A family of fully implicit Milstein methods for stiff stochastic differential equations with multiplicative noise by Wang, Xiaojie, Gan, Siqing, Wang, Desheng

“…In this paper a family of fully implicit Milstein methods are introduced for solving stiff stochastic differential equations (SDEs). It is proved that the methods are convergent with strong order 1.0 for a class of SDEs. …”
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Characterization of stochastic equilibrium controls by the Malliavin calculus by Nguwi, Jiang Yu, Privault, Nicolas

Subjects: “…Backward Stochastic Differential Equation…”
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Numerical solution of the modified and non-Newtonian Burgers equations by stochastic coded trees by Nguwi, Jiang Yu, Privault, Nicolas

“…Our implementation uses neural networks that yield a functional space-time domain estimation, and includes numerical comparisons with the deep Galerkin (DGM) and deep backward stochastic differential equation (BSDE) methods.…”
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Robust time-inconsistent stochastic linear-quadratic control with drift disturbance by Han, Bingyan, Pun, Chi Seng, Wong, Hoi Ying

“…Under a general framework allowing random parameters, we derive a sufficient condition for equilibrium controls using the forward-backward stochastic differential equation approach. We also provide analytical solutions to mean-variance portfolio problems for various settings. …”
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A deep branching solver for fully nonlinear partial differential equations by Nguwi, Jiang Yu, Penent, Guillaume, Privault, Nicolas

“…Numerical experiments presented show that this algorithm can outperform deep learning approaches based on backward stochastic differential equations or the Galerkin method, and provide solution estimates that are not obtained by those methods in fully nonlinear examples.…”
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Nonlocal fully nonlinear parabolic differential equations arising in time-inconsistent problems by Lei, Qian, Pun, Chi Seng

“…Moreover, we reveal that the solution of a nonlocal fully nonlinear parabolic PDE is an adapted solution to a flow of second-order forward-backward stochastic differential equations.…”
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