Pension Fund Management in a Stochastic Optimization Framework

The pension system has become more and more complex and structured all over Europe in the last decades. Because of the financial and social crisis, several countries implemented strong reforms in the state welfare in order to reduce the pension costs on the state budget balance. Furthermore, they allowed and encouraged the establishment of private pension facilities. We have to consider the three pillars. The first one concerns the state pension system. The second concerns the relationship between the employer and the employee. The third pillar consists in individual investment plans typically issued by insurance companies. This thesis analyzes a pension fund from the point of view of the three main actors involved: the pension plan provider, who decides the tactical allocation of the pension funds, the fund manager who takes care of the strategic investment problem, and the individual investor who faces the problem to allocate his/her savings in a retirement perspective. All these problems involve the analysis of a long-term choice and require to take into consideration some elements of uncertainty. Therefore, it is natural to face them using the instruments provided by Stochastic Programming. After a thorough review of the literature and a particular focus on the liability side of a pension fund, this thesis addresses the problem of a private pension plan sponsor who has to define the best pension funds for its members. This study is the first to face this problem from a quantitative point of view and proposes an innovative double step approach consisting of a cluster analysis of the pension fund population and of a portfolio optimization multistage stochastic program. The most important contribution relies on the introduction of the stochastic dominance in a real-life problem of an individual investor in a retirement perspective. Moreover, the proposed model considers a withdraw event allowed by the Italian pension system. The objective of the model is to minimize the Average Value at Risk Deviation measure (AV@RD) and to satisfy wealth goals. Three different wealth target formulations are considered. The first is a deterministic wealth target, i.e. a comparison between the accumulated average wealth and a fixed threshold. The second and the third are two stochastic dominance relations, first-order and second-order, which need to introduce a benchmark portfolio and then require the optimal portfolio to satisfy the stochastic dominance constraints with respect to the benchmark wealth.