Zobrazeno 1 - 10
of 270
pro vyhledávání: '"TANG, SHANJIAN"'
In this article, from the viewpoint of control theory, we discuss the relationships among the commonly used monotonicity conditions that ensure the well-posedness of the solutions arising from problems of mean field games (MFGs) and mean field type c
Externí odkaz:
http://arxiv.org/abs/2412.05189
In this paper, we study a class of degenerate mean field games (MFGs) with state-distribution dependent and unbounded functional diffusion coefficients. With a probabilistic method, we study the well-posedness of the forward-backward stochastic diffe
Externí odkaz:
http://arxiv.org/abs/2410.12404
This paper is devoted to a general solvability of multi-dimensional non-Markovian backward stochastic differential equations (BSDEs) with interactively quadratic generators. Some general structures of the generator $g$ are posed for both local and gl
Externí odkaz:
http://arxiv.org/abs/2410.08748
In this paper, we study the Cauchy problem for backward stochastic partial differential equations (BSPDEs) involving fractional Laplacian operator. Firstly, by employing the martingale representation theorem and the fractional heat kernel, we constru
Externí odkaz:
http://arxiv.org/abs/2409.07052
Publikováno v:
Comptes Rendus. Mathématique, Vol 358, Iss 2, Pp 227-235 (2020)
We prove a uniqueness result of the unbounded solution for a quadratic backward stochastic differential equation whose terminal condition is unbounded and whose generator $g$ may be non-Lipschitz continuous in the state variable $y$ and non-convex (n
Externí odkaz:
https://doaj.org/article/f00971d9acc94f35a490cefcb03f834d
Autor:
Tang, Shanjian, Zhou, Jianjun
In this article, a notion of viscosity solutions is introduced for fully nonlinear second order path-dependent partial differential equations in the spirit of [Zhou, Ann. Appl. Probab., 33 (2023), 5564-5612]. We prove the existence, comparison princi
Externí odkaz:
http://arxiv.org/abs/2405.06309
In several linear spaces of possibly unbounded endowments, we represent the dynamic concave utilities (hence the dynamic convex risk measures) as the solutions of backward stochastic differential equations (BSDEs) with unbounded terminal values, with
Externí odkaz:
http://arxiv.org/abs/2404.14059
Autor:
Tang, Shanjian, Zhou, Jianjun
Optimal control and the associated second-order path-dependent Hamilton-Jacobi-Bellman (PHJB) equation are studied for unbounded functional stochastic evolution systems in Hilbert spaces. The notion of viscosity solution without B-continuity is intro
Externí odkaz:
http://arxiv.org/abs/2402.15998
Autor:
Liang, Jiahao, Tang, Shanjian
In this paper, we investigate a semilinear stochastic parabolic equation with a linear rough term $du_{t}=\left[L_{t}u_{t}+f\left(t, u_{t}\right)\right]dt+\left(G_{t}u_{t}+g_{t}\right)d\mathbf{X}_{t}+h\left(t, u_{t}\right)dW_{t}$, where $\left(L_{t}\
Externí odkaz:
http://arxiv.org/abs/2401.16815
We study the well-posedness of a system of forward-backward stochastic differential equations (FBSDEs) corresponding to a degenerate mean field type control problem, when the diffusion coefficient depends on the state together with its measure and al
Externí odkaz:
http://arxiv.org/abs/2311.09138