Strategic asset allocation and ALM for pension plans.

Summary This thesis focuses on strategic asset allocation models and their application to the management of financial reserves in pay-as-you-go pension plans, particularly those that are partially funded. The study of the usefulness of reserves for a pay-as-you-go system and a fortiori their management remains a little explored subject. Conventional assumptions are sometimes considered too restrictive to describe the complex evolution of reserves. New models and results are developed at three levels: the generation of economic scenarios (GSE), numerical optimization techniques and the choice of the optimal strategic allocation in an asset-liability management (ALM) context. Within the framework of economic and financial scenario generation, some performance measurement indicators of the GSE have been studied. In addition, improvements have been made compared to what is usually done in the construction of the GSE, particularly in the choice of the correlation matrix between the modeled variables. Concerning the calibration of the GSE, a set of tools allowing the estimation of its different parameters has been presented. This thesis has also paid particular attention to the numerical techniques for finding the optimum, which remain essential issues for the implementation of an allocation model. A reflection on a global optimization algorithm for a non-convex and noisy function has been developed. The algorithm allows to easily modulate, by means of two parameters, the reiteration of draws in a neighborhood of the discovered solution points, or conversely the exploration of the function in unexplored areas. We then present innovative ALM techniques based on stochastic programming. Their application has been developed for the choice of the strategic asset allocation of partially funded pay-as-you-go pension plans. A new methodology for the generation of the scenario tree was adopted at this level. Finally, a comparative study of the developed ALM model with the one based on the Fixed-Mix strategy was performed. Various sensitivity tests were also carried out to measure the impact of changes in certain key input variables on the results produced by our ALM model.