| Summary: | In this paper, we propose a semi-Markov chain to model the salary levels of participants in<br />a pension scheme. The aim of the models is to understand the evolution in time of the salary of active<br />workers in order to implement it in the construction of the actuarial technical balance sheet. It is<br />worth mentioning that the level of the contributions in a pension scheme is directly proportional to<br />the incomes of the active workers; in almost all cases, it is a percentage of the worker’s incomes. As a<br />consequence, an adequate modeling of the salary evolution is essential for the determination of the<br />contributions paid to the fund and thus for the determination of the fund’s sustainability, especially<br />currently, when all jobs and salaries are subject to changes due to digitalization, ICT, innovation, etc.<br />The model is applied to a large dataset of a real compulsory Italian pension scheme of the first pillar.<br />The semi-Markovian hypothesis is tested, and the advantages with respect to Markov chain models<br />are assessed.
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