Optimal consumption policies in illiquid markets

We investigate optimal consumption policies in the liquidity risk model introduced in [5]. Our main result is to derive smoothness C 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-order ODE. Finally, numerical illustrations of the behavior of optimal consumption strategies between two trading dates are given.