Alessandra Cretarola, Fausto Gozzi, Huyên Pham, Peter Tankov
Published 2008-07-02Version 1
We investigate optimal consumption policies in the liquidity risk model introduced in Pham and Tankov (2007). Our main result is to derive smoothness 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.
Approximating the value functions for stochastic differential games with the ones having bounded second derivatives
Utility maximization in incomplete markets
Some results on optimal stopping problems for one-dimensional regular diffusions
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