  We discuss the role of integrated chance constraints (ICC) as quantitative
risk constraints in asset and liability management (ALM) for pension funds. We
define two types of ICC: the one period integrated chance constraint (OICC) and
the multiperiod integrated chance constraint (MICC). As their names suggest,
the OICC covers only one period whereas several periods are taken into account
with the MICC. A multistage stochastic linear programming model is therefore
developed for this purpose and a special mention is paid to the modeling of the
MICC.
  Based on a numerical example, we firstly analyse the effects of the OICC and
the MICC on the optimal decisions (asset allocation and contribution rate) of a
pension fund. By definition, the MICC is more restrictive and safer compared to
the OICC. Secondly, we quantify this MICC safety increase. The results show
that although the optimal decisions from the OICC and the MICC differ, the
total costs are very close, showing that the MICC is definitely a better
approach since it is more prudent.
