Seminario di Fausto Gozzi (Dipartimento di Economia e Finanza - Università
LUISS Guido Carli)
Giovedi' 20 aprile 2017 - ore 10:30 - aula 200
Università Cattolica del Sacro cuore, Milano, Dipartimento di Discipline
matematiche, Finanza matematica ed Econometria
Via Necchi, 9 - Milano
TITLE: Optimal portfolio choice with path dependent labor income: The
infinite horizon case
ABSTRACT: We consider an infinite horizon portfolio choice problem with
borrowing constraints where an agent receives labor income that adjusts
slowly to financial market shocks. The novelty of the model is the
path-dependence of the wage income process, which leads to an infinite
dimensional stochastic optimal control problem.
We solve completely the problem, and find explicitly the optimal controls
in feedback form. This is possible because we are able to find an explicit
solution to the associated infinite dimensional Hamilton-Jacobi-Bellman
(HJB) equation, even if state constraints are present. To the best of our
knowledge, this is the first infinite dimensional generalization of
Merton's optimal portfolio problem where explicit solutions can be found.
The explicit solution allows us to study and discuss the behavior of
optimal solutions. We conclude, if there is time, by showing how the
solution strategy used here can be deployed to solve other problems, such
as the finite horizon version of the model.
Joint work with Enrico Biffis and Cecilia Prosdocimi
Tutti gli interessati sono invitati a partecipare.