Consistency of robust optimization with application to portfolio optimization
نویسنده
چکیده
In recent years the robust counterpart approach, introduced and made popular by Ben-Tal, Nemirovski and El Ghaoui, gained more and more interest among both academics and practitioners. However, to the best of our knowledge, only very few results on the relationship between the original problem instance and the robust counterpart have been established. This exposition aims at closing this gap by showing that the robust counterpart to an already well-posed problem remains well-posed under some mild regularity and uniqueness assumption on the solution of the original problem instance. As a consequence, sufficient conditions will be established under which the solution of the robust counterpart converges to the original solution, if the level of robustification is decreased to zero. Based on the well-posedness of the robust counterpart, it will also be demonstrated how any consistent plug-in estimator can be supplemented by a corresponding consistent robust estimator based on a proper choice of the confidence set of the plug-in estimator. Finally, this consistency result leads to a generalization of already known consistency results in the framework of mean-variance portfolio optimization.
منابع مشابه
A Robust Knapsack Based Constrained Portfolio Optimization
Many portfolio optimization problems deal with allocation of assets which carry a relatively high market price. Therefore, it is necessary to determine the integer value of assets when we deal with portfolio optimization. In addition, one of the main concerns with most portfolio optimization is associated with the type of constraints considered in different models. In many cases, the resulted p...
متن کاملRobustness-based portfolio optimization under epistemic uncertainty
In this paper, we propose formulations and algorithms for robust portfolio optimization under both aleatory uncertainty (i.e., natural variability) and epistemic uncertainty (i.e., imprecise probabilistic information) arising from interval data. Epistemic uncertainty is represented using two approaches: (1) moment bounding approach and (2) likelihood-based approach. This paper first proposes a ...
متن کاملPrimal and dual robust counterparts of uncertain linear programs: an application to portfolio selection
This paper proposes a family of robust counterpart for uncertain linear programs (LP) which is obtained for a general definition of the uncertainty region. The relationship between uncertainty sets using norm bod-ies and their corresponding robust counterparts defined by dual norms is presented. Those properties lead us to characterize primal and dual robust counterparts. The researchers show t...
متن کاملRobust Portfolio Optimization with risk measure CVAR under MGH distribution in DEA models
Financial returns exhibit stylized facts such as leptokurtosis, skewness and heavy-tailness. Regarding this behavior, in this paper, we apply multivariate generalized hyperbolic (mGH) distribution for portfolio modeling and performance evaluation, using conditional value at risk (CVaR) as a risk measure and allocating best weights for portfolio selection. Moreover, a robust portfolio optimizati...
متن کاملRobustness in portfolio optimization based on minimax regret approach
Portfolio optimization is one of the most important issues for effective and economic investment. There is plenty of research in the literature addressing this issue. Most of these pieces of research attempt to make the Markowitz’s primary portfolio selection model more realistic or seek to solve the model for obtaining fairly optimum portfolios. An efficient frontier in the ...
متن کاملRobust portfolio selection with polyhedral ambiguous inputs
Ambiguity in the inputs of the models is typical especially in portfolio selection problem where the true distribution of random variables is usually unknown. Here we use robust optimization approach to address the ambiguity in conditional-value-at-risk minimization model. We obtain explicit models of the robust conditional-value-at-risk minimization for polyhedral and correlated polyhedral am...
متن کامل