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We will consider optimal portfolio problems that include stress scenarios. As we do not make any probabilistic assumptions on the occurrence of the possible stresses, the usual continuous-time portfolio problem is turned into a min-max-problem that will be solved by a combination of optimality and indifference arguments. Further, we show how the uncertainty about the possible stresses can be combined with ambiguity about the market coefficients. Special cases of this combined uncertainty problem can still be solved.
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