The dynamics of pension funds in a stochastic environment

The problem of studying the dynamic management of a pension fund for a sufficiently long time interval can be, in our opinion, faced, mainly with models which use either stochastic processes or simulations. The second approach was developed through Monte Carlo methods (Tomassetti, 1979) or with actuarial mean values (Manca, 1988; Manca & Volpe, 1988). The stochastic models to describe the phenomenon was developed in other papers (see Balcer & Sahin, 1983; De Dominicis & Manca, 1985). But up to now, while the simulation models can consider all the aspects of the complex phenomenon in study, the stochastic approach, in our opinion, was not sufficient to describe completely the dynamic management of a pension fund. This paper (Footnote§) contains the final results of a joint research started in 1981 with a paper by Carravetta et al. (1981), in particular it is a generalization of a study presented by De Dominicis & Manca (1985). For the purpose of the application we introduce another stochastic process, such that it is possible to consider the worker seniority in the model. The new process is a generalization of the Discrete-Time Non-Homogeneous Semi-Markov Reward Process (DTNHSMRP), already introduced by the same authors in 1985. It is evident that all the rewards depend on seniority and by introducing it in the study, pension fund management can be analysed in a more suitable way. Furthermore, it should be pointed out that the process we present in the paper is general and can be usefully applied in other problems as well (e.g. the reliability of repairable complex systems).