For 2BSDEs with an exogenous random stopping time, the paper shows well-posedness and comparison under a shared conditional-density assumption, then links the equations to stochastic control and to a fully nonlinear PDE.
Adaptive robust control under model uncertainty.SIAM Journal on Control and Optimization, 57(2):925–946, 2019
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2BSDE with uncertain horizon and application to stochastic control in erratic environments
For 2BSDEs with an exogenous random stopping time, the paper shows well-posedness and comparison under a shared conditional-density assumption, then links the equations to stochastic control and to a fully nonlinear PDE.