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.
A stochastic control problem with delay arising in a pension fund model
S. FedericoPrimo
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 algorithmsPubblicazioni consigliate
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