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Although the traditional CVaR-based portfolio methods are successfully used in practice, the size of a portfolio with thousands of assets makes optimizing them difficult, if not impossible to solve. In this article we introduce a large CVaR-based portfolio selection method by imposing weight constraints on the standard CVaR-based portfolio selection model, which effectively avoids extreme positions often emerging in traditional methods. We propose to solve the large CVaR-based portfolio model with weight constraints using penalized quantile regression techniques, which overcomes the difficulties of large scale optimization in traditional methods. We illustrate the method via empirical analysis of optimal portfolios on Shanghai and Shenzhen 300 (HS300) index and Shanghai Stock Exchange Composite (SSEC) index of China. The empirical results show that our method is efficient to solve a large portfolio selection and performs well in dispersing tail risk of a portfolio by only using a small amount of financial assets. AbstractAlthough the traditional CVaR-based portfolio methods are successfully used in practice, the size of a portfolio with thousands of assets makes optimizing them difficult, if not impossible to solve. In this article we introduce a large CVaR-based portfolio selection method by imposing weight constraints on the standard CVaR-based portfolio selection model, which effectively avoids extreme positions often emerging in traditional methods. We propose to solve the large CVaR-based portfolio model with weight constraints using penalized quantile regression techniques, which overcomes the difficulties of large scale optimization in traditional methods. We illustrate the method via empirical analysis of optimal portfolios on Shanghai and Shenzhen 300 (HS300) index and Shanghai Stock Exchange Composite (SSEC) index of China. The empirical results show that our method is efficient to solve a large portfolio selection and performs well in dispersing tail risk of a portfolio by only using a small amount of financial assets.

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Abstract:The increasing public attention on green products prompted firms and government to focus on the design and manufacturing of these products. This study focuses on a supply chain system that consists of three members, namely, supplier, manufacturer, and government, and then investigates the effects of government subsidies on social welfare and the profits of supply chain members. We utilize game and optimization theories to calculate and compare the optimal decisions and profits of players in the following scenarios: (i) the government provides a subsidy rate to the cost of manufacturer's greenness efforts (first subsidy policy); and (ii) the government grants a per unit subsidy to the manufacturer for the demand for green product (second subsidy policy). We also derive the necessary condition for the most effective subsidy policy that maximizes expected social welfare and profits. Our analysis derives the following findings: (i) under the first subsidy policy, the government tends to provide high subsidy rate to a manufacturer with low marginal profit; (ii) under the second subsidy policy, the government tends to offer low subsidy to a manufacturer with low marginal profit; and (iii) a government's selection of subsidy policy depends on the sensitivity of consumers to price.

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