Relevant bibliographies by topics / Backward stochastic Volterra integral equation

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  2. Dissertations / Theses
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Academic literature on the topic 'Backward stochastic Volterra integral equation'

Author: Grafiati
Published: 18 June 2021
Last updated: 12 February 2022

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Journal articles on the topic "Backward stochastic Volterra integral equation"

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Hu, Yaozhong, and Bernt Øksendal. "Linear Volterra backward stochastic integral equations." Stochastic Processes and their Applications 129, no. 2 (2019): 626–33. http://dx.doi.org/10.1016/j.spa.2018.03.016.

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Wang, Hanxiao, and Jiongmin Yong. "Time-inconsistent stochastic optimal control problems and backward stochastic volterra integral equations." ESAIM: Control, Optimisation and Calculus of Variations 27 (2021): 22. http://dx.doi.org/10.1051/cocv/2021027.

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An optimal control problem is considered for a stochastic differential equation with the cost functional determined by a backward stochastic Volterra integral equation (BSVIE, for short). This kind of cost functional can cover the general discounting (including exponential and non-exponential) situations with a recursive feature. It is known that such a problem is time-inconsistent in general. Therefore, instead of finding a global optimal control, we look for a time-consistent locally near optimal equilibrium strategy. With the idea of multi-person differential games, a family of approximate equilibrium strategies is constructed associated with partitions of the time intervals. By sending the mesh size of the time interval partition to zero, an equilibrium Hamilton–Jacobi–Bellman (HJB, for short) equation is derived, through which the equilibrium value function and an equilibrium strategy are obtained. Under certain conditions, a verification theorem is proved and the well-posedness of the equilibrium HJB is established. As a sort of Feynman–Kac formula for the equilibrium HJB equation, a new class of BSVIEs (containing the diagonal value Z(r, r) of Z(⋅ , ⋅)) is naturally introduced and the well-posedness of such kind of equations is briefly presented.
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Shi, Yufeng, Tianxiao Wang, and Jiongmin Yong. "Mean-field backward stochastic Volterra integral equations." Discrete & Continuous Dynamical Systems - B 18, no. 7 (2013): 1929–67. http://dx.doi.org/10.3934/dcdsb.2013.18.1929.

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Lin, Jianzhong. "Adapted solution of a backward stochastic nonlinear Volterra integral equation." Stochastic Analysis and Applications 20, no. 1 (2002): 165–83. http://dx.doi.org/10.1081/sap-120002426.

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WANG, ZHIDONG, and XICHENG ZHANG. "NON-LIPSCHITZ BACKWARD STOCHASTIC VOLTERRA TYPE EQUATIONS WITH JUMPS." Stochastics and Dynamics 07, no. 04 (2007): 479–96. http://dx.doi.org/10.1142/s0219493707002128.

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In this paper, we prove the existence and uniqueness of solution for the backward stochastic Volterra integral equation with non-Lipschitz coefficients and driven by Brownian motion and jump process. Moreover, when the equation is driven only by Brownian motion, we also study the continuity of the solution with respect to the time.
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Wen, Jiaqiang, and Yufeng Shi. "Solvability of anticipated backward stochastic Volterra integral equations." Statistics & Probability Letters 156 (January 2020): 108599. http://dx.doi.org/10.1016/j.spl.2019.108599.

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Wei, Jiaqin. "Backward stochastic Volterra integral equations on Markov chains." Stochastics 90, no. 4 (2017): 605–39. http://dx.doi.org/10.1080/17442508.2017.1381096.

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Shi, Yufeng, and Tianxiao Wang. "SOLVABILITY OF GENERAL BACKWARD STOCHASTIC VOLTERRA INTEGRAL EQUATIONS." Journal of the Korean Mathematical Society 49, no. 6 (2012): 1301–21. http://dx.doi.org/10.4134/jkms.2012.49.6.1301.

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Djordjević, Jasmina, and Svetlana Janković. "Backward stochastic Volterra integral equations with additive perturbations." Applied Mathematics and Computation 265 (August 2015): 903–10. http://dx.doi.org/10.1016/j.amc.2015.05.077.

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Yong, Jiong-min. "Backward stochastic Volterra integral equations — a brief survey." Applied Mathematics-A Journal of Chinese Universities 28, no. 4 (2013): 383–94. http://dx.doi.org/10.1007/s11766-013-3189-4.

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Dissertations / Theses on the topic "Backward stochastic Volterra integral equation"

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Hamaguchi, Yushi. "Extended backward stochastic Volterra integral equations and their applications to time-inconsistent stochastic recursive control problems." Doctoral thesis, Kyoto University, 2021. http://hdl.handle.net/2433/263434.

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Pokalyuk, Stanislav [Verfasser], and Christian [Akademischer Betreuer] Bender. "Discretization of backward stochastic Volterra integral equations / Stanislav Pokalyuk. Betreuer: Christian Bender." Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2012. http://d-nb.info/1052338488/34.

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Knani, Habiba. "Backward stochastic differential equations driven by Gaussian Volterra processes." Electronic Thesis or Diss., Université de Lorraine, 2020. http://www.theses.fr/2020LORR0014.

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Cette thèse porte sur les équations différentielles stochastiques rétrogrades (EDSR) dirigées par une classe de processus de Volterra qui contient le mouvement brownien multifractionnaire et le processus Ornstein-Uhlenbeck multifractionnaire. Dans la première partie, nous étudions la solution des EDSRs multidimensionnelles avec des générateurs linéaires. Par la formule d’Itô pour les processus de Volterra nous réduisons l’EDSR à une équation aux dérivées partielles (EDP) de second ordre linéaire avec la condition terminale. Sous une condition d’intégrabilité dans un voisinage du temps terminal de la variance du processus de Volterra, nous résolvons l’EDP associée explicitement et en déduisons la solution des EDSR linéaire. Puis, nous discutons une application dans le contexte des stratégies autofinancées. La seconde partie de la thèse traite des EDSRs non linéaires dirigées par la même classe de processus de Volterra. Les résultats principaux sont l’existence et l’unicité de la solution de l’EDSR dans un espace de fonctionnelles régulières du processus de Volterra et un théorème de comparaison qui porte sur les générateurs et les conditions terminales. Nous donnons deux preuves de l’existence et de l’unicité de la solution de l’EDSR, l’une basée sur l’EDP associée et l’autre sans référence à l’EDP, mais avec des méthodes probabilistes. Cette seconde preuve est techniquement difficile et, en raison de l’absence de propriétés de martingale dans le contexte des processus de Volterra, la preuve nécessite différentes normes sur l’espace de Hilbert sous-jacent défini par le noyau du processus de Volterra. Pour la construction de la solution, nous avons besoin de la notion de l’espérance quasi-conditionnelle, d’une formule de type Clark-Ocone et d’une autre formule d’Itô pour les processus de Volterra. Contrairement au cas classique des EDSR dirigées par le mouvement brownien ou brownien fractionnaire, une hypothèse sur le comportement du noyau est nécessaire pour l’existence et l’unicité de la solution de l’EDSR. Pour le mouvement brownien multifractionnaire, cette hypothèse est liée à la fonction de Hurst<br>This thesis treats of backward stochastic differential equations (BSDE) driven by a class of Gaussian Volterra processes that includes multifractional Brownian motion and multifractional Ornstein-Uhlenbeck processes. In the first part we study multidimensional BSDE with generators that are linear functions of the solution. By means of an Itoˆ formula for Volterra processes, a linear second order partial differential equation (PDE) with terminal condition is associated to the BSDE. Under an integrability condition on a functional of the second moment of the Volterra process in a neighbourhood of the terminal time, we solve the associated PDE explicitely and deduce the solution of the linear BSDE. We discuss an application in the context of self-financing trading stategies. The second part of the thesis treats of non-linear BSDE driven by the same class of Gaussian Volterra processes. The main results are the existence and uniqueness of the solution in a space of regular functionals of the Volterra process, and a comparison theorem for the solutions of BSDE. We give two proofs for the existence and uniqueness of the solution, one is based on the associated PDE and a second one without making reference to this PDE, but with probabilistic and functional theoretic methods. Especially this second proof is technically quite complex, and, due to the absence of mar- tingale properties in the context of Volterra processes, requires to work with different norms on the underlying Hilbert space that is defined by the kernel of the Volterra process. For the construction of the solution we need the notion of quasi-conditional expectation, a Clark-Ocone type formula and another Itoˆ formula for Volterra processes. Contrary to the more classical cases of BSDE driven by Brownian or fractional Brownian motion, an assumption on the behaviour of the kernel of the driv- ing Volterra process is in general necessary for the wellposedness of the BSDE. For multifractional Brownian motion this assumption is closely related to the behaviour of the Hurst function
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Cormier, Quentin. "Comportement en temps long d'un modèle champ moyen de neurones à décharge en interactions." Thesis, Université Côte d'Azur, 2021. http://www.theses.fr/2021COAZ4008.

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Nous étudions le comportement en temps long d'une équation différentielle stochastique (EDS) de type McKean-Vlasov, dirigée par une mesure de Poisson. En neurosciences, cette EDS modélise la dynamique du potentiel de membrane d'un neurone typique dans un grand réseau. Le modèle peut-être obtenu en considérant un réseau fini de neurones de type Intègre-Et-Tire généralisé et en prenant la limite où le nombre de neurones tend vers l'infini. Cette EDS est donc un modèle champ moyen de neurones à décharge.Nous étudions l'existence et l'unicité de la solution de cette EDS McKean-Vlasov et nous donnons ses mesures de probabilité invariantes. Si le paramètre d'interaction J est suffisamment petit, nous prouvons l'unicité et la stabilité globale de la mesure invariante. Pour un J quelconque cependant, il peut y avoir plusieurs mesures de probabilité invariantes. Nous donnons une condition suffisante assurant la stabilité locale d'une telle mesure invariante. Notre critère fait intervenir les zéros d'une fonction holomorphe associée à la solution stationnaire considérée. Lorsque tous les zéros sont de partie réelle négative, nous prouvons la stabilité. Nous donnons finalement des conditions générales suffisantes assurant l'existence de solutions périodiques par le biais d'une bifurcation de Hopf : pour un certain paramètre d'interaction critique J0, la probabilité invariante perd sa stabilité et des solutions périodiques apparaissent pour J suffisamment proche de J0. Pour obtenir ces résultats, nous combinons des méthodes probabilistes et déterministes. En particulier, dans cette analyse, un outil clé est l'équation intégrale de Volterra non linéaire satisfaite par le courant synaptique. Enfin, nous illustrons ces résultats par des exemples que l'on peut traiter de manière analytique. En outre, nous donnons des méthodes numériques pour approximer la solution de l'équation champ moyen et pour prédire numériquement les bifurcations<br>We study the long time behavior of a McKean-Vlasov stochastic differential equation (SDE), driven by a Poisson measure. In neuroscience, this SDE models the dynamics of the membrane potential of a typical neuron in a large network. The model can be derived by considering a finite network of generalized Integrate-And-Fire neurons and by taking the limit where the number of neurons goes to infinity. Hence the McKean-Vlasov SDE is a mean-field model of spiking neurons.We study existence and uniqueness of the solution this McKean-Vlasov SDE and describe its invariant probability measures. For small enough interaction parameter J, we prove uniqueness and global stability of the invariant measure. For J arbitrary large however, the invariant measures may not be unique. We give a sufficient condition ensuring the local stability of such a given invariant probability measure. Our criterion involves the location of the zeros of an explicit holomorphic function associated to the considered stationary solution. When all the zeros have negative real part, we prove that stability holds. We then give sufficient general conditions ensuring the existence of periodic solutions through a Hopf bifurcation: at some critical interaction parameter J0, the invariant probability losses its stability and periodic solutions appear for J close to J0. To obtain these results, we combine probabilistic and deterministic methods. In particular, a key tool in this analysis is a nonlinear Volterra Integral equation satisfied by the synaptic current.Finally, we illustrate these results with examples which are tractable analytically. Additionally, we give numerical methods to approximate the solution of the mean-field equation and to predict numerically the bifurcations
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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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Hernandez, Ramirez Miguel Camilo. "Me, Myself and I: time-inconsistent stochastic control, contract theory and backward stochastic Volterra integral equations." Thesis, 2021. https://doi.org/10.7916/d8-xtef-ay87.

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This thesis studies the decision-making of agents exhibiting time-inconsistent preferences and its implications in the context of contract theory. We take a probabilistic approach to continuous-time non-Markovian time-inconsistent stochastic control problems for sophisticated agents. By introducing a refinement of the notion of equilibrium, an extended dynamic programming principle is established. In turn, this leads to consider an infinite family of BSDEs analogous to the classical Hamilton–Jacobi–Bellman equation. This system is fundamental in the sense that its well-posedness is both necessary and sufficient to characterise equilibria and its associated value function. In addition, under modest assumptions, the existence and uniqueness of a solution is established. With the previous results in mind, we then study a new general class of multidimensional type-I backward stochastic Volterra integral equations. Towards this goal, the well-posedness of a system of an infinite family of standard backward stochastic differential equations is established. Interestingly, its well-posedness is equivalent to that of the type-I backward stochastic Volterra integral equation. This result yields a representation formula in terms of semilinear partial differential equation of Hamilton–Jacobi–Bellman type. In perfect analogy to the theory of backward stochastic differential equations, the case of Lipschitz continuous generators is addressed first and subsequently the quadratic case. In particular, our results show the equivalence of the probabilistic and analytic approaches to time-inconsistent stochastic control problems. Finally, this thesis studies the contracting problem between a standard utility maximiser principal and a sophisticated time-inconsistent agent. We show that the contracting problem faced by the principal can be reformulated as a novel class of control problems exposing the complications of the agent’s preferences. This corresponds to the control of a forward Volterra equation via constrained Volterra type controls. The structure of this problem is inherently related to the representation of the agent’s value function via extended type-I backward stochastic differential equations. Despite the inherent challenges of this class of problems, our reformulation allows us to study the solution for different specifications of preferences for the principal and the agent. This allows us to discuss the qualitative and methodological implications of our results in the context of contract theory: (i) from a methodological point of view, unlike in the time-consistent case, the solution to the moral hazard problem does not reduce, in general, to a standard stochastic control problem; (ii) our analysis shows that slight deviations of seminal models in contracting theory seem to challenge the virtues attributed to linear contracts and suggests that such contracts would typically cease to be optimal in general for time-inconsistent agents; (iii) in line with some recent developments in the time-consistent literature, we find that the optimal contract in the time-inconsistent scenario is, in general, non-Markovian in the state process X.
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Čoupek, Petr. "Stochastické integrály řízené isonormálními gaussovskými procesy a aplikace." Master's thesis, 2013. http://www.nusl.cz/ntk/nusl-328307.

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Stochastic Integrals Driven by Isonormal Gaussian Processes and Applications Master Thesis - Petr Čoupek Abstract In this thesis, we introduce a stochastic integral of deterministic Hilbert space valued functions driven by a Gaussian process of the Volterra form βt = t 0 K(t, s)dWs, where W is a Brownian motion and K is a square integrable kernel. Such processes generalize the fractional Brownian motion BH of Hurst parameter H ∈ (0, 1). Two sets of conditions on the kernel K are introduced, the singular case and the regular case, and, in particular, the regular case is studied. The main result is that the space H of β-integrable functions can be, in the strictly regular case, embedded in L 2 1+2α ([0, T]; V ) which corresponds to the space L 1 H ([0, T]) for the fractional Brownian mo- tion. Further, the cylindrical Gaussian Volterra process is introduced and a stochastic integral of deterministic operator-valued functions, driven by this process, is defined. These results are used in the theory of stochastic differential equations (SDE), in particular, measurability of a mild solution of a given SDE is proven.
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Book chapters on the topic "Backward stochastic Volterra integral equation"

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Nayak, Sukanta. "Numerical Solution of Fuzzy Stochastic Volterra-Fredholm Integral Equation with Imprecisely Defined Parameters." In Lecture Notes in Mechanical Engineering. Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-15-0287-3_9.

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"Backward stochastic Volterra integral equations." In AMS/IP Studies in Advanced Mathematics. American Mathematical Society, 2008. http://dx.doi.org/10.1090/amsip/042.2/17.

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Bender, Christian, and Stanislav Pokalyuk. "Discretization of backward stochastic Volterra integral equations." In Recent Developments in Computational Finance. WORLD SCIENTIFIC, 2012. http://dx.doi.org/10.1142/9789814436434_0005.

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Conference papers on the topic "Backward stochastic Volterra integral equation"

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Lv, Wen, and Cunxia Liu. "Backward stochastic Volterra integral equations driven by a Lévy process." In 2010 2nd International Conference on Education Technology and Computer (ICETC). IEEE, 2010. http://dx.doi.org/10.1109/icetc.2010.5529291.

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Wen, Xiaoxia, and Jin Huang. "A Numerical Method for Linear Stochastic Ito-Volterra Integral Equation Driven by Fractional Brownian Motion." In 2019 IEEE International Conference on Artificial Intelligence and Computer Applications (ICAICA). IEEE, 2019. http://dx.doi.org/10.1109/icaica.2019.8873448.

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Kumar, Pankaj, and S. Narayanan. "Nonlinear Stochastic Dynamics, Chaos and Reliability Analysis for Single Degree Freedom Model of a Rotor Blade." In ASME Turbo Expo 2008: Power for Land, Sea, and Air. ASMEDC, 2008. http://dx.doi.org/10.1115/gt2008-50736.

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In turbo machinery, the analysis of systems subjected to stochastic or periodic excitation becomes highly complex in the presence of nonlinearities. Nonlinear rotor systems exhibit a variety of dynamic behaviours that include periodic, quasi periodic, chaotic motion, limit cycle, jump phenomena etc. The transitional probability density function (pdf) for the random response of nonlinear systems under white or coloured noise excitation (delta-correlated) is governed by both the forward Fokker-Planck (FP) and backward Kolmogorov equations. This paper presents efficient numerical solution of the stationary and transient form of the forward FP equation corresponding to two state nonlinear systems by standard sequential finite element (FE) method using C0 shape functions and Crank-Nicholson time integration scheme. For computing the reliability of system, the transient FP equation is solved on the safe domain defined by D barriers using the FE method. New approach for numerical implementation of path integral (PI) method based on non-Gaussian transition pdf and Gauss-Legendre scheme is developed. In this study, PI solution procedure is employed to solve the FP equation numerically to examine some features of chaotic and stochastic response of nonlinear rotor systems.
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