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Seminário DMAT - Novembro 2014

05/11/2014 (14:00 - 15:00)
Instituto de Matemática

Nuno Azevedo - ESEIG-IPP & UM



Dynamic programming for a Markov-switching jump-diffusion

Data:  5 de Novembro de 2014 (QUARTA-FEIRA)
Hora: 14:00h
Lugar: Sala 13


We consider an optimal control problem with a deterministic finite horizon and state variable dynamics given by a Markov-switching jump–diffusion stochastic differential equation. Our main results extend the dynamic programming technique to this larger family of stochastic optimal control problems. More specifically, we provide a detailed proof of Bellman’s optimality principle (or dynamic programming principle) and obtain the corresponding Hamilton–Jacobi–Belman equation, which turns out to be a partial integro-differential equation due to the extra terms arising from the Lévy process and the Markov process. As an application of our results, we study a finite horizon consumption–investment problem for a jump–diffusion financial market consisting of one risk-free asset and one risky asset whose coefficients are assumed to depend on the state of a continuous time finite state Markov process. We provide a detailed study of the optimal strategies for this problem, for the economically relevant families of power utilities and logarithmic utilities. Trabalho conjunto com Diogo Pinheiro e G.-W. Weber.