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1. Backward stochastic differential equations (BSDEs). BSDEs are stochastic differential equations of Ito type on a time interval where the value of one unknown process is given at the final time. In the nonlinear case these equations were first addressed and solved by Pardoux and Peng in 1990. At present there is a large literature on this subject and its applications. A basic connection with partial differential equations (PDEs) is the fact that, by appropriately coupling a BSDE with another stochastic differential equation (called “forward”, since this time the initial value is specified), the resulting forward-backward system provides a representation formula for the solution to a nonlinear deterministic PDE. BSDEs can also be used to characterize optimal controls and the value function for a controlled stochastic differential equation. 2. Optimal control for stochastic PDEs. Optimal control problems for stochastic partial differential equations can be reformulated as control problems for stochastic evolution equations in an infinite-dimensional space, typically a Hilbert space. These, in turn, can be studied by different techniques,, for instance by addressing the Hamilton-Jacobi-Bellman equation of dynamic programming or by extending the connections with BSDEs to this infinite-dimensional framework. Linear-quadratic optimal control problems are usually addressed via a suitable Riccati equation. A difficult problem is to study such equations in cases when the solution is constrained to remain nonnegative, either because of a singular drift or by the occurrence of a reflection measure.