Nonlinear portfolio selection using approximate parametric Value-at-Risk

Cui, Xueting; Zhu, Shushang; Sun, Xiaoling; Li, Duan

doi:10.1016/j.jbankfin.2013.01.036

Cited by 33 publications

(14 citation statements)

References 25 publications

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“…Castellacci and Siclari (2003) used the Cornish-Fisher method to calculate the first-order moments of the distribution of portfolio value changes. Cui et al (2013) studied Delta-Normal and Delta-Gamma-Theta-Normal VaR as well as parametric VaR asymptotic methods for nonlinear portfolios and discussed their computational effectiveness.…”

Section: Shrinkage Estimationmentioning

confidence: 99%

Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review

Sun¹,

Liu

et al. 2019

JRFM

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The literature on portfolio selection and risk measurement has considerably advanced in recent years. The aim of the present paper is to trace the development of the literature and identify areas that require further research. This paper provides a literature review of the characteristics of financial data, commonly used models of portfolio selection, and portfolio risk measurement. In the summary of the characteristics of financial data, we summarize the literature on fat tail and dependence characteristic of financial data. In the portfolio selection model part, we cover three models: mean-variance model, global minimum variance (GMV) model and factor model. In the portfolio risk measurement part, we first classify risk measurement methods into two categories: moment-based risk measurement and moment-based and quantile-based risk measurement. Moment-based risk measurement includes time-varying covariance matrix and shrinkage estimation, while moment-based and quantile-based risk measurement includes semi-variance, VaR and CVaR.

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Section: Shrinkage Estimationmentioning

confidence: 99%

Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review

Sun¹,

Liu

et al. 2019

JRFM

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“…Software packages such as CPLEX can be used to solve small-to-medium sized problems of this type. Recently, Cui et al (2013) propose a second-order cone programming method to solve a mean-VaR model when VaR is estimated by its first-order or second-order approximations. Bai et al (2012) propose a penalty decomposition method for probabilistically constrained programs including the mean-VaR problem.…”

Section: Introductionmentioning

confidence: 99%

Asset Allocation Under the Basel Accord Risk Measures

et al. 2013

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Financial institutions are currently required to meet more stringent capital requirements than they were before the recent financial crisis; in particular, the capital requirement for a large bank's trading book under the Basel 2.5 Accord more than doubles that under the Basel II Accord. The significant increase in capital requirements renders it necessary for banks to take into account the constraint of capital requirement when they make asset allocation decisions. In this paper, we propose a new asset allocation model that incorporates the regulatory capital requirements under both the Basel 2.5 Accord, which is currently in effect, and the Basel III Accord, which was recently proposed and is currently under discussion. We propose an unified algorithm based on the alternating direction augmented Lagrangian method to solve the model; we also establish the first-order optimality of the limit points of the sequence generated by the algorithm under some mild conditions. The algorithm is simple and easy to implement; each step of the algorithm consists of solving convex quadratic programming or * We are grateful to Steven Kou for his insightful comments to the paper. Zaiwen Wen was partially supported by the NSFC grant 11101274 and research fund (20110073120069)

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“…And the latter can be viewed as a VaR model with Eξ as the random variable. Recently, such a formulation has been studied in Cui et al (2013) and Wen et al (2013) in the context of the portfolio selection problem. In particular, Wen et al (2013) show that an alternating direction augmented Lagrangian method (ADM) can be applied to solve the problem very efficiently in that case.…”

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confidence: 99%

A Composite Risk Measure Framework for Decision Making Under Uncertainty

Qian

Wang

Wen

2018

J. Oper. Res. Soc. China

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In this paper, we present a unified framework for decision making under uncertainty. Our framework is based on the composite of two risk measures, where the inner risk measure accounts for the risk of decision given the exact distribution of uncertain model parameters, and the outer risk measure quantifies the risk that occurs when estimating the parameters of distribution. We show that the model is tractable under mild conditions. The framework is a generalization of several existing models, including stochastic programming, robust optimization, distributionally robust optimization, etc. Using this framework, we study a few new models which imply probabilistic guarantees for solutions and yield less conservative results comparing to traditional models. Numerical experiments are performed on portfolio selection problems to demonstrate the strength of our models. Qian, Wang and Wen: A Composite Risk Measure Framework for Decision Making under Uncertainty 2The existence of the uncertain parameters distinguishes the problem from ordinary optimization problems and has led to several decision making paradigms.One of the earliest attempts to deal with such decision making problems under uncertainty was proposed by Dantzig (1955), where it was assumed that the distribution of ξ is known exactly and the decision is chosen to minimize the expectation of H(x, ξ). Such an approach is called stochastic programming. Another approach named robust optimization initiated by Soyster (1973) supposes that all possible values of ξ lie within an uncertainty set, and the decision should be made to minimize the worst-case value of H(x, ξ). Stochastic programming and robust optimization models can be viewed as two extremes in the spectrum of available information in decision making under uncertainty. There are models in between these two extremes. For example, distributionally robust models (Scarf et al. 1958, Dupačová 1987, Delage and Ye 2010 take into account both the stochastic and the robust aspects, where the distribution of ξ is assumed to belong to a certain distribution set and the worst-case expectation of H(x, ξ) is minimized. There are also various models which minimize certain risk (Rockafellar and Uryasev 2000, Gaivoronski and Pflug 2005, etc.) or the worst-case risk (El Ghaoui et al. 2003, Zhu and Fukushima 2009, etc.) of H(x, ξ). We will present a more detailed review of these models in Section 2. In addition to the study of individual models, there have been recent efforts to seek connections between different models and to put forward more general models. For instance, Bertsimas and Brown (2009) and Natarajan et al. (2009) show that uncertainty sets can be constructed according to decision maker's risk preference, Bertsimas et al. (2014) propose a general framework for data-driven robust optimization, and Wiesemann et al. (2014) propose a framework for distributionally robust models. While some models have demonstrated their effectiveness in practice, there are still some ignored issues in the existing literature: ...

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Nonlinear portfolio selection using approximate parametric Value-at-Risk

Cited by 33 publications

References 25 publications

Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review

Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review

Asset Allocation Under the Basel Accord Risk Measures

A Composite Risk Measure Framework for Decision Making Under Uncertainty

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