Unknown Distribution: Maximin Criterion and Duality Approach

In this chapter, a case is studied in which the appreciation rates, volatilities, and their prior distributions are unknown. The optimal investment problem is stated as a problem with a maximin performance criterion. This criterion is to ensure that a strategy is found such that the utility minimum over all distributions of parameters is maximal. It is shown that the duality theorem holds for the problem. Thus, the maximin problem is reduced to the minimax problem. This minimax problem is computationally a much easier problem.