Browsing by Subject "Conditional Value-at-Risk"

Now showing 1 - 4 of 4

Open Access
On robust portfolio and naïve diversification: mixing ambiguous and unambiguous assets
(Springer New York LLC, 2018) Paç, A. B.; Pınar, Mustafa Çelebi
Effect of the availability of a riskless asset on the performance of naïve diversification strategies has been a controversial issue. Defining an investment environment containing both ambiguous and unambiguous assets, we investigate the performance of naïve diversification over ambiguous assets. For the ambiguous assets, returns follow a multivariate distribution involving distributional uncertainty. A nominal distribution estimate is assumed to exist, and the actual distribution is considered to be within a ball around this nominal distribution. Complete information is assumed for the return distribution of unambiguous assets. As the radius of uncertainty increases, the optimal choice on ambiguous assets is shown to converge to the uniform portfolio with equal weights on each asset. The tendency of the investor to avoid ambiguous assets in response to increasing uncertainty is proven, with a shift towards unambiguous assets. With an application on the CVaR risk measure, we derive rules for optimally combining uniform ambiguous portfolio with the unambiguous assets.
Open Access
Risk-averse multi-class support vector machines
(2018-12) Karagöz, Ayşenur
A classification problem aims to identify the class of new observations based on the previous observations whose classes are known. It has many applications in a variety of disciplines such as medicine, finance and artificial intelligence. However, presence of outliers and noise in previous observations may have significant impact on the classification performance. Support vector machine (SVM) is a classifier introduced to solve binary classification problems under the presence of noise and outliers. In the literature, risk-averse SVM is shown to be more stable to noise and outliers compared to the original SVM formulations. However, we often observe more than two classes in real-life datasets. In this study, we aim to develop riskaverse multi-class SVMs following the idea of risk-averse binary SVM. We use risk measures, VaR and CVaR, to implement risk-aversion to multi-class SVMs. Since VaR constraints are nonconvex in general, SVMs with VaR constraints are more complex than SVMs with CVaR. Therefore, we propose a strong big-M formulation to solve multi-class SVM problems with VaR constraints efficiently. We also provide a computational study on the classification performance of the original multi-class SVM formulations and the proposed risk-averse formulations using artificial and real-life datasets. The results show that multi-class SVMs with VaR are more stable to outliers and noise compared to multi-class SVMs with CVaR, and both of them are more stable than the original formulations.
Open Access
Robust portfolio optimization with risk measures under distributional uncertainty
(2016-07) Paç, A. Burak
In this study, we consider the portfolio selection problem with different risk measures and different perspectives regarding distributional uncertainty. First, we consider the problem of optimal portfolio choice using the first and second lower partial moment risk measures, for a market consisting of n risky assets and a riskless asset, with short positions allowed. We derive closed-form robust portfolio rules minimizing the worst case risk measure under uncertainty of the return distribution given the mean/covariance information. A criticism levelled against distributionally robust portfolios is sensitivity to uncertainties or estimation errors in the mean return data, i.e., Mean Return Ambiguity. Modeling ambiguity in mean return via an ellipsoidal set, we derive results for a setting with mean return and distributional uncertainty combined. Using the adjustable robustness paradigm we extend the single period results to multiple periods in discrete time, and derive closed-form dynamic portfolio policies. Next, we consider the problem of optimal portfolio choice minimizing the Conditional Value-at-Risk (CVaR) and Value-at-Risk (VaR) measures under the minimum expected return constraint. We derive the optimal portfolio rules for the ellipsoidal mean return vector and distributional ambiguity setting. In the presence of a riskless asset, the robust CVaR and VaR measures, coupled with a minimum mean return constraint, yield simple, mean-variance efficient optimal portfolio rules. In a market without the riskless asset, we obtain a closed-form portfolio rule that generalizes earlier results, without a minimum mean return restriction. In the final problem, we have a change of perspective regarding uncertainty. Rather than the information on first and second moments, knowledge of a nominal distribution of asset returns is assumed, and the actual distribution is considered to be within a ball around this nominal distribution. The metric choice on the probability space is the Kantorovich distance. We investigate convergence of the risky investment to uniform portfolio when a riskless asset is available. While uniform investment to risky assets becomes optimal, it is shown that as the uncertainty radius increases, the total allocation to risky assets diminishes. Hence, as uncertainty increases, the risk averse investor is driven out of the risky market.
Open Access
Stochastic shelter site location under multi-hazard scenarios
(2018-06) Özbay, Eren
In some cases, natural disasters happen successively (e.g. a tsunami following an earthquake) in close proximity of each other, even if they are not correlated. This study locates shelter sites and allocates the a ected population to the established set of shelters by considering the aftershock(s) following the initial earthquake, via a three-stage stochastic mixed-integer programming model. In each stage, before the uncertainty, which is the number of a ected people, in the corresponding stage is resolved, shelters are established, and after the uncertainty is resolved, a ected population is allocated to the established set of shelters. To manage the inherent risk related to the uncertainty, conditional value-atrisk is utilized as a risk measure in allocation of victims to the established set of shelters. Computational results on the Istanbul dataset are presented to emphasize the necessity of considering secondary disaster(s), along with a heuristic method to improve the solution times and qualities. During these computational analyses, it is observed that the original single-objective model poses some obstacles in parameter selection. As in humanitarian operations, choosing parameters may cause con ict of interests and hence may be criticized, a multi-objective framework is developed with various formulations. Some generalizations regarding the performance and applicability of the developed formulations are discussed and nally, another heuristic for the multi-objective formulation is presented to tackle the curse of dimensionality and improve the solution times.