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GENERAL COUPLED MEAN-FIELD REFLECTED FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS
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作者 李俊松 米超 +1 位作者 邢传智 赵德豪 《Acta Mathematica Scientia》 SCIE CSCD 2023年第5期2234-2262,共29页
In this paper we consider general coupled mean-field reflected forward-backward stochastic differential equations(FBSDEs),whose coefficients not only depend on the solution but also on the law of the solution.The firs... In this paper we consider general coupled mean-field reflected forward-backward stochastic differential equations(FBSDEs),whose coefficients not only depend on the solution but also on the law of the solution.The first part of the paper is devoted to the existence and the uniqueness of solutions for such general mean-field reflected backward stochastic differential equations(BSDEs)under Lipschitz conditions,and for the one-dimensional case a comparison theorem is studied.With the help of this comparison result,we prove the existence of the solution for our mean-field reflected forward-backward stochastic differential equation under continuity assumptions.It should be mentioned that,under appropriate assumptions,we prove the uniqueness of this solution as well as that of a comparison theorem for mean-field reflected FBSDEs in a non-trivial manner. 展开更多
关键词 refected backward stochastic differential equations forward-backward stochastic diferential equations comparison theorem Wasserstein metric MEAN-FIELD
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ANTICIPATED BACKWARD STOCHASTIC VOLTERRA INTEGRAL EQUATIONS WITH JUMPS AND APPLICATIONS TO DYNAMIC RISK MEASURES
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作者 缪亮亮 陈燕红 +1 位作者 肖肖 胡亦钧 《Acta Mathematica Scientia》 SCIE CSCD 2023年第3期1365-1381,共17页
In this paper, we focus on anticipated backward stochastic Volterra integral equations(ABSVIEs) with jumps. We solve the problem of the well-posedness of so-called M-solutions to this class of equation, and analytical... In this paper, we focus on anticipated backward stochastic Volterra integral equations(ABSVIEs) with jumps. We solve the problem of the well-posedness of so-called M-solutions to this class of equation, and analytically derive a comparison theorem for them and for the continuous equilibrium consumption process. These continuous equilibrium consumption processes can be described by the solutions to this class of ABSVIE with jumps.Motivated by this, a class of dynamic risk measures induced by ABSVIEs with jumps are discussed. 展开更多
关键词 anticipated backward stochastic Volterra integral equations comparison theorems dynamic risk measures
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Asymptotic Expansions of Backward Equations for Two-time-scale Markov Chains in Continuous Time
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作者 Dung Tien Nguyen 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2009年第3期457-476,共20页
This work develops asymptotic expansions for solutions of systems of backward equations of time- inhomogeneous Maxkov chains in continuous time. Owing to the rapid progress in technology and the increasing complexity ... This work develops asymptotic expansions for solutions of systems of backward equations of time- inhomogeneous Maxkov chains in continuous time. Owing to the rapid progress in technology and the increasing complexity in modeling, the underlying Maxkov chains often have large state spaces, which make the computa- tional tasks ihfeasible. To reduce the complexity, two-time-scale formulations are used. By introducing a small parameter ε〉 0 and using suitable decomposition and aggregation procedures, it is formulated as a singular perturbation problem. Both Markov chains having recurrent states only and Maxkov chains including also tran- sient states are treated. Under certain weak irreducibility and smoothness conditions of the generators, the desired asymptotic expansions axe constructed. Then error bounds are obtained. 展开更多
关键词 Markov chain backward equation two-time scale asymptotic expansion
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MULTI-DIMENSIONAL REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND THE COMPARISON THEOREM 被引量:5
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作者 吴臻 消华 《Acta Mathematica Scientia》 SCIE CSCD 2010年第5期1819-1836,共18页
In this article, we study the multi-dimensional reflected backward stochastic differential equations. The existence and uniqueness result of the solution for this kind of equation is proved by the fixed point argument... In this article, we study the multi-dimensional reflected backward stochastic differential equations. The existence and uniqueness result of the solution for this kind of equation is proved by the fixed point argument where every element of the solution is forced to stay above the given stochastic process, i.e., multi-dimensional obstacle, respectively. We also give a kind of multi-dimensional comparison theorem for the reflected BSDE and then use it as the tool to prove an existence result for the multi-dimensional reflected BSDE where the coefficient is continuous and has linear growth. 展开更多
关键词 backward stochastic differential equations comparison theorem local time
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Nonhomogeneous(H,Q)-Process:The Backward and Forward Equations
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作者 陈柳鑫 李俊平 《Journal of Southeast University(English Edition)》 EI CAS 2002年第2期180-183,共4页
As for the backward and forward equation of nonhomogeneous(H, Q) -processes,we proof them in a new way. On the base of that, this paper gives the direct computational formalfor one dimensional distribution of the nonh... As for the backward and forward equation of nonhomogeneous(H, Q) -processes,we proof them in a new way. On the base of that, this paper gives the direct computational formalfor one dimensional distribution of the nonhomogeneous(H, Q) -process. 展开更多
关键词 nonhomogeneous(H Q)-process backward and forward equations one-dimensional distribution
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Backward stochastic Volterra integral equations——a brief survey 被引量:2
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作者 YONG Jiong-min 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2013年第4期383-394,共12页
In this paper, we present a brief survey on the updated theory of backward stochas-tic Volterra integral equations (BSVIEs, for short). BSVIEs are a natural generalization of backward stochastic diff erential equati... In this paper, we present a brief survey on the updated theory of backward stochas-tic Volterra integral equations (BSVIEs, for short). BSVIEs are a natural generalization of backward stochastic diff erential equations (BSDEs, for short). Some interesting motivations of studying BSVIEs are recalled. With proper solution concepts, it is possible to establish the corresponding well-posedness for BSVIEs. We also survey various comparison theorems for solutions to BSVIEs. 展开更多
关键词 backward stochastic diff erential equation backward stochastic Volterra integral equation M-solution comparison theorem
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FULLY COUPLED FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH GENERAL MARTINGALE 被引量:1
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作者 李娟 《Acta Mathematica Scientia》 SCIE CSCD 2006年第3期443-450,共8页
The article first studies the fully coupled Forward-Backward Stochastic Differential Equations (FBSDEs) with the continuous local martingale. The article is mainly divided into two parts. In the first part, it consi... The article first studies the fully coupled Forward-Backward Stochastic Differential Equations (FBSDEs) with the continuous local martingale. The article is mainly divided into two parts. In the first part, it considers Backward Stochastic Differential Equations (BSDEs) with the continuous local martingale. Then, on the basis of it, in the second part it considers the fully coupled FBSDEs with the continuous local martingale. It is proved that their solutions exist and are unique under the monotonicity conditions. 展开更多
关键词 backward stochastic differential equations local martingale predictable representation property of martingale
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Forward-backward Stochastic Differential Equations and Backward Linear Quadratic Stochastic Optimal Control Problem 被引量:1
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作者 ZHANG DE-TAO 《Communications in Mathematical Research》 CSCD 2009年第5期402-410,共9页
In this paper, we use the solutions of forward-backward stochastic differential equations to get the optimal control for backward stochastic linear quadratic optimal control problem. And we also give the linear feedba... In this paper, we use the solutions of forward-backward stochastic differential equations to get the optimal control for backward stochastic linear quadratic optimal control problem. And we also give the linear feedback regulator for the optimal control problem by using the solutions of a group of Riccati equations. 展开更多
关键词 backward stochastic differential equations optimal control Riccati equation
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ON SOLUTIONS OF BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH JUMPS,WITH UNBOUNDED STOPPING TIMES AS TERMINAL AND WITH NON-LIPSCHITZ COEFFICIENTS,AND PROBABILISTIC INTERPRETATION OF QUASI-LINEAR ELLIPTIC TYPE INTEGRO-DIFFERENTIAL EQUATIO 被引量:1
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作者 司徒荣 王越平 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第6期659-672,共14页
The existence and uniqueness of solutions to backward stochastic differential equations with jumps and with unbounded stopping time as terminal under the non_Lipschitz condition are obtained. The convergence of soluti... The existence and uniqueness of solutions to backward stochastic differential equations with jumps and with unbounded stopping time as terminal under the non_Lipschitz condition are obtained. The convergence of solutions and the continuous dependence of solutions on parameters are also derived. Then the probabilistic interpretation of solutions to some kinds of quasi_linear elliptic type integro_differential equations is obtained. 展开更多
关键词 backward stochastic differential equations(BSDEs) with jumps unbounded stopping time adapted solutions convergence of solutions quasi_linear elliptic equations integro_differential operators.
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A Comparison Theorem for Solution of the Fully Coupled Backward Stochastic Differential Equations 被引量:1
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作者 郭子君College of Science Donghua University +5 位作者 Shanghai Science College South China Agriculture University Guangzhou associate professor 吴让泉 《Journal of Donghua University(English Edition)》 EI CAS 2004年第4期156-158,共3页
The comparison theorems of solutions for BSDEs in fully coupled forward-backward stochastic differential equations (FBSDEs) are studied in this paper, here in the fully coupled FBSDEs the forward SDEs are the same str... The comparison theorems of solutions for BSDEs in fully coupled forward-backward stochastic differential equations (FBSDEs) are studied in this paper, here in the fully coupled FBSDEs the forward SDEs are the same structure. 展开更多
关键词 The fully coupled backward stochastic differential equations Comparison theorem Stopping time
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A New Second Order Numerical Scheme for Solving Forward Backward Stochastic Differential Equations with Jumps 被引量:1
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作者 Hongqiang Zhou Yang Li Zhe Wang 《Applied Mathematics》 2016年第12期1408-1414,共8页
In this paper, we propose a new second order numerical scheme for solving backward stochastic differential equations with jumps with the generator  linearly depending on . And we theoretically prove that the conv... In this paper, we propose a new second order numerical scheme for solving backward stochastic differential equations with jumps with the generator  linearly depending on . And we theoretically prove that the convergence rates of them are of second order for solving  and of first order for solving  and  in  norm. 展开更多
关键词 Numerical Scheme Error Estimates backward Stochastic Differential equations
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Fractional backward Kolmogorov equations
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作者 张红 李国华 罗懋康 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第6期1-5,共5页
This paper derives the fractional backward Kolmogorov equations in fractal space-time based on the construction of a model for dynamic trajectories. It shows that for the type of fractional backward Kolmogorov equatio... This paper derives the fractional backward Kolmogorov equations in fractal space-time based on the construction of a model for dynamic trajectories. It shows that for the type of fractional backward Kolmogorov equation in the fractal time whose coefficient functions are independent of time, its solution is equal to the transfer probability density function of the subordinated process X(Sα (t)), the subordinator Sα (t) is termed as the inverse-time a-stable subordinator and the process X(τ) satisfies the corresponding time homogeneous Ito stochastic differential equation. 展开更多
关键词 anomalous diffusive fractional backward Kolmogorov equations subordinated process
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On existence and uniqueness of solutions to uncertain backward stochastic differential equations
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作者 FEI Wei-yin 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2014年第1期53-66,共14页
This paper is concerned with a class of uncertain backward stochastic differential equations (UBSDEs) driven by both an m-dimensional Brownian motion and a d-dimensional canonical process with uniform Lipschitzian c... This paper is concerned with a class of uncertain backward stochastic differential equations (UBSDEs) driven by both an m-dimensional Brownian motion and a d-dimensional canonical process with uniform Lipschitzian coefficients. Such equations can be useful in mod- elling hybrid systems, where the phenomena are simultaneously subjected to two kinds of un- certainties: randomness and uncertainty. The solutions of UBSDEs are the uncertain stochastic processes. Thus, the existence and uniqueness of solutions to UBSDEs with Lipschitzian coeffi- cients are proved. 展开更多
关键词 Uncertain backward stochastic differential equations(UBSDEs) canonical process existence and uniqueness Lipschitzian condition martingale representation theorem
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A variational formula for controlled backward stochastic partial differential equations and some application
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作者 MENG Qing-xin TANG Mao-ning 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2014年第3期295-306,共12页
An optimal control problem for a controlled backward stochastic partial differential equation in the abstract evolution form with a Bolza type performance functional is considered. The control domain is not assumed to... An optimal control problem for a controlled backward stochastic partial differential equation in the abstract evolution form with a Bolza type performance functional is considered. The control domain is not assumed to be convex, and all coefficients of the system are allowed to be random. A variational formula for the functional in a given control process direction is derived, by the Hamiltonian and associated adjoint system. As an application, a global stochastic maximum principle of Pontraygins type for the optimal controls is established. 展开更多
关键词 Variational formula stochastic evolution equation backward stochastic evolution equation stochastic maximum principle spike variation.
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A General Converse Comparison Theorem for Backward Stochastic Differential Equation with Non-lipschitz Coefficient
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作者 LU Min WANG Zeng-wu 《Chinese Quarterly Journal of Mathematics》 CSCD 2009年第4期568-573,共6页
In this article, we first introduce g-expectation via the solution of backward stochastic differential equation(BSDE in short) with non-Lipschitz coefficient, and give the properties of g-expectation, then we establ... In this article, we first introduce g-expectation via the solution of backward stochastic differential equation(BSDE in short) with non-Lipschitz coefficient, and give the properties of g-expectation, then we establish a general converse comparison theorem for backward stochastic differential equation with non-Lipschitz coefficient. 展开更多
关键词 backward stochastic differential equation with non-Lipschitz coefficient GENERATOR G-EXPECTATION converse comparison theorem.
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Monotone Iterative Technique for Duffie-Epstein Type Backward Stochastic Differential Equations
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作者 孙晓君 吴玥 《Journal of Donghua University(English Edition)》 EI CAS 2005年第3期136-138,共3页
For Duffle-Epstein type Backward Stochastic Differential Equations, the comparison theorem is proved. Based on the comparison theorem, by monotone iterative technique, the existence of the minimal and maximal solution... For Duffle-Epstein type Backward Stochastic Differential Equations, the comparison theorem is proved. Based on the comparison theorem, by monotone iterative technique, the existence of the minimal and maximal solutions of the equations are proved. 展开更多
关键词 backward Stochastic Differential equation Conditional Expectation Maximal Solution Minimal Solution
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A Limit Theorem for Solutions of Backward Stochastic Differential Equations
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作者 BAI Shan HE Jiao 《Journal of China University of Mining and Technology》 2005年第3期271-274,共4页
A limit theorem for solutions of backward stochastic differential equations was established. It extends aresult of Briand et al.
关键词 backward stochastic differential equation GENERATOR converse comparison theorem
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Research on problem about technology insurance pricing based on backward stochastic differential equation theory
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作者 Siyun Xu Zhuhua Han 《International Journal of Technology Management》 2015年第6期5-7,共3页
The development of Backward Stochastic Differential Equation Theory is just a thing happened in the past years. Although its development and application is far behind Forward Stochastic Differential Equation, its wide... The development of Backward Stochastic Differential Equation Theory is just a thing happened in the past years. Although its development and application is far behind Forward Stochastic Differential Equation, its wide application prospect on financial mathematics gets more and more attention. The meaning of Backward Stochastic Differential Equation is that change a already-known final (usually uncertain) goal into a present certain answer to make a present resolution. But Insurance Pricing happens to know the final result, it' s certain that the result is uncertain, that is to say, to get out of danger or not. And then make present insurance price according to the future uncertain result. The Insurance Pricing just follows the meaning of Backward Stochastic Differential Equation. Insurance Pricing itself is also a research field sprang up in past scores of years, because insurance pricing is the indisputable core of insurance work, and gets quite a few researchers' attention. This article adopts backward stochastic differential equation theory and do research on problem about technology insurance pricing. 展开更多
关键词 backward Stochastic Differential equation Theory Technology Insurance Pricing research.
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Uniqueness Problem for the Backward Differential Equation of a Continuous-State Branching Process
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作者 Pei Sen LI Zeng Hu LI 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2024年第8期1825-1836,共12页
The distributional properties of a multi-dimensional continuous-state branching process are determined by its cumulant semigroup,which is defined by the backward differential equation.We provide a proof of the asserti... The distributional properties of a multi-dimensional continuous-state branching process are determined by its cumulant semigroup,which is defined by the backward differential equation.We provide a proof of the assertion of Rhyzhov and Skorokhod(Theory Probab.Appl.,1970)on the uniqueness of the solutions to the equation,which is based on a characterization of the process as the pathwise unique solution to a system of stochastic equations. 展开更多
关键词 Continuous-state branching process MULTI-DIMENSIONAL backward differential equation stochastic equation generator
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Backward Doubly Stochastic Differential Equations with Stochastic Non-Lipschitz Coefficients
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作者 Si-yan XU Yi-dong ZHANG 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2024年第4期908-928,共21页
In this paper,we prove an existence and uniqueness theorem for backward doubly stochastic differential equations under a new kind of stochastic non-Lipschitz condition which involves stochastic and timedependent condi... In this paper,we prove an existence and uniqueness theorem for backward doubly stochastic differential equations under a new kind of stochastic non-Lipschitz condition which involves stochastic and timedependent condition.As an application,we use the result to obtain the existence of stochastic viscosity solution for some nonlinear stochastic partial differential equations under stochastic non-Lipschitz conditions. 展开更多
关键词 Stochastic non-Lipschitz coefficients backward doubly stochastic differential equation stochastic viscosity solutions
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