A realistic non-homogeneous stochastic pension fund model on scenario basis

As far as we know, this paper presents for the first time a general, rigorous and tractable stochastic evolution time model for pension fund called the discrete time non-homogeneous semi-Markov model, or in short, the DTNHSM pension fund model taking into account both economic, financial and demographic evolution factors so that it becomes a real-life model. The most important factors are: seniority, general age dependence, rate of inflation and salary lines. The model starts from a set of m states and each member of the fund is necessarily in one and only one of these states at each time epoch, for example each year. The main probabilistic assumption is that the successive state transitions together with transition time epochs constitute a two-dimensional non-homogeneous Markov additive process on which the state at any time epoch t is defined by the imbedded non-homogeneous semi-Markov process. Let us say that we introduce as other fundamental tool the concept of scenario both with strategic choices of the society and the one of economic scenario for the impact of the future economic environment. Finally let us mention that the problem of the statistical estimation problem of the two-dimensional semi-Markov kernel using internal and external data is solved.