Risk management of pension fund: A model for salary evolution

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