Untitled in english

Author(s)

Carlos Antonio Bueno Raymundo

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Escola Politécnica (EP/BC)
• Defense date: 1999-08-04

Examining board members

Oswaldo Luiz do Valle Costa; Ricardo Bianconi; Ricardo Paulino Marques; Marco Henrique Terra; Joao Bosco Ribeiro do Val

• Advisor: Oswaldo Luiz do Valle Costa

Abstract

This work is concerned with a family of stochastic processes named piecewise deterministic Markov processes (PDPs). Our main goal is to propose impulse control with continuous control on some local parameters of the PDP, namely the jump rate and transition measure. At first we will consider the problem of optimal shopping with continuous control on the jump rate and transition measure. Afterwords we extend the results for the impulsive control problem. Under this approach the variational and quasi variational inequalities are obtained in terms of the infinitesimal operator and its solution is equivalent to the fixed point of the first jump operator of the PDP. With this procedure we show that if the final cost is absolutely continuous along the trajectories, then the value function of the optimal stopping problem with continuous control will also be, the same happening with the value function of the impulse control problem. With these results we believe that we have extended and generalized the current results in the literature. (AU)