semimartingales. We formulate this as a maximin problem that will be solved by duality methods. keywords: duality theory; risk … theory which we developed in this paper. Example 2.7 We consider a Black-Scholes model, i.e. S is given through dSt = St …] H. F¨ollmer and D. Kramkov. Optional decompositions under constraints. Probability Theory Related Fields, 109 …