, ainsi qu'à la manière dont les symétries de l'EDP sont connectées à celles de l'EDSRP.Enfin, nous proposons un recalcul des symétries de l'équation différentielle stochastique rétrograde (EDSR) et de l'EDSRP, en adoptant une nouvelle approche. Cette approche se distingue par le fait que le groupe de symétries qui opère sur le temps dépend lui-même du processus Y, qui constitue la solution de l'EDSR. Cette dépendance ouvre de nouvelles perspectives sur l'interaction entre les symétries temporelles et les solutions des équations<br>This thesis is dedicated to studying the Lie symmetries of a particular class of partialdifferential equations (PDEs), known as the backward Kolmogorov equation. This equa-tion plays a crucial role in financial modeling, particularly in relation to the Longstaff-Schwartz model, which is widely used for pricing options and derivatives.In a broader context, our study focuses on analyzing the Lie symmetries of thebackward Kolmogorov equation by introducing a nonlinear term. This generalization issignificant, as the modified equation is linked to a forward backward stochastic differ-ential equation (FBSDE) through the generalized (nonlinear) Feynman-Kac formula.We also examine the symmetries of this stochastic equation and how the symmetriesof the PDE are connected to those of the BSDE.Finally, we propose a recalculation of the symmetries of the BSDE and FBSDE,adopting a new approach. This approach is distinguished by the fact that the symme-try group acting on time itself depends also on the process Y , which is the solutionof the BSDE. This dependence opens up new perspectives on the interaction betweentemporal symmetries and the solutions of the equations
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Mtiraoui, Ahmed. "I. Etude des EDDSRs surlinéaires II. Contrôle des EDSPRs couplées." Thesis, Toulon, 2016. http://www.theses.fr/2016TOUL0010/document.

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Cette thèse aborde deux sujets de recherches, le premier est sur l’existence et l’unicité des solutions des Équations Différentielles Doublement Stochastiques Rétrogrades (EDDSRs) et les Équations aux Dérivées partielles Stochastiques (EDPSs) multidimensionnelles à croissance surlinéaire. Le deuxième établit l’existence d’un contrôle optimal strict pour un système controlé dirigé par des équations différentielles stochastiques progressives rétrogrades (EDSPRs) couplées dans deux cas de diffusions dégénérée et non dégénérée.• Existence et unicité des solutions des EDDSRs multidimensionnels :Nous considérons EDDSR avec un générateur de croissance surlinéaire et une donnée terminale de carré intégrable. Nous introduisons une nouvelle condition locale sur le générateur et nous montrons qu’elle assure l’existence, l’unicité et la stabilité des solutions. Même si notre intérêt porte sur le cas multidimensionnel, notre résultat est également nouveau en dimension un. Comme application, nous établissons l’existence et l’unicité des solutions des EDPS semi-linéaires.• Contrôle des EDSPR couplées :Nous étudions un problème de contrôle avec une fonctionnelle coût non linéaire dont le système contrôlé est dirigé par une EDSPR couplée. L’objective de ce travail est d’établir l’existence d’un contrôle optimal dans la classe des contrôle stricts, donc on montre que ce contrôle vérifie notre équation et qu’il minimise la fonctionnelle coût. La méthode consiste à approcher notre système par une suite de systèmes réguliers et on montre la convergence. En passant à la limite, sous des hypothèses de convexité, on obtient l’existence d’un contrôle optimal strict. on suit cette méthode théorique pour deux cas différents de diffusions dégénérée et non dégénérée<br>In this Phd thesis, we considers two parts. The first one establish the existence and the uniquness of the solutions of multidimensional backward doubly stochastic differential equations (BDSDEs in short) and the stochastic partial differential equations (SPDEs in short) in the superlinear growth generators. In the second part, we study the stochastic controls problems driven by a coupled Forward-Backward stochastic differentialequations (FBSDEs in short).• BDSDEs and SPDEs with a superlinear growth generators :We deal with multidimensional BDSDE with a superlinear growth generator and a square integrable terminal datum. We introduce new local conditions on the generator then we show that they ensure the existence and uniqueness as well as the stability of solutions. Our work go beyond the previous results on the subject. Although we are focused on multidimensional case, the uniqueness result we establish is new in one dimensional too. As application, we establish the existence and uniqueness of probabilistic solutions tosome semilinear SPDEs with superlinear growth generator. By probabilistic solution, we mean a solution which is representable throughout a BDSDEs.• Controlled coupled FBSDEs :We establish the existence of an optimal control for a system driven by a coupled FBDSE. The cost functional is defined as the initial value of the backward component of the solution. We construct a sequence of approximating controlled systems, for which we show the existence of a sequence of feedback optimal controls. By passing to the limit, we get the existence of a feedback optimal control. The convexity condition is used to ensure that the optimal control is strict. In this part, we study two cases of diffusions : degenerate and non-degenerate
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Wu, Yue. "Pathwise anticipating random periodic solutions of SDEs and SPDEs with linear multiplicative noise." Thesis, Loughborough University, 2014. https://dspace.lboro.ac.uk/2134/15991.

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In this thesis, we study the existence of pathwise random periodic solutions to both the semilinear stochastic differential equations with linear multiplicative noise and the semilinear stochastic partial differential equations with linear multiplicative noise in a Hilbert space. We identify them as the solutions of coupled forward-backward infinite horizon stochastic integral equations in general cases, and then perform the argument of the relative compactness of Wiener-Sobolev spaces in C([0, T],L2Ω,Rd)) or C([0, T],L2(Ω x O)) and Schauder's fixed point theorem to show the existence of a solution of the coupled stochastic forward-backward infinite horizon integral equations.
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Zhang, Liangliang. "Essays on numerical solutions to forward-backward stochastic differential equations and their applications in finance." Thesis, 2017. https://hdl.handle.net/2144/26430.

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In this thesis, we provide convergent numerical solutions to non-linear forward-BSDEs (Backward Stochastic Differential Equations). Applications in mathematical finance, financial economics and financial econometrics are discussed. Numerical examples show the effectiveness of our methods.
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Books on the topic "Forward Backward Stochastic Differential Equations (FBSDE)"

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Ma, Jin, and Jiongmin Yong. Forward-Backward Stochastic Differential Equations and their Applications. Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-48831-6.

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Ma, Jin. Forward-backward stochastic differential equations and their applications. Springer, 1999.

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Forward-Backward Stochastic Differential Equations and Their Applications. Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/bfb0092524.

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Yong, Jiongmin, and Jin Ma. Forward-Backward Stochastic Differential Equations and Their Applications. Springer London, Limited, 2007.

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Chassagneux, Jean-François, Hinesh Chotai, and Mirabelle Muûls. A Forward-Backward SDEs Approach to Pricing in Carbon Markets. Springer, 2017.

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Ma, Jin, and Jiongmin Yong. Forward-Backward Stochastic Differential Equations and their Applications (Lecture Notes in Mathematics). Springer, 2007.

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Book chapters on the topic "Forward Backward Stochastic Differential Equations (FBSDE)"

1

Zhang, Jianfeng. "Forward-Backward SDEs." In Backward Stochastic Differential Equations. Springer New York, 2017. http://dx.doi.org/10.1007/978-1-4939-7256-2_8.

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Delong, Łukasz. "Forward-Backward Stochastic Differential Equations." In EAA Series. Springer London, 2013. http://dx.doi.org/10.1007/978-1-4471-5331-3_4.

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Chassagneux, Jean-François, Hinesh Chotai, and Mirabelle Muûls. "Introduction to Forward-Backward Stochastic Differential Equations." In A Forward-Backward SDEs Approach to Pricing in Carbon Markets. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-63115-8_2.

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Ma, Jin, and Tim Zajic. "Rough Asymptotics of Forward-Backward Stochastic Differential Equations." In Control of Distributed Parameter and Stochastic Systems. Springer US, 1999. http://dx.doi.org/10.1007/978-0-387-35359-3_29.

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Kebiri, Omar, Lara Neureither, and Carsten Hartmann. "Adaptive Importance Sampling with Forward-Backward Stochastic Differential Equations." In Stochastic Dynamics Out of Equilibrium. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-15096-9_7.

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Kohlmann, Michael. "Reflected Forward Backward Stochastic Differential Equations and Contingent Claims." In Control of Distributed Parameter and Stochastic Systems. Springer US, 1999. http://dx.doi.org/10.1007/978-0-387-35359-3_27.

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Kim, Jin Won, and Sebastian Reich. "On Forward–Backward SDE Approaches to Conditional Estimation." In Mathematics of Planet Earth. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-70660-8_6.

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AbstractIn this chapter, we investigate the representation of conditional expectation values for partially observed diffusion processes in terms of appropriate estimators. The work of Kalman and Bucy has established a duality between filtering and estimation in the context of time-continuous linear systems. This duality has recently been extended to time-continuous nonlinear systems in terms of an optimization problem constrained by a backward stochastic partial differential equation. Here we revisit this problem from the perspective of appropriate forward-backward stochastic differential equations. Our approach sheds new light on the conditional estimation problem and provides a unifying perspective. It is also demonstrated that certain formulations of the estimation problem lead to deterministic formulations similar to the linear Gaussian case as originally investigated by Kalman and Bucy. Finally, we discuss an application of the proposed formulation to optimal control problem on partially observed diffusion processes.
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Jiménez-Pastor, A., K. G. Larsen, M. Tribastone, and M. Tschaikowski. "Forward and Backward Constrained Bisimulations for Quantum Circuits." In Tools and Algorithms for the Construction and Analysis of Systems. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-57249-4_17.

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AbstractEfficient methods for the simulation of quantum circuits on classic computers are crucial for their analysis due to the exponential growth of the problem size with the number of qubits. Here we study lumping methods based on bisimulation, an established class of techniques that has been proven successful for (classic) stochastic and deterministic systems such as Markov chains and ordinary differential equations. Forward constrained bisimulation yields a lower-dimensional model which exactly preserves quantum measurements projected on a linear subspace of interest. Backward constrained bisimulation gives a reduction that is valid on a subspace containing the circuit input, from which the circuit result can be fully recovered. We provide an algorithm to compute the constraint bisimulations yielding coarsest reductions in both cases, using a duality result relating the two notions. As applications, we provide theoretical bounds on the size of the reduced state space for well-known quantum algorithms for search, optimization, and factorization. Using a prototype implementation, we report significant reductions on a set of benchmarks. Furthermore, we show that constraint bisimulation complements state-of-the-art methods for the simulation of quantum circuits based on decision diagrams.
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"FBSDEs with Reflections." In Forward-Backward Stochastic Differential Equations and their Applications. Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-48831-6_7.

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"Applications of FBSDEs." In Forward-Backward Stochastic Differential Equations and their Applications. Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-48831-6_8.

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Conference papers on the topic "Forward Backward Stochastic Differential Equations (FBSDE)"

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Exarchos, Ioannis, and Evangelos A. Theodorou. "Learning optimal control via forward and backward stochastic differential equations." In 2016 American Control Conference (ACC). IEEE, 2016. http://dx.doi.org/10.1109/acc.2016.7525237.

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Exarchos, Ioannis, Evangelos A. Theodorou, and Panagiotis Tsiotras. "Game-theoretic and risk-sensitive stochastic optimal control via forward and backward stochastic differential equations." In 2016 IEEE 55th Conference on Decision and Control (CDC). IEEE, 2016. http://dx.doi.org/10.1109/cdc.2016.7799215.

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Shanshan, Zuo, and Min Hui. "Optimal control problems of mean-field forward-backward stochastic differential equations with partial information." In 2013 25th Chinese Control and Decision Conference (CCDC). IEEE, 2013. http://dx.doi.org/10.1109/ccdc.2013.6561841.

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Ashok Naarayan, Aadhithya, and Panos Parpas. "Stable Multilevel Deep Neural Networks for Option Pricing and xVAs Using Forward-Backward Stochastic Differential Equations." In ICAIF '24: 5th ACM International Conference on AI in Finance. ACM, 2024. http://dx.doi.org/10.1145/3677052.3698598.

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Hawkins, Kelsey P., Ali Pakniyat, and Panagiotis Tsiotras. "On the Time Discretization of the Feynman-Kac Forward-Backward Stochastic Differential Equations for Value Function Approximation." In 2021 60th IEEE Conference on Decision and Control (CDC). IEEE, 2021. http://dx.doi.org/10.1109/cdc45484.2021.9683583.

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