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Abstract
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It is often the case that optimization problems are formulated on a somewhat artificial domain such as bounded functions/random variables or those satisfying artificial integrability constraints. Although intended to simplify the treatment, this in fact results in major difficulties when trying to catch the optimal solution or when looking for a good dual system. A more reasonable approach is to let the problem itself induce the correct, most natural domain of optimization. These domains turn out to be Orlicz spaces, which are generalizations of L^p spaces. And we will see that if one is willing to go beyond the L^p world - at a mild cost - things may be surprisingly smooth. Part I. Introduction on Orlicz spaces. Part II. Applications to Math. Finance: portfolio optimization, non-linear pricing and risk measures. |
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