2008/07/02 by Alessandra Cretarola, Fausto Gozzi, Cretarola, Alessandra +5
Mathematics · #35F20 #49K22 #49L25 #91B28 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:35F20 #msc:49K22 #msc:49L25 #msc:91B28
paper · pdf · doi:10.48550/arxiv.0807.0326
arxiv created 2008/07/02 · arxiv updated 2009/12/01
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.