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.