Insights for stochastic dominance extension in a multistage framework

Stochastic dominance has proven to be an efficient tool to compare random variables. This is particularly true in financial application when one wants to compare the outcome of an optimal strategy with the outcome of a given benchmark. A classical example is the Asset and Liability Management problem that aims at defining the optimal allocation of the assets of a Pension Fund. The recent literature proposes univariate stochastic dominance constraints to guarantee that the optimal strategy is able to stochastically dominate a benchmark portfolio. The purpose of this work is (1) to provide an extended literature of the recent findings about stochastic dominance in pension fund management and (2) to propose some hints to investigate new formulations of stochastic dominance that could be particularly important when multivariate random variables are involved and when one of their dimension is the time.