Shadow prices and well-posedness in the problem of optimal investment and consumption with transaction costs

Jin Hyuk Choi, Carnegie Mellon University

Time: 3:35 pm, Room: LOV 201

Abstract: We revisit the optimal investment and consumption model of Davis and Norman (1990), following a shadow-price approach. We reformulate and reduce the HJB equation for this singular stochastic control problem to a non-standard free-boundary problem for a first-order ODE with an integral constraint. Having shown that the free boundary problem has a smooth solution, we use it to construct the solution of the original optimal investment/consumption problem in a self-contained manner and without any recourse to the dynamic programming principle. Furthermore, we provide an explicit characterization of model parameters for which the value function is finite.