Analysis of Conditional Value-at-Risk for Newsvendor with Holding and Backorder Cost under Market Search

We consider a distribution system with one supplier and two retailers. For the two retailers, they face different demand and are both risk averse. We study a single period model which the supplier has ample goods and the retailers order goods separately. Market search is measured as the fraction of customers who unsatisfied with their ＂local＂ retailer due to stock-out, and search for the goods at the other retailer before leaving the system. We investigate how the retailers game for order quantity in a Conditional Value-at-Risk framework and study how risk averse degree, market search level, holding cost and backorder cost influence the optimal order strategies. Furthermore, we use uniform distribution to illustrate these results and obtain Nash equilibrium of order strategies.

Conditional Value-at-Risk for Random Immediate Reward Variables in Markov Decision Processes

We consider risk minimization problems for Markov decision processes. From a standpoint of making the risk of random reward variable at each time as small as possible, a risk measure is introduced using conditional value-at-risk for random immediate reward variables in Markov decision processes, under whose risk measure criteria the risk-optimal policies are characterized by the optimality equations for the discounted or average case. As an application, the inventory models are considered.

基于动态CoVar模型的商业银行系统性风险研究

文章构建了银行系统性风险的动态CoVar研究模型,旨为度量各个银行系统性风险的溢出价值,分析各银行系统性风险的溢出价值以及对银行整体的贡献情况。研究发现,工商银行、中国银行、建设银行和交通银行这4个大型国有制银行的风险溢出价值比其他股份制银行高,对整个银行系统造成的风险冲击较大,且与以往经验基本一致。

OPTIMAL DECISIONS WHEN BALANCING EXPECTED PROFIT AND CONDITIONAL VALUE-AT-RISK IN NEWSVENDOR MODELS

This paper investigates a risk-averse inventory model by balancing the expected profit and conditional value-at-risk （CVaR） in a newsvendor model setting. We find out that： i） The optimal order quantity is increasing in the shortage cost for both the CVaR only criterion and the tradeoff objective, ii） For the case of zero shortage cost, the optimal order quantity to the CVaR criterion or tradeoff objective is increasing in the selling price, respectively. However, it may not be monotonic in the selling price when incorporating a substantial shortage cost. Moreover, it may be larger or less than the risk-neutral solution, iii） Under the tradeoff objective function, although the optimal order quantity for the model without shortage cost is increasing in the weight put on the expected profit, this property may not be true in general for the model with a substantial shortage cost. Some numerical examples are conducted to verify our results and observations.

Optimization of water use structure and plantation benefit of unit water consumption using fractional programming and conditional value-at-risk model

For optimizing the water-use structure and increasing plantation benefit of unit water consumption,a multi-objective model for water resources utilization was established based on fractional programming(FP).Meanwhile,considering the stochasticity of water availability in the study area,the impact of the risk factor(λ)from a quantitative and qualitative perspective was analyzed.The chance-constrained programming(CCP)and conditional value-at-risk(CVaR)models were introduced into five important major grain production areas in Sanjiang Plain,and the crop planting structure under this condition was optimized.The results showed that,after optimization,overall benefit of cultivation increased from 42.07 billion Yuan to 42.47 billion Yuan,water consumption decreased from 15.90 billion m3 to 11.95 billion m3,the plantation benefit of unit water consumption increased from 2.65 Yuan/m3 to 3.55 Yuan/m3.Furthermore,the index of water consumption,benefit of cultivation and plantation benefit of unit water consumption showed an increasing trend with the increase of violation likelihood.However,through the quantification ofλfrom an economic perspective,the increasing ofλcould not enhance plantation benefit of unit water consumption significantly.

Real-time Risk-averse Dispatch of an Integrated Electricity and Natural Gas System via Condi-tional Value-at-risk-based Lookup-table Ap-proximate Dynamic Programming

The real-time risk-averse dispatch problem of an integrated electricity and natural gas system(IEGS)is studied in this paper.It is formulated as a real-time conditional value-at-risk(CVaR)-based risk-averse dis-patch model in the Markov decision process framework.Because of its stochasticity,nonconvexity and nonlinearity,the model is difficult to analyze by traditional algorithms in an acceptable time.To address this non-deterministic polynomial-hard problem,a CVaR-based lookup-table approximate dynamic programming(CVaR-ADP)algo-rithm is proposed,and the risk-averse dispatch problem is decoupled into a series of tractable subproblems.The line pack is used as the state variable to describe the impact of one period’s decision on the future.This facilitates the reduction of load shedding and wind power curtailment.Through the proposed method,real-time decisions can be made according to the current information,while the value functions can be used to overview the whole opti-mization horizon to balance the current cost and future risk loss.Numerical simulations indicate that the pro-posed method can effectively measure and control the risk costs in extreme scenarios.Moreover,the decisions can be made within 10 s,which meets the requirement of the real-time dispatch of an IEGS.Index Terms—Integrated electricity and natural gas system,approximate dynamic programming,real-time dispatch,risk-averse,conditional value-at-risk.

极端市场条件下我国金融体系系统性风险度量

在中国金融体制深化改革过程中,实时监测金融体系系统性风险的来源和累积过程非常必要。本文基于EVT-GARCH-Co VaR模型,利用2008—2013年股票市场数据,对极端市场条件下银行业、证券业和保险业内单个金融机构对中国金融体系系统性风险的贡献及其随时间变动的趋势进行了动态测算。主要研究结论包括:1国有商业银行引致的系统性风险最大,证券公司最小,股份制商业银行和保险公司介于二者之间;2研究期内所有金融机构对系统性风险的贡献都有上升,尤其是国有商业银行,但金融风险在证券、保险和银行业间的传染效应还比较微弱;3工行、中行、建行和人寿保险具有显著的系统重要性,应进行全面综合监管。其他金融机构需按微观审慎原则加强其自身风险管理。

尾部风险网络视角下的金融机构系统性风险贡献研究

金融机构的尾部风险关联模式及结构在金融系统性风险的形成演化中发挥重要作用。利用CoVaR指标及分位数回归方法,衡量金融机构之间的尾部风险传染强度,进而建立金融机构尾部风险动态网络。分析全连接网络及阈值法下过滤网络的全局和局部拓扑结构特征及其动态演化规律。建立面板数据回归模型,研究网络拓扑结构特征对金融机构系统性风险贡献的影响。实证研究发现,全连接网络的节点强度,能有效地衡量金融机构尾部风险传染强度及承受强度,并揭示其动态变化规律;各机构的尾部风险传染强度及承受强度排序匹配性存在差异;随着时间推进,各金融机构间的平均尾部风险传染路径缩短、系统性风险更易迅速累积和爆发;滞后一期的节点出度、节点入度及聚集系数越大,相应金融机构的系统性风险贡献越小;滞后一期的节点介数和节点接近中心度越大,相应金融机构的系统性风险贡献越大。研究结果对于金融机构的宏观审慎监管及系统性风险管理,提供了一个全新的基于金融机构尾部风险网络的视角。

风险管理的CVaR法及其在银行信用风险度量中的运用

作为银行主要风险的信用风险,在中国经济体制转轨时期表现得更加尖锐。鉴于现有测度体系对风险度量方法的研究和探索存在一定缺陷,笔者通过引入一种VaR的修正模型CVaR,率先将此方法运用于度量信用风险,建立了具体的数学模型,给出了求解方法及步骤,从而测算出银行贷款组合的CVaR值,得到了银行信用风险的预警值,并总结出目前CVaR风险测度法在我国运用的难度,最后提出建议。

相依结构、动态系统性风险测度与后验分析

本文利用Copula相依结构理论扩展和求解了现有的系统性风险测度Co VaR,以得到适用于不同类型常参数和时变参数Copula函数及不同分布假设的动态系统性风险测度。为了验证和评估模型设定的准确性与应用价值,本文构建了适用于该动态系统性风险测度Co VaR的严谨后验分析工具。除"无条件覆盖性"、"独立性"和"条件覆盖性"外,本文首次提出了"混合独立性"检验。基于我国14家上市商业银行的实证分析表明:我国上市商业银行与我国银行业之间的相依结构呈现多样化特征;无论是样本内还是样本外预测区间,本文的动态Copula-Co VaR模型能够有效地捕捉典型系统性风险事件;严谨的后验分析不仅需要检验系统性风险测度Co VaR,也需要检验条件事件的临界值VaR。

Strong Consistency of CVaR Optimal Estimator

Conditional Value-at-Risk (CVaR) is one of the commonly used risk measures. The paper shows that the optimal estimator of CVaR is strong consistency if the first-order moment of the population exists. We subsequently carry out numerical simulations to test the conclusion. We use the results to make an empirical analysis of Shenzhen A shares.

基于藤Copula的中美股市风险溢出研究

文章首先通过GARCH(1,1)-t模型对各主要股市指数收益率数据的边缘分布进行拟合,并提取降噪处理后的残差序列;接着采用极值理论中的GPD分布残差序列的尾部进行拟合;然后基于高维的C-Vine Copula模型确定各个收益率间的相依关系及联合分布;然后结合C-Vine Copula模型与条件风险(CoVaR)计算中美几个重要股市间的风险溢出效应。结果表明:美国股票市场尤其是纳斯达克市场对中国股市有强溢出效应,且主要是通过香港市场对内地市场进行风险传染。

Risk-Averse Two-Stage Distributionally Robust Economic Dispatch Model Under Uncertain Renewable Energy

With the participation of large quantities of renewable energy in power system operations,their volatility and intermittence increases the difficulties and challenges of power system economic scheduling.Considering the uncertainty of renewable energy generation,based on the distributionally robust optimization method,a two-stage economic dispatch model is proposed to minimize the total operation costs.In this paper,it is assumed that the fluctuating of renewable power generation follows the unknown probability distribution that is restricted in an ambiguity set,which is established by utilizing the first-order moment information of available historical data.Furthermore,the theory of conditional value-at-risk is introduced to transform the model into a tractable model,which we call robust counterpart formulation.Based on the stochastic dual dynamic programming method,an improved iterative algorithm is proposed to solve the robust counterpart problem.Specifically,the convergence optimum can be obtained by the improved iterative algorithm,which performs a forward pass and backward pass repeatedly in each iterative process.Finally,by comparing with other methods,the results on the modified IEEE 6-bus,118-bus,and 300-bus system show the effectiveness and advantages of the proposed model and method.

系统风险外溢、市场约束机制与银行股票回报率——基于CoVaR和时变条件β指标的研究

风险外溢意味着私人成本更多地由社会来承担,作为市场机制的自然反应,投资者是否会因此对系统风险外溢明显的银行股票要求更高收益率?本文借助DCC-MGARCH方法构建时变协方差系数CoVaR和时变条件β指标测度上市银行间的风险外溢程度,未发现"大而不能倒"的证据,大型银行反而在系统风险上升时会发挥"稳定器"效果;从周期性视角来看,银行的风险外溢具有顺周期特征,且风险外溢因子可以较好地解释银行股收益率的变化。市场约束机制可以对"负外部性"的银行提出更高的风险补偿要求,表现出一定的矫正机制,但对尾部风险定价失灵,仍需监管者实施流动性指标监管和稳健货币政策以规避系统危机。此外,ΔCoVaR指标能够较好地吸收和反映宏观变量信息,时变条件β指标则能够更好地吸收和反映资本充足率指标和流动性比率等银行层面信息,二者具有互补性。

Security Constrained Distributed Transaction Model for Multiple Prosumers

Massive access of renewable energy has prompted demand-side distributed resources to participate in regulation and improve flexibility of power systems. With large-scale access of massive, decentralized, and diverse distributed resources, demand-side market members have transformed from traditional “consumers” to “prosumers”. To explore the distributed transaction model of prosumers, in this paper, a multi-prosumer distributed transaction model is proposed, and the Conditional Value-at-Risk (CVaR) theory is applied to quantify potential risks caused by the stochastic characteristics inherited from renewable energy. First, a prosumer model under constraints of the distribution network including photovoltaic units, fuel cells, energy storage system, central air conditioning and flexible loads is established, and a multi-prosumer distributed transaction strategy is proposed to achieve power sharing among multiple prosumers. Second, a prosumer transaction model based on CVaR is constructed to measure risks inherited from the uncertainty of PV output within the prosumer and ensure safety of system operation in extreme PV output scenarios. Then, the alternating direction multiplier method (ADMM) is utilized to solve the constructed model efficiently. Finally, distributed transaction costs of prosumers are distributed fairly based on the generalized Nash equilibrium to maximize social benefits. Simulation results show the multi-prosumer distributed transaction mechanism established under the proposed generalized Nash equilibrium method can encourage power sharing among prosumers, increasing their own income and social benefits. Also, the CVaR can assist decision making of prosumers in weighting the risks and benefits, improving system resilience through energy management of prosumers.

产业链视角下我国房地产市场的风险溢出效应研究

房地产市场与其超长产业链的相关行业存在紧密、复杂的关联。本文运用DCC-GARCH模型测算了房地产与产业链代表性行业间的动态条件相关性,并在此基础上度量了房地产市场对相关行业的风险溢出效应。研究表明:第一,房地产市场与产业链各行业间均有较高的动态条件相关性,两者之间存在显著的风险溢出效应,风险溢出程度随着房地产市场波动程度的加剧而增强;第二,房地产市场与产业链各行业间的风险溢出效应及风险溢出程度变动规律基本一致,具有十分显著的趋同性,与该行业处在产业链的上游或下游无直接关系;第三,房地产行业的融资需求十分庞大,房地产市场风险暴露并大量外溢,将导致金融端的银行业与非银金融行业面临巨大的违约风险。

Operation Cost Optimization Method of Regional Integrated Energy System in Electricity Market Environment Considering Uncertainty

In the electricity market environment,the regional integrated energy system(RIES)can reduce the total operation cost by participating in electricity market transactions.However,the RIES will face the risk of load and electricity price uncertainties,which may make its operation cost higher than expected.This paper proposes a method to optimize the operation cost of the RIES in the electricity market environment considering uncertainty.Firstly,based on the operation cost structure of the RIES in the electricity market environment,the energy flow relationship of the RIES is analyzed,and the operation cost model of the RIES is built.Then,the electricity purchase costs of the RIES in the medium-and long-term electricity markets,the spot electricity market,and the retail electricity market are analyzed.Finally,considering the risk of load and electricity price uncertainties,the operation cost optimization model of the RIES is established based on conditional value-at-risk.Then it is solved to obtain the operation cost optimization strategy of the RIES.Verification results show that the proposed operation cost optimization method can reduce the operation cost of high electricity price scenario by optimizing the energy purchase and distribution strategy,constrain the risk of load and electricity price uncertainties,and help balance the risks and benefits.

A PRICE-SETTING NEWSVENDOR MODEL UNDER CVAR DECISION CRITERION WITH EMERGENCY PROCUREMENT

In this paper, we consider a newsvendor model in which a risk-averse manager faces a stochastic price-dependent demand in either an additive or a multiplicative form. An emergency purchase option is allowed after the realization of demand to satisfy the units that are short. By adopting Conditional value-at-risk （CVaR） as the decision criterion, we aim to investigate the optimal pricing and ordering decisions, and the effects of parameter changes in such a setting. We provide sufficient conditions for the uniqueness of the optimal policy for both demand models. We perforl~, comparative statics analysis to show how the optimal pricing and ordering decision behaves when changing parameters. We also compare our results with those of the newsvendor with a general utility function and with CVaR criterion under lost sales assumption. Our key results include： （i） For both demand models, the optimal selling price is decreasing in risk aversion. Hence, the optimal price of a risk-averse newsvendor is not greater than the optimal price of a risk-neutral newsvendor. （it） In contrary to the lost sales case, for the multiplicative demand model, the optimal order quantity may not be monotonic in risk aversion. Consequently, the optimal risk-averse order quantity may be lower or higher than the optimal risk- neutral counterpart. （iii） For the additive model, the optimal order quantity is strictly increasing in the emergency purchase price, while for the multiplicative model the optimal order quantity has no such a monotonic property. Some numerical examples are conducted to verify our claims and gain more insights about the risk-averse decision-making behaviors.

Comparative Analysis of Optimal Strategies with Two Purchase Modes under Different Risk-Averse Criterions

Consider a risk-averse newsvendor who has an option to purchase the units that are short at an emergency purchase price after demand is realized. We use the conditional value-at-risk （CVaR） as the risk measure. The aim of the study is to investigate the optimal ordering decision in such a setting under CVaR only and mean-CVaR criterions. For each case, we derive the closed-form optimal solution and perform comparative statics to show the monotonicity properties and other characteristics of the optimal decisions. We also compare our results with those of risk-neutral newsvendor.

Optimal Day-ahead Scheduling of Islanded Microgrid Considering Risk-based Reserve Decision

Due to the lack of support from the main grid,the intermittency of renewable energy sources(RESs)and the fluctuation of load will derive uncertainties to the operation of islanded microgrids(IMGs).It is crucial to allocate appropriate reserve capacity for the economic and reliable operation of IMGs.With the high penetration of RESs,it faces both economic and environmental challenges if we only use spinning reserve for reserve support.To solve these problems,a multi-type reserve scheme for IMGs is proposed according to different operation characteristics of generation,load,and storage.The operation risk due to reserve shortage is modeled by the conditional value-at-risk(CVaR)method.The correlation of input variables is considered for the forecasting error modeling of RES and load,and Latin hypercube sampling(LHS)is adopted to generate the random scenarios of the forecasting error,so as to avoid the dimension disaster caused by conventional large-scale scenario sampling approaches.Furthermore,an optimal day-ahead scheduling model of joint energy and reserve considering riskbased reserve decision is established to coordinate the security and economy of the operation of IMGs.Finally,the comparison of numerical results of different schemes demonstrate the rationality and effectiveness of the proposed scheme and model.