Optimal consumption policies in illiquid markets

@article{Cretarola2008OptimalCP,
  title={Optimal consumption policies in illiquid markets},
  author={Alessandra Cretarola and Fausto Gozzi and Huy{\^e}n Pham and Peter Tankov},
  journal={Finance and Stochastics},
  year={2008},
  volume={15},
  pages={85-115}
}
We investigate optimal consumption policies in the liquidity risk model introduced by Pham and Tankov (Math. Finance 18:613–627, 2008). Our main result is to derive smoothness C1 results for the value functions of the portfolio/consumption choice problem. As an important consequence, we can prove the existence of the optimal control (portfolio/consumption strategy) which we characterize both in feedback form in terms of the derivatives of the value functions and as the solution of a second… 

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