Optimal redeeming strategy of stock loans under drift uncertainty

We consider the optimal redeeming problem of stock loans under incomplete information presented by the uncertainty  trend of underlying stock. Due to the unavoidable estimating of the trend when making decisions, the HJB... [ view full abstract ]

We consider the optimal redeeming problem of stock loans under incomplete information presented by the uncertainty  trend of underlying stock. Due to the unavoidable estimating of the trend when making decisions, the HJB equation turns out to be a degenerate parabolic PDE which is very hard to obtain its regularity by standard approaches, making the problem distinguish from the existing ones without drift uncertainty. We provide a thorough and delicate probabilistic analysis to obtain the regularity and the optimal redeeming strategies. The latter is shown to be significantly different  for the bull and bear trends.