Portfolio selection under distributional uncertainty: A relative robust CVaR approach

Huang, Dashan; Zhu, Shushang; Fabozzi, Frank J.; Fukushima, Masao

doi:10.1016/j.ejor.2009.07.010

Cited by 114 publications

(54 citation statements)

References 37 publications

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“…Not surprisingly, the robust optimisation within the Portfolio Theory has its counterpart; among others, see El Ghaoui, Oks, and Oustry (2003) , Fukushima (2009) , Polak, Rogers, andSweeney (2010) , Zymler, Kuhn, and Rustem (2013) and Kakouris and Rustem (2014) . The worst-case and worst-case regret CVaRbased decisions in portfolio optimisation are discussed in Huang, Zhu, Fabozzi, and Fukushima (2010) . According to our knowledge, the optimal insurance contract problem under parameter/model uncertainty has been investigated only by Balbás, Balbás, Balbás, and Heras (2015) , where only the worst-case is investigated for a large class of risk measures that includes CVaR, but not VaR, and a particular choice of the uncertainty set of probability measures.…”

Section: Optimal Insurancementioning

confidence: 99%

Robust and Pareto Optimality of Insurance Contracts

et al. 2017

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a b s t r a c tThe optimal insurance problem represents a fast growing topic that explains the most efficient contract that an insurance player may get. The classical problem investigates the ideal contract under the assumption that the underlying risk distribution is known, i.e. by ignoring the parameter and model risks. Taking these sources of risk into account, the decision-maker aims to identify a robust optimal contract that is not sensitive to the chosen risk distribution. We focus on Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR)-based decisions, but further extensions for other risk measures are easily possible. The Worst-case scenario and Worst-case regret robust models are discussed in this paper, which have been already used in robust optimisation literature related to the investment portfolio problem. Closed-form solutions are obtained for the VaR Worst-case scenario case, while Linear Programming (LP) formulations are provided for all other cases. A caveat of robust optimisation is that the optimal solution may not be unique, and therefore, it may not be economically acceptable, i.e. Pareto optimal. This issue is numerically addressed and simple numerical methods are found for constructing insurance contracts that are Pareto and robust optimal. Our numerical illustrations show weak evidence in favour of our robust solutions for VaR-decisions, while our robust methods are clearly preferred for CVaR-based decisions.

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Section: Optimal Insurancementioning

confidence: 99%

Robust and Pareto Optimality of Insurance Contracts

et al. 2017

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“…Zhu and Fukushima [53] derive the worstcase CVaR portfolio optimization formulation for special cases of probability distributions, such as a box uncertainty set and a mixture distribution of some possible distribution scenarios. Huang et al [54] consider a related problem of portfolio selection under distributional uncertainty in a relative robust CVaR approach, where relative CVaR is related to the worst-case risk of the portfolio relative to a benchmark. Natarajan et al [55] derive the worst-case CVaR portfolio optimization problem for all distributions of uncertain returns with given moment information.…”

Section: Distributional Uncertaintymentioning

confidence: 99%

Robust Portfolio Selection

Pachamanova

2011

Wiley Encyclopedia of Operations Research and Management Science

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Robust portfolio selection is the process of allocating assets in such a way that the resulting portfolio is less sensitive to errors in the predicted behavior of the assets in the portfolio. Tools from robust and Bayesian statistics, simulation, and stochastic and robust optimization are often used to improve the stability, theoretical properties, and computational tractability of models for portfolio selection.

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“…For further details, see Huang et al (2010) and Asimit et al (2017). A Bayesian-type representation would be to average each possible model by allocating various weights to every single model according to the prior knowledge that the modeler might have.…”

Section: Problem Formulationmentioning

confidence: 99%

“…That is, the modeler does not know which probability model is appropriate and the optimal decision is produced by incorporating the risk measurements under all (but in a finite number) of the possible probability models. That is, the uncertainty set is constructed over a finite number of models as in Zhu and Fukushima (2009), Huang et al (2010) and Asimit et al (2017), where the first two papers considered a convex hull of the candidate models. This approach leads to a large uncertainty set that may be detrimental to the robust optimal decision and therefore, it would be better to consider a non-convex uncertainty set that is purely composed of the possible models as explained in Asimit et al (2017).…”

Section: Introductionmentioning

confidence: 99%

Optimal Robust Insurance with a Finite Uncertainty Set

Asimit

Xie

2018

SSRN Journal

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Decision-makers who usually face model/parameter risk may prefer to act prudently by identifying optimal contracts that are robust to such sources of uncertainty. In this paper, we tackle this issue under a finite uncertainty set that contains a number of probability models that are candidates for the "true", but unknown model. Various robust optimisation models are proposed, some of which are already known in the literature, and we show that all of them could be efficiently solved. The numerical experiments are run for various risk preference choices and it is found that for relatively large sample size, the modeler should focus on finding the best possible fit for the unknown probability model in order to achieve the most robust decision. If only small samples are available, then the modeler should consider two robust optimisation models, namely the Weighted Average Model or Weighted Worst-case Model, rather than focusing on statistical tools aiming to estimate the probability model. Amongst those two, the better choice of the robust optimisation model depends on how much interest the modeler puts on the tail risk when defining its objective function. These findings suggest that one should be very careful when robust optimal decisions are sought in the sense that the modeler should first understand the features of its 1 Corresponding author. Phone: +861064494702. Fax: +861064495024. 1 2 objective function and the size of the available data, and then to decide whether robust optimisation or statistical inferences is the best practical approach.

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Portfolio selection under distributional uncertainty: A relative robust CVaR approach

Cited by 114 publications

References 37 publications

Robust and Pareto Optimality of Insurance Contracts

Robust and Pareto Optimality of Insurance Contracts

Robust Portfolio Selection

Optimal Robust Insurance with a Finite Uncertainty Set

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