Anticipated backward stochastic differential equations, studied the first time in 2007, are equations of the following type:{-dY t = f(t1, Y t1 , Z t1 , Y t+δ(t) , Z t+ζ(t) )dt Z t dB t1 , t ∈ [0, T ], Y t = ξ t1 ...Anticipated backward stochastic differential equations, studied the first time in 2007, are equations of the following type:{-dY t = f(t1, Y t1 , Z t1 , Y t+δ(t) , Z t+ζ(t) )dt Z t dB t1 , t ∈ [0, T ], Y t = ξ t1 , t ∈ [T, T + K], Z t = η t1 , t ∈ [T, T + K].In this paper, we give a necessary and sufficient condition under which the comparison theorem holds for multidimensional anticipated backward stochastic differential equations with generators independent of the anticipated term of Z.展开更多
In this paper we study multi-dimensional mean-field backward doubly stochastic differential equations(BDSDEs),that is,BDSDEs whose coefficients depend not only on the solution processes but also on their law.The first...In this paper we study multi-dimensional mean-field backward doubly stochastic differential equations(BDSDEs),that is,BDSDEs whose coefficients depend not only on the solution processes but also on their law.The first part of the paper is devoted to the comparison theorem for multi-dimensional mean-field BDSDEs with Lipschitz conditions.With the help of the comparison result for the Lipschitz case we prove the existence of a solution for multi-dimensional mean-field BDSDEs with an only continuous drift coefficient of linear growth,and we also extend the comparison theorem to such BDSDEs with a continuous coefficient.展开更多
In this paper the existence and uniqueness of the smallest g-supersolution for BSDE is discussed in the case without Lipschitz condition imposing on both constraint function and drift coefficient in the different meth...In this paper the existence and uniqueness of the smallest g-supersolution for BSDE is discussed in the case without Lipschitz condition imposing on both constraint function and drift coefficient in the different method from the one with Lipschitz condition.Then by considering (ξ,g) as a parameter of BSDE,and ( ξ α,g α) as a class of parameters for BSDE,where α belongs to a set A,for every α ∈A there exists a pair of solution { Y α,Z α } for the BSDE,the properties of sup α ∈A{ Y α } which is also a solution for some BSDE is studied.This result may be used to discuss optimal problems with recursive utility.展开更多
We prove a general existence and uniqueness result of solutions for a backward stochastic differential equation(BSDE)with a stochastic Lipschitz condition.We also establish a continuous dependence property and a compa...We prove a general existence and uniqueness result of solutions for a backward stochastic differential equation(BSDE)with a stochastic Lipschitz condition.We also establish a continuous dependence property and a comparison theorem for solutions to this type of BSDEs,thus strengthening existing results.展开更多
A new class of generalized backward doubly stochastic differential equations （GBDSDEs in short） driven by Teugels martingales associated with Levy process are investigated. We establish a comparison theorem which al...A new class of generalized backward doubly stochastic differential equations （GBDSDEs in short） driven by Teugels martingales associated with Levy process are investigated. We establish a comparison theorem which allows us to derive an existence result of solutions under continuous and linear growth conditions.展开更多
In this paper,the authors study a class of general mean-field BDSDEs whose coefficients satisfy some stochastic conditions.Specifically,the authors prove the existence and uniqueness theorem of solution under stochast...In this paper,the authors study a class of general mean-field BDSDEs whose coefficients satisfy some stochastic conditions.Specifically,the authors prove the existence and uniqueness theorem of solution under stochastic Lipschitz condition and obtain the related comparison theorem.Besides,the authors further relax the conditions and deduce the existence theorem of solutions under stochastic linear growth and continuous conditions,and the authors also prove the associated comparison theorem.Finally,an asset pricing problem is discussed,which demonstrates the application of the general meanfield BDSDEs in finance.展开更多
This paper is devoted to the L^p(p > 1) solutions of one-dimensional backward stochastic differential equations(BSDEs for short) with general time intervals and generators satisfying some non-uniform conditions in ...This paper is devoted to the L^p(p > 1) solutions of one-dimensional backward stochastic differential equations(BSDEs for short) with general time intervals and generators satisfying some non-uniform conditions in t and ω. An existence and uniqueness result,a comparison theorem and an existence result for the minimal solutions are respectively obtained, which considerably improve some known works. Some classical techniques used to deal with the existence and uniqueness of L^p(p > 1) solutions of BSDEs with Lipschitz or linear-growth generators are also developed in this paper.展开更多
文摘Anticipated backward stochastic differential equations, studied the first time in 2007, are equations of the following type:{-dY t = f(t1, Y t1 , Z t1 , Y t+δ(t) , Z t+ζ(t) )dt Z t dB t1 , t ∈ [0, T ], Y t = ξ t1 , t ∈ [T, T + K], Z t = η t1 , t ∈ [T, T + K].In this paper, we give a necessary and sufficient condition under which the comparison theorem holds for multidimensional anticipated backward stochastic differential equations with generators independent of the anticipated term of Z.
基金supported in part by the NSF of P.R.China(11871037,11222110)Shandong Province(JQ201202)+1 种基金NSFC-RS(11661130148,NA150344)111 Project(B12023)。
文摘In this paper we study multi-dimensional mean-field backward doubly stochastic differential equations(BDSDEs),that is,BDSDEs whose coefficients depend not only on the solution processes but also on their law.The first part of the paper is devoted to the comparison theorem for multi-dimensional mean-field BDSDEs with Lipschitz conditions.With the help of the comparison result for the Lipschitz case we prove the existence of a solution for multi-dimensional mean-field BDSDEs with an only continuous drift coefficient of linear growth,and we also extend the comparison theorem to such BDSDEs with a continuous coefficient.
文摘In this paper the existence and uniqueness of the smallest g-supersolution for BSDE is discussed in the case without Lipschitz condition imposing on both constraint function and drift coefficient in the different method from the one with Lipschitz condition.Then by considering (ξ,g) as a parameter of BSDE,and ( ξ α,g α) as a class of parameters for BSDE,where α belongs to a set A,for every α ∈A there exists a pair of solution { Y α,Z α } for the BSDE,the properties of sup α ∈A{ Y α } which is also a solution for some BSDE is studied.This result may be used to discuss optimal problems with recursive utility.
基金funded by the Graduate Innovation Program of China University of Mining and Technology(Grant No.2023WLKXJ121)the Postgraduate Research&Practice Innovation Program of Jiangsu Province.Shengjun Fan is supported by the National Natural Science Foundation of China(Grant No.12171471).
文摘We prove a general existence and uniqueness result of solutions for a backward stochastic differential equation(BSDE)with a stochastic Lipschitz condition.We also establish a continuous dependence property and a comparison theorem for solutions to this type of BSDEs,thus strengthening existing results.
基金supported by TWAS Research Grants to individuals (No. 09-100 RG/MATHS/AF/AC-IUNESCO FR: 3240230311)
文摘A new class of generalized backward doubly stochastic differential equations （GBDSDEs in short） driven by Teugels martingales associated with Levy process are investigated. We establish a comparison theorem which allows us to derive an existence result of solutions under continuous and linear growth conditions.
基金supported by the Zhiyuan Science Foundation of BIPT under Grant No.2024212National Key R&D Program of China under Grant No.2018YFA0703900+1 种基金the National Natural Science Foundation of China under Grant Nos.11871309 and 11371226Natural Science Foundation of Shandong Province under Grant No.ZR2020QA026.
文摘In this paper,the authors study a class of general mean-field BDSDEs whose coefficients satisfy some stochastic conditions.Specifically,the authors prove the existence and uniqueness theorem of solution under stochastic Lipschitz condition and obtain the related comparison theorem.Besides,the authors further relax the conditions and deduce the existence theorem of solutions under stochastic linear growth and continuous conditions,and the authors also prove the associated comparison theorem.Finally,an asset pricing problem is discussed,which demonstrates the application of the general meanfield BDSDEs in finance.
基金supported by the Fundamental Research Funds for the Central Universities(No.2017XKQY98)。
文摘This paper is devoted to the L^p(p > 1) solutions of one-dimensional backward stochastic differential equations(BSDEs for short) with general time intervals and generators satisfying some non-uniform conditions in t and ω. An existence and uniqueness result,a comparison theorem and an existence result for the minimal solutions are respectively obtained, which considerably improve some known works. Some classical techniques used to deal with the existence and uniqueness of L^p(p > 1) solutions of BSDEs with Lipschitz or linear-growth generators are also developed in this paper.
