We propose a non-robust interpretation of the distributionally robust optimization (DRO) problem by relating the impact of uncertainties around the distribution on the impact of constraining the objective through tail probabilities. Our interpretation allows utility maximizers to figure out the size of the ambiguity set through parameters that are directly linked to the chance parameters  . We first show that  for general \phi-divergences, a DRO problem is asymptotically equivalent to a class of mean-deviation problems , where the ambiguity radius controls investor's risk preference . Based on this non-robust reformulation, we then show that when a boundedness constraint is added to the investment strategy. The DRO problem can be cast as a chance-constrained optimization (CCO) problem without distributional uncertainties . Without the boundedness constraint, the CCO problem is shown to perform uniformly better than the DRO problem, irrespective of the radius of the ambiguity set, the choice of the divergence measure, or the tail heaviness of the center distribution. Besides the widely-used Kullback-Leibler (KL) divergence which requires the distribution of the objective function to be exponentially bounded, our results apply to divergence measures that accommodate well heavy tail distribution such as the student t-distribution and the lognormal distribution . Comprehensive testings on synthetic data and real data are provided .
This paper provides a non-robust interpretation of the distributionally robust optimization (DRO) problem by relating the distributional uncertainties to the chance probabilities. Our analysis allows a decision-maker to interpret the size of the ambiguity set , which is often lack of business meaning, through the chance parameters constraining the objective function . We first show that , for general \phi-divergences, a DRO problem is asymptotically equivalent to a class of mean-deviation problems . These mean-deviation problems are not subject to uncertain distributions, and the ambiguity radius in the original DRO problem now plays the role of controlling the risk preference of the decision-maker. We then demonstrate that a DRO problem can be cast as a chance-constrained optimization (CCO) problem when a boundedness constraint is added to the decision variables . Without the boundedness constraint, the CCO problem is shown to perform uniformly better than the DRO problem, irrespective of the radius of the ambiguity set, the choice of the divergence measure, or the tail heaviness of the center distribution. Thanks to our high-order expansion result, a notable feature of our analysis is that it applies to divergence measures that accommodate well heavy tail distributions such as the student t-distribution and the lognormal distribution , besides the widely-used Kullback-Leibler (KL) divergence, which requires the distribution of the objective function to be exponentially bounded. Using the portfolio selection problem as an example, our comprehensive testings on multivariate heavy-tail datasets, both synthetic and real-world, shows that this business-interpretation approach is indeed useful and insightful .
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high-order expansion result, a notable feature of our analysis is that it applies
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, besides the widely-used Kullback-Leibler (KL) divergence, which requires the distribution of the objective function to be exponentially bounded. Using the portfolio selection problem as an example, our comprehensive testings on multivariate heavy-tail datasets, both synthetic and real-world, shows that this business-interpretation approach is indeed useful and insightful