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 / Federico, Salvatore. - In: FINANCE AND STOCHASTICS. - ISSN 0949-2984. - STAMPA. - 15:(2011), pp. 421-459. [10.1007/s00780-010-0146-4]
A stochastic control problem with delay arising in a pension fund model
FEDERICO, SALVATORE
2011
Abstract
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 algorithmsFile | Dimensione | Formato | |
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