This paper deals with the optimal control of a stochastic delay differential equation arising in the management of a pension fund with surplus. The problem is approached by the tool of the representation in infinite dimension. We show the equivalence between the 1-dimensional delay problem and the associated infinite dimensional problem without delay. Then we prove that the value function is continuous in this infinite dimensional setting. These results represent a starting point for the investigation of the associated infinite dimensional Hamilton-Jacobi-Bellman equation in the viscosity sense and for approaching the problem by numerical algorithms
A stochastic control problem with delay arising in a pension fund model / S. Federico. - In: FINANCE AND STOCHASTICS. - ISSN 0949-2984. - 15:3(2011), pp. 421-459.
Titolo: | A stochastic control problem with delay arising in a pension fund model | |
Autori: | FEDERICO, SALVATORE (Primo) | |
Parole Chiave: | Pension funds ; Stochastic optimal control with delay ; Infinite dimensional Hamilton-Jacobi-Bellman equations ; Viscosity solutions | |
Settore Scientifico Disciplinare: | Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie Settore MAT/06 - Probabilita' e Statistica Matematica | |
Data di pubblicazione: | 2011 | |
Rivista: | ||
Tipologia: | Article (author) | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s00780-010-0146-4 | |
Appare nelle tipologie: | 01 - Articolo su periodico |