Linear Quadratic Stochastic Control Problems with Stochastic Terminal Constraint

@article{Bank2016LinearQS,
  title={Linear Quadratic Stochastic Control Problems with Stochastic Terminal Constraint},
  author={Peter Bank and Moritz Vo{\ss}},
  journal={SIAM J. Control. Optim.},
  year={2016},
  volume={56},
  pages={672-699}
}
We study a linear quadratic optimal control problem with stochastic coefficients and a terminal state constraint, which may be in force merely on a set with positive, but not necessarily full, probability. Under such a partial terminal constraint, the usual approach via a coupled system of a backward stochastic Riccati equation and a linear backward equation breaks down. As a remedy, we introduce a family of auxiliary problems parametrized by the supersolutions to this Riccati equation alone… 

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