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
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