Pension fund management with investment certificates and stochastic dominance

This paper considers an extension of the common asset universe of a pension fund to investment certificates. Investment certificates are a class of structured products particularly interesting for their special payoff structures and they are acquiring relevancy in the worldwide markets. In fact, some subclasses of certificates offer loss protection and show high liquidity and, thus, they can be very appreciated by pension fund managers. We consider the problem of a pension fund manager who has to implement an Asset and Liability Management model trying to achieve a long-term sustainability. Therefore, we formulate a multi-stage stochastic programming problem adopting a discrete scenario tree and a multi-objective function. We propose a technique to price highly structured products such as investment certificates on a discrete scenario tree. Finally, we solve the investment problem considering some investment certificate types both in term of payoff structure and protection level, and we test whether they are preferred or not to standard hedging contract such as put options. Moreover, we test the inclusion of first-order and second-order stochastic dominance constraints on multiple stages with respect to a benchmark portfolio. Numerical results show that the portfolio composition reacts to the inclusion of the stochastic dominance constraints, and that the optimal portfolio is efficiently able to reach several targets such as liquidity, returns, sponsor’s extraordinary contribution and funding gap.