A Non-homogeneous semi-Markov approach to financial choices

In the choices over the time between different sums the preference relation and the related indifference relation are of great interest in the development of the deterministic finance theory. In some previous paper we showed how is possible to face this kind of problem in a stochastic environment by means of Semi-Markov processes. In this paper we will enhance the previous results giving a larger weight to the non-homogeneous case that, in spite of the greatest difficulty, seems to be a more natural approach to the problem. In the paper will be also presented some new results on the numerical solution of this kind of processes. Furthermore an applicative example will be given.