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- Ying Hu, Shanjian Tang
- 2007

In this paper, we study a multi-dimensional backward stochastic differential equation (BSDE) with oblique reflection, which is a BSDE reflected on the boundary of a special unbounded convex domain along an oblique direction, and which arises naturally in the study of optimal switching problem. The existence of the adapted solution is obtained by the… (More)

- Shanjian Tang
- SIAM J. Control and Optimization
- 2003

- Michael Kohlmann, Shanjian Tang
- SIAM J. Control and Optimization
- 2003

Multi-dimensional backward stochastic Riccati di erential equations (BSRDEs in short) are studied. A closed property for solutions of BSRDEs with respect to their coeÆcients is stated and is proved for general BSRDEs, which is used to obtain the existence of a global adapted solution to some BSRDEs. The global existence and uniqueness results are obtained… (More)

- Shanjian Tang
- SIAM J. Control and Optimization
- 2015

We are concerned with the linear-quadratic optimal stochastic control problem where all the coefficients of the control system and the running weighting matrices in the cost functional are allowed to be predictable (but essentially bounded) processes and the terminal state-weighting matrix in the cost functional is allowed to be random. Under suitable… (More)

We obtain the global existence and uniqueness result for a one-dimensional backward stochastic Riccati equation, whose generator contains a quadratic term of L (the second unknown component). This solves the one-dimensional case of BismutPeng's problem which was initially proposed by Bismut (1978) in the Springer yellow book LNM 649. We use an approximation… (More)

- Michael Kohlmann, Shanjian Tang
- SIAM J. Control and Optimization
- 2003

- Shanjian Tang, Xu Zhang
- SIAM J. Control and Optimization
- 2009

The BMOmartingale theory is extensively used to study nonlinear multi-dimensional stochastic equations (SEs) inRp (p ∈ [1,∞)) and backward stochastic differential equations (BSDEs) in Rp × Hp (p ∈ (1,∞)) and in R∞ × H∞, with the coefficients being allowed to be unbounded. In particular, the probabilistic version of Fefferman’s inequality plays a crucial… (More)

- Shanjian Tang, Wei Zhong, Hyeng Keun Koo
- SIAM J. Control and Optimization
- 2011

In this paper, the optimal switching problem is proposed for one-dimensional reflected backward stochastic differential equations (BSDEs, for short) where the generators, the terminal values, and the barriers are all switched with positive costs. The value process is characterized by a system of multi-dimensional reflected BSDEs with oblique reflection,… (More)

- Shanjian Tang, Zhou Yang
- SIAM J. Control and Optimization
- 2013

A Dynkin game is considered for stochastic differential equations with random coefficients. We first apply Qiu and Tang’s maximum principle for backward stochastic partial differential equations to generalize Krylov estimate for the distribution of a Markov process to that of a non-Markov process, and establish a generalized Itô-Kunita-Wentzell’s formula… (More)