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1. Set-valued backward stochastic differential equations

   https://doi.org/10.1214/22-AAP1896  

   Ararat, Çağın; Ma, Jin; Wu, Wenqian (October 2023, The Annals of Applied Probability)

   In this paper, we establish an analytic framework for studying setvalued backward stochastic differential equations (set-valued BSDE), motivated largely by the current studies of dynamic set-valued risk measures for multi-asset or network-based financial models. Our framework will make use of the notion of the Hukuhara difference between sets, in order to compensate the lack of “inverse” operation of the traditional Minkowski addition, whence the vector space structure in set-valued analysis. While proving the well-posedness of a class of set-valued BSDEs, we shall also address some fundamental issues regarding generalized Aumann–Itô integrals, especially when it is connected to the martingale representation theorem. In particular, we propose some necessary extensions of the integral that can be used to represent set-valued martingales with nonsingleton initial values. This extension turns out to be essential for the study of set-valued BSDEs. 

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2. Splitting scheme for backward doubly stochastic differential equations

   https://doi.org/10.1007/s10444-023-10053-z  

   Bao, Feng; Cao, Yanzhao; Zhang, He (August 2023, Advances in Computational Mathematics)
3. Data informed solution estimation for forward-backward stochastic differential equations

   https://doi.org/10.1142/S0219530520400102  

   Bao, Feng; Cao, Yanzhao; Yong, Jiongmin (May 2021, Analysis and Applications)

   null (Ed.)

   Forward-backward stochastic differential equation (FBSDE) systems were introduced as a probabilistic description for parabolic type partial differential equations. Although the probabilistic behavior of the FBSDE system makes it a natural mathematical model in many applications, the stochastic integrals contained in the system generate uncertainties in the solutions which makes the solution estimation a challenging task. In this paper, we assume that we could receive partial noisy observations on the solutions and introduce an optimal filtering method to make a data informed solution estimation for FBSDEs. 

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4. Forward backward doubly stochastic differential equations and the optimal filtering of diffusion processes

   https://doi.org/10.4310/CMS.2020.v18.n3.a3  

   Bao, Feng; Cao, Yanzhao; Han, Xiaoying (January 2020, Communications in Mathematical Sciences)
5. Strong solutions of forward–backward stochastic differential equations with measurable coefficients

   Peng Luo and Olivier Menoukeu-Pamen and Ludovic Tangpi (October 2021, Stochastic processes and their applications)