Abstract
In the context of expected utility maximization for utilities defined on the whole real line, we define a new class of admissible strategies in terms of dynamic bounds on losses under the historical measure . More precisely, the loss control is given by a -martingale which is compatible with the preferences of the investor. The main result is the Ansel–Stricker-type Lemma 3.3 which shows that the admissible strategies are supermartingales under all sigma-martingale measures with finite relative entropy, therefore, allowing for a duality theory for the optimization problem.
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