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A stochastic control problem with delay arising in a pension fund model

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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 a representation in infinite dimension. We show the equivalence between the one-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. Also an example with complete solution of a simpler but similar problem is provided.

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Authors and Affiliations

  1. Scuola Normale Superiore, Piazza dei Cavalieri, 56125, Pisa, Italy

    Salvatore Federico

  2. Laboratoire de Probabilités et Modéles Aléatoires du CNRS (UMR 7599) de l’Université Paris Diderot, Paris VII, France

    Salvatore Federico

  3. Alma Research SAS, La Grande Arche Paroi Nord, 92044, Paris La Défense, France

    Salvatore Federico

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  1. Salvatore Federico
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Correspondence to Salvatore Federico.

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Dedicated to my father.

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Federico, S. A stochastic control problem with delay arising in a pension fund model. Finance Stoch 15, 421–459 (2011). https://doi.org/10.1007/s00780-010-0146-4

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