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

Saturday, May 19, 2012 - 1:30pm - 2:15pm
Keller 3-180
Mihai Sirbu (The University of Texas at Austin)
We revisit the optimal investment and consumption
model of Davis and Norman (1990) and Shreve and Soner (1994),
following a shadow-price approach similar to that of Kallsen and
Muhle-Karbe (2010). Making use of the completeness of the model
without transaction costs, we reformulate and reduce the
Hamilton-Jacobi-Bellman 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. The presentation is based on joint work with Jin Hyuk Choi and Gordan Zitkovic.
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