A mean-CVaR-skewness portfolio optimization model based on asymmetric Laplace distribution

Zhao, Shangmei; Qi, Lü; Han, Liyan; Liu, Yong; Hu, Fei

doi:10.1007/s10479-014-1654-y

Cited by 40 publications

(26 citation statements)

References 18 publications

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“…The conditional value at risk theory (CVaR) is derived from VaR and refers to the conditional mean of loss exceeding VaR, reflecting the average potential loss that may be exceeded by the VaR value. The schematic diagram of CVaR is shown in Figure .…”

Section: Portfolio Optimization Theorymentioning

confidence: 99%

Trading risk control model of electricity retailers in multi‐level power market of China

Sun

2019

Energy Science & Engineering

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The decision-making and risk assessment of electricity purchase and sales is the key to adapt to the electricity market for independent electricity retailers in China. This research carried out the purchase and sales risks of electricity for electricity retailers and constructed the multi-level market purchase and sales combination optimization model. Based on the portfolio optimization theory, the conditional value at risk theory (CVaR) was proposed. Based on the evaluation index about the conditional risk profit and CVaR, electricity retailers purchase and sales combined optimization model has been constructed to explore the impact of purchase and sales risks by different factors in multi-level electricity market. The example analysis was carried out by the fixed spread mode and the linkage spread mode. The results showed that the mathematical mean and variance of market spread had great influence on the electricity purchase and sales combination. Especially in the mature electricity market, the mathematical mean of spread and risk in medium-and long-term market was smaller than that in spot market, and the best point of the electricity purchase and sales combination was shown on the smallest value of CVaR, while the electricity purchase and sales combination was optimal under limited conditions. K E Y W O R D Sconditional value at risk theory, electricity retailer, risk assessment, spread model

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Section: Portfolio Optimization Theorymentioning

confidence: 99%

Trading risk control model of electricity retailers in multi‐level power market of China

Sun

2019

Energy Science & Engineering

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“…We use Monte Carlo simulation to numerically test the estimation accuracy of our KEM in comparison to the EDM and CFM in CVaR hedge models. Among various probability distributions Zhao et al () argue that the ALD is suitable for describing the leptokurtosis, fat‐tail, and skewness characteristics of the return of a financial asset. In order to obtain the true CVaR under ALD, we first introduce two lemmas as follows.Lemma (Kotz et al ) Suppose that Y = ( Y 1 , Y 2 , … , Y d ) ′ ~ AL d ( μ , ∑) and w is a d × 1 real vector.…”

Section: Simulationmentioning

confidence: 99%

“…Then the random variable w ′ Y ~ AL 1 ( w ′ μ , w ′ ∑ w ). AL d ( μ , ∑) denotes d ‐dimensional ALD with mean μ and covariance matrix ∑ + μμ ′ .Lemma (Zhao et al ) If X ~ AL 1 ( μ , τ 2 ), then the CVaR of random variable X is

italicCVaR ((), X) = - \frac{τk}{\sqrt{2}} \ln \frac{α ((), 1 + k^{2})}{k^{2}} + \frac{τk}{\sqrt{2}}

, where

k = \frac{\sqrt{2} τ}{μ + \sqrt{μ^{2} + 2 τ^{2}}}

.…”

Section: Simulationmentioning

confidence: 99%

Nonparametric Kernel Method to Hedge Downside Risk

Huang

Ding

2019

Int Rev Finance

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We propose a nonparametric kernel estimation method (KEM) that determines the optimal hedge ratio by minimizing the downside risk of a hedged portfolio, measured by conditional value‐at‐risk (CVaR). We also demonstrate that the KEM minimum‐CVaR hedge model is a convex optimization. The simulation results show that our KEM provides more accurate estimations and the empirical results suggest that, compared to other conventional methods, our KEM yields higher effectiveness in hedging the downside risk in the weather‐sensitive markets.

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“…Rockafellar and Uryasev (2002) studied a broad description of methods for minimizing CVaR and its related optimization problems with CVaR constraints. The mean-CVaR (MC) framework has been investigated in recent research (Agarwal, Naik 2006;Ahmed 2006;Yao et al 2013;Dai, Wen 2014;Zhao et al 2015;Moazeni et al 2016). Roman et al (2007) investigated the mean-variance-CVaR (MVC) optimization model and concluded that the MVC model does not dismiss both MV and MC models but embeds them and that the resulting solutions are efficient for mean-variance-CVaR.…”

Section: Introductionmentioning

confidence: 99%

Scaled and Stable Mean-Variance-Evar Portfolio Selection Strategy With Proportional Transaction Costs

Mills

2017

Journal of Business Economics and Management

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This paper studies a portfolio optimization problem with variance and Entropic Value-at-Risk (evar) as risk measures. As the variance measures the deviation around the expected return, the introduction of evar in the mean-variance framework helps to control the downside risk of portfolio returns. This study utilized the squared l2-norm to alleviate estimation risk problems arising from the mean estimate of random returns. To adequately represent the variance-evar risk measure of the resulting portfolio, this study pursues rescaling by the capital accessible after payment of transaction costs. The results of this paper extend the classical Markowitz model to the case of proportional transaction costs and enhance the efficiency of portfolio selection by alleviating estimation risk and controlling the downside risk of portfolio returns. The model seeks to meet the requirements of regulators and fund managers as it represents a balance between short tails and variance. The practical implications of the findings of this study are that the model when applied, will increase the amount of capital for investment, lower transaction cost and minimize risk associated with the deviation around the expected return at the expense of a small additional risk in short tails.

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A mean-CVaR-skewness portfolio optimization model based on asymmetric Laplace distribution

Cited by 40 publications

References 18 publications

Trading risk control model of electricity retailers in multi‐level power market of China

Trading risk control model of electricity retailers in multi‐level power market of China

Nonparametric Kernel Method to Hedge Downside Risk

Scaled and Stable Mean-Variance-Evar Portfolio Selection Strategy With Proportional Transaction Costs

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