This note analytically derives lower and upper bounds for Value-at-Risk and convex risk measures of a portfolio of weighted risks in the context of positive dependence.The bounds serve as extensions of the correspondi...This note analytically derives lower and upper bounds for Value-at-Risk and convex risk measures of a portfolio of weighted risks in the context of positive dependence.The bounds serve as extensions of the corresponding ones due to Bignozzi et al.(2015).Also, DU-spread of value-at-risk and expected shortfall of Bignozzi et al.(2015) are also improved in some particular cases.展开更多
An expectile can be considered a generalization of a quantile.While expected shortfall is a quantile-based risk measure,we study its counterpart-the expectile-based expected shortfall-where expectile takes the place o...An expectile can be considered a generalization of a quantile.While expected shortfall is a quantile-based risk measure,we study its counterpart-the expectile-based expected shortfall-where expectile takes the place of a quantile.We provide its dual representation in terms of a Bochner integral.Among other properties,we show that it is bounded from below in terms of the convex combination of expected shortfalls,and also from above by the smallest law invariant,coherent,and comonotonic risk measures,for which we give the explicit formulation of the corresponding distortion function.As a benchmark to the industry standard expected shortfall,we further provide its comparative asymptotic behavior in terms of extreme value distributions.Based on these results,we finally explicitly compute the expectile-based expected shortfall for selected classes of distributions.展开更多
虚拟电厂(virtual power plant,VPP)技术是解决可再生能源并网,帮助柔性负荷和电动汽车等需求侧资源参与电力市场交易的有效途径。文章分析了虚拟电厂中各成员特性和权责,拟定了虚拟电厂运营商对各成员基于价格弹性的调用合同,设计了包...虚拟电厂(virtual power plant,VPP)技术是解决可再生能源并网,帮助柔性负荷和电动汽车等需求侧资源参与电力市场交易的有效途径。文章分析了虚拟电厂中各成员特性和权责,拟定了虚拟电厂运营商对各成员基于价格弹性的调用合同,设计了包含主能量和辅助服务的日前实时两阶段电力市场交易流程。基于条件风险价值(conditional value at risk,CVaR)建立虚拟电厂风险厌恶模型,文章定量分析了市场交易下各成员的夏普利值和边际期望损失(marginal expected shortfall,MES),并据此给出虚拟电厂内部利益分配方法。算例说明了虚拟电厂能照顾各方利益,并定量分析了不同市场策略下的风险效益,其结果证明了所提方法的有效性。展开更多
In this paper,we apply the structural vector autoregression(SVAR)model to decompose the international oil price shock into oil supply shocks,aggregate demand shocks and oil-specific demand shocks,and then use the DCC-...In this paper,we apply the structural vector autoregression(SVAR)model to decompose the international oil price shock into oil supply shocks,aggregate demand shocks and oil-specific demand shocks,and then use the DCC-GARCH model to analyse the dynamic correlations between these three kinds of oil price shocks and the macroeconomic variables of several oil importing and exporting countries.To quantify the intensity of the effect of oil shocks on these variables,we propose a measure,conditional expectation(Co E),to capture the percent change of the economic variable under oil price shocks relative to the median state.The time-varying copula model is employed to estimate the proposed measure through time.The empirical results show that,for instance,the impacts of oil price shocks on macroeconomic variables are different in different periods,showing the time-varying characteristics.Additionally,the impacts of oil price shocks on macroeconomic variables show great differences and some similarities among different countries.Finally,we give some policy suggestions for these countries,in particular for China’s special results.展开更多
文摘This note analytically derives lower and upper bounds for Value-at-Risk and convex risk measures of a portfolio of weighted risks in the context of positive dependence.The bounds serve as extensions of the corresponding ones due to Bignozzi et al.(2015).Also, DU-spread of value-at-risk and expected shortfall of Bignozzi et al.(2015) are also improved in some particular cases.
基金This research is supported by National Science Foundation of China(Grant No.11971310,11671257)“Assessment of Risk and Uncertainty in Finance”(Grant No.AF0710020)from Shanghai Jiao Tong University.
文摘An expectile can be considered a generalization of a quantile.While expected shortfall is a quantile-based risk measure,we study its counterpart-the expectile-based expected shortfall-where expectile takes the place of a quantile.We provide its dual representation in terms of a Bochner integral.Among other properties,we show that it is bounded from below in terms of the convex combination of expected shortfalls,and also from above by the smallest law invariant,coherent,and comonotonic risk measures,for which we give the explicit formulation of the corresponding distortion function.As a benchmark to the industry standard expected shortfall,we further provide its comparative asymptotic behavior in terms of extreme value distributions.Based on these results,we finally explicitly compute the expectile-based expected shortfall for selected classes of distributions.
文摘虚拟电厂(virtual power plant,VPP)技术是解决可再生能源并网,帮助柔性负荷和电动汽车等需求侧资源参与电力市场交易的有效途径。文章分析了虚拟电厂中各成员特性和权责,拟定了虚拟电厂运营商对各成员基于价格弹性的调用合同,设计了包含主能量和辅助服务的日前实时两阶段电力市场交易流程。基于条件风险价值(conditional value at risk,CVaR)建立虚拟电厂风险厌恶模型,文章定量分析了市场交易下各成员的夏普利值和边际期望损失(marginal expected shortfall,MES),并据此给出虚拟电厂内部利益分配方法。算例说明了虚拟电厂能照顾各方利益,并定量分析了不同市场策略下的风险效益,其结果证明了所提方法的有效性。
基金the National Natural Science Foundation of China(71571008,71271015)。
文摘In this paper,we apply the structural vector autoregression(SVAR)model to decompose the international oil price shock into oil supply shocks,aggregate demand shocks and oil-specific demand shocks,and then use the DCC-GARCH model to analyse the dynamic correlations between these three kinds of oil price shocks and the macroeconomic variables of several oil importing and exporting countries.To quantify the intensity of the effect of oil shocks on these variables,we propose a measure,conditional expectation(Co E),to capture the percent change of the economic variable under oil price shocks relative to the median state.The time-varying copula model is employed to estimate the proposed measure through time.The empirical results show that,for instance,the impacts of oil price shocks on macroeconomic variables are different in different periods,showing the time-varying characteristics.Additionally,the impacts of oil price shocks on macroeconomic variables show great differences and some similarities among different countries.Finally,we give some policy suggestions for these countries,in particular for China’s special results.
