Robust asset allocation under model ambiguity

A decision maker, when facing a decision problem, often considers several models to represent the outcomes of the decision variable considered. More often than not, the decision maker does not trust fully any of those models and hence displays ambiguity or model uncertainty aversion. In this PhD thesis, focus is given to the specific case of asset allocation problem under ambiguity faced by financial investors. The aim is not to find an optimal solution for the investor, but rather come up with a general methodology that can be applied in particular to the asset allocation problem and allows the investor to find a tractable, easy to compute solution for this problem, taking into account ambiguity. This PhD thesis is structured as follows: First, some classical and widely used models to represent asset returns are presented. It is shown that the performance of the asset portfolios built using those single models is very volatile. No model performs better than the others consistently over the period considered, which gives empirical evidence that: no model can be fully trusted over the long run and that several models are needed to achieve the best asset allocation possible. Therefore, the classical portfolio theory must be adapted to take into account ambiguity or model uncertainty. Many authors have in an early stage attempted to include ambiguity aversion in the asset allocation problem. A review of the literature is studied to outline the main models proposed. However, those models often lack flexibility and tractability. The search for an optimal solution to the asset allocation problem when considering ambiguity aversion is often difficult to apply in practice on large dimension problems, as the ones faced by modern financial investors. This constitutes the motivation to put forward a novel methodology easily applicable, robust, flexible and tractable. The Ambiguity Robust Adjustment (ARA) methodology is theoretically presented and then tested on a large empirical data set. Several forms of the ARA are considered and tested. Empirical evidence demonstrates that the ARA methodology improves portfolio performances greatly. Through the specific illustration of the asset allocation problem in finance, this PhD thesis proposes a new general methodology that will hopefully help decision makers to solve numerous different problems under ambiguity