A Defined Benefit Pension Fund ALM Model through Multistage Stochastic Programming

Abstract

We consider an asset-liability management (ALM) problem for a defined benefit pension fund (PF). The PF manager is assumed to follow a maximal fund valuation problem facing an extended set of risk factors: due to the longevity of the PF members, the inflation affecting salaries in real terms and future incomes, interest rates and market factors affecting jointly the PF liability and asset portfolio. The problem is formulated as a stochastic programming problem in discrete time and with a discrete set of relevant future economic and demographic scenarios. In real world applications, this class of decision problems under uncertainty leads to very large scale and complex management problems, due to pending regulatory constraints and the need to preserve the PF funding conditions. Dynamic stochastic programming is shown under such conditions to provide a natural and effective mathematical and numerical approach.