An ALM model for pension funds using integrated chance constraints

Abstract

We discuss integrated chance constraints in their role of short-term risk constraints in a strategic ALM model for Dutch pension funds. The problem is set up as a multistage recourse model, with special attention for modeling short-term risk prompted by the development of new guidelines by the regulating authority for Dutch pension funds. The paper concludes with a numerical illustration of the importance of such short-term risk constraints.

Risk aversion in multistage stochastic programming: A modeling and algorithmic perspective

“…Using data generated according to the distributions described on page 57 of Haneveld et al (2010), we consider a four stage problem whose scenario tree has ten bifurcations per node, for a total of 1000 scenarios. There are four types of assets, from riskier (with higher returns) to safer (lower returns): stocks, real state, bonds and cash.…”

“…We illustrate the applicability of ECRMs by using it in a pension fund problem proposed by Haneveld et al (2010). This numerical example illustrates two important aspects of ECRMs: first, the simplicity of implementation when the CVaR is used as an ingredient for the ECRM-indeed, we use standard software for risk-neutral multistage programs available in the literature to solve the corresponding risk-averse problem.…”

“…We illustrate the application of the E-CVaR to a pension fund problem described in Haneveld et al (2010). The problem is a defined benefit model in which a large Dutch…”

“…In the original paper the authors do not include any risk measure in the objective function: the objective is to minimize the expected value of the sum, for all stages, of remedial contributions and contribution rates for the participants. A full description of the model can be found in Haneveld et al (2010).…”

ALM models based on second order stochastic dominance

“…In addition, they require binary variables to be implemented, thus increasing computational complexity. An alternative SP approach is the Integrated Chance Constraint Programming (ICCP), proposed by Klein Haneveld (1986) and Klein Haneveld and Van Der Vlerk (2006), used in the context of ALM by Klein Haneveld et al (2010). With the above notations, an ICCP constraint requires that E[max{λL − A, 0}] ≤ θ , where θ is the maximum amount of average underfunding that a decision maker accepts.…”