Robust Decision under Model Uncertainty

In the present paper, we propose a robust decision methodology, when there is some ambiguity concerning the potential future scenarii about decision variables. The decision maker considers several prior models for those scenarii and displays an ambiguity aversion against them. A two step ambiguity robust methodology is introduced, offering the advantage to be more tractable and easier to implement than the various approaches proposed in the literature. This methodology decomposes the ambiguity aversion into a model specific absolute ambiguity aversion and a relative ambiguity aversion across the set of different priors. The optimal solutions inferred by each prior are transformed through a generic absolute ambiguity function. Then, the optimal transformed solutions are mixed through a measure that reflects the relative ambiguity aversion of the decision maker for the different priors considered. We propose as an illustration a portfolio asset allocation theoretical and empirical example, based on our proposed methodology