Optimal impulse control on an unbounded domain with nonlinear cost functions |
| |
Authors: | Stefano Baccarin Simona Sanfelici |
| |
Institution: | (1) Department of Applied Mathematics, University of Torino, Piazza Arbarello 8, 10122 Torino, Italy;(2) Department of Economics, University of Parma, Via J.F. Kennedy 6, 43100 Parma, Italy |
| |
Abstract: | In this paper we consider the optimal impulse control of a system which evolves randomly in accordance with a homogeneous
diffusion process in ℜ1. Whenever the system is controlled a cost is incurred which has a fixed component and a component which increases with the
magnitude of the control applied. In addition to these controlling costs there are holding or carrying costs which are a positive
function of the state of the system. Our objective is to minimize the expected discounted value of all costs over an infinite
planning horizon. Under general assumptions on the cost functions we show that the value function is a weak solution of a
quasi-variational inequality and we deduce from this solution the existence of an optimal impulse policy. The computation
of the value function is performed by means of the Finite Element Method on suitable truncated domains, whose convergence
is discussed.
Mathematics Subject Classification:
49J40, 60G40, 65N30 |
| |
Keywords: | Impulse control stochastic cash management quasi-variational inequalities finite element approximation |
本文献已被 SpringerLink 等数据库收录! |
|