Insurance companies and banks regularly have to face stress tests performed by regulatory instances. We extend the worst-case scenario approach to portfolio optimization for explicitly considering an investment decision problem that includes stress scenarios. Thus, the resulting optimal portfolios are already stress test prone by construction. Based on the concept of Knightian uncertainty, we assume that the stress scenarios can all happen, but make no probabilistic assumption if and  when they occur. A key challenge in our model is, that there are different types of stresses, and therefore there is the additional uncertainty of not knowing in which order the stresses occur. 

By defining the relative worst-case loss and introducing the concept of minimum constant portfolio processes, we generalize the traditional concepts of the indifference frontier and the indifference-optimality principle. We prove the existence of a minimum constant portfolio process that is optimal for the multi-stress worst-case problem. Via numerical solution of various worst-case problems with stresses, we demonstrate that an investor who chooses the worst-case optimal portfolio process may have a preference regarding the order of stresses, but there may also be stress scenarios where he/she is indifferent regarding the order and time of occurrence.