Optimal position targeting with stochastic linear-quadratic costs

@article{Ankirchner2015OptimalPT,
  title={Optimal position targeting with stochastic linear-quadratic costs},
  author={Stefan Ankirchner and Thomas Kruse},
  journal={Banach Center Publications},
  year={2015},
  volume={104},
  pages={9-24}
}
We consider the dynamic control problem of attaining a target position at a finite time T , while minimizing a linear-quadratic cost functional depending on the position and speed. We assume that the coefficients of the linearquadratic cost functional are stochastic processes adapted to a Brownian filtration. We provide a probabilistic solution in terms of two coupled backward stochastic differential equations possessing a singularity at the terminal time T . We verify optimality of the… 
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