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 ...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.展开更多
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 va...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.展开更多
A new stochastic volatility（SV）method to estimate the conditional value at risk（CVaR）is put forward.Firstly,it makes use of SV model to forecast the volatility of return.Secondly,the Markov chain Monte Carlo（MCMC...A new stochastic volatility（SV）method to estimate the conditional value at risk（CVaR）is put forward.Firstly,it makes use of SV model to forecast the volatility of return.Secondly,the Markov chain Monte Carlo（MCMC）simulation and Gibbs sampling have been used to estimate the parameters in the SV model.Thirdly,in this model,CVaR calculation is immediate.In this way,the SV-CVaR model overcomes the drawbacks of the generalized autoregressive conditional heteroscedasticity value at risk（GARCH-VaR）model.Empirical study suggests that this model is better than GARCH-VaR model in this field.展开更多
The subset sum problem is a combinatorial optimization problem,and its complexity belongs to the nondeterministic polynomial time complete(NP-Complete)class.This problem is widely used in encryption,planning or schedu...The subset sum problem is a combinatorial optimization problem,and its complexity belongs to the nondeterministic polynomial time complete(NP-Complete)class.This problem is widely used in encryption,planning or scheduling,and integer partitions.An accurate search algorithm with polynomial time complexity has not been found,which makes it challenging to be solved on classical computers.To effectively solve this problem,we translate it into the quantum Ising model and solve it with a variational quantum optimization method based on conditional values at risk.The proposed model needs only n qubits to encode 2ndimensional search space,which can effectively save the encoding quantum resources.The model inherits the advantages of variational quantum algorithms and can obtain good performance at shallow circuit depths while being robust to noise,and it is convenient to be deployed in the Noisy Intermediate Scale Quantum era.We investigate the effects of the scalability,the variational ansatz type,the variational depth,and noise on the model.Moreover,we also discuss the performance of the model under different conditional values at risk.Through computer simulation,the scale can reach more than nine qubits.By selecting the noise type,we construct simulators with different QVs and study the performance of the model with them.In addition,we deploy the model on a superconducting quantum computer of the Origin Quantum Technology Company and successfully solve the subset sum problem.This model provides a new perspective for solving the subset sum problem.展开更多
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 ...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.展开更多
The global financial crisis （GFC） has placed the creditworthiness of banks under intense scrutiny. In particular, capital adequacy has been called into question. Current capital requirements make no allowance for ca...The global financial crisis （GFC） has placed the creditworthiness of banks under intense scrutiny. In particular, capital adequacy has been called into question. Current capital requirements make no allowance for capital erosion caused by movements in the market value of assets. This paper examines default probabilities of Swiss banks under extreme conditions using structural modeling techniques. Conditional Value at Risk （CVaR） and Conditional Probability of Default （CPD） techniques are used to measure capital erosion. Significant increase in Probability of Default （PD） is found during the GFC period. The market asset value based approach indicates a much higher PD than external ratings indicate. Capital adequacy recommendations are formulated which distinguish between real and nominal capital based on asset fluctuations.展开更多
随着能源系统互联化和能源交易市场化的高度发展,通过多综合能源系统(Multi-Integrated Energy System,MIES)的区域互联使综合能源系统(Integrated Energy System,IES)的能源利用率更高效、经济收益更可观。首先,文中构建多能源市场背...随着能源系统互联化和能源交易市场化的高度发展,通过多综合能源系统(Multi-Integrated Energy System,MIES)的区域互联使综合能源系统(Integrated Energy System,IES)的能源利用率更高效、经济收益更可观。首先,文中构建多能源市场背景下的MIES合作联盟的能量共享架构,建立MIES之间的电能和备用点对点(Point To Point,P2P)交易模型;其次,对新能源出力的不确定性,电价及备用价格波动风险进行分析,文中采用条件风险价值(Conditional Value-at-Risk,CVaR)理论,构建风险成本函数,并将其纳入综合运行成本模型;最后,选择交替方向乘子法(Alternating Direction Method Of Multipliers,ADMM)进行分布式求解,并通过算例分析验证模型的正确性与合理性,实现MIES运行成本的最小化和支付收益最大化,体现不同条件风险厌恶系数对MIES的影响。展开更多
针对当前省内分时电价机制忽略省级以上电力市场交易成本影响且忽视代理购电商购电成本传导风险的问题,提出一种考虑多级市场代理购电成本传导风险的分时电价定价模型。首先,基于购电成本最小化目标,设计多级市场购电决策模型;然后,采...针对当前省内分时电价机制忽略省级以上电力市场交易成本影响且忽视代理购电商购电成本传导风险的问题,提出一种考虑多级市场代理购电成本传导风险的分时电价定价模型。首先,基于购电成本最小化目标,设计多级市场购电决策模型;然后,采用概率场景描述现货市场价格预测偏差和用户响应预测偏差,并以条件风险价值(conditional value at risk,CVaR)作为传导风险评估指标,建立最大化传导上级市场购电成本变动和最小化代理购电商传导风险为目标的分时电价模型;最后,采用k-means和粒子群算法进行求解。算例分析结果表明,所提出的分时电价模型能更准确传导多级市场的成本与风险,向用户释放多级电力市场的综合价格信号,并能够为代理购电商提供多级市场交易情境下的风险分析。展开更多
基金Supported by the National Natural Science Foundation of China (70471034, A0324666)
文摘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.
文摘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.
基金Sponsored by the National Natural Science Foundation of China(70571010)
文摘A new stochastic volatility（SV）method to estimate the conditional value at risk（CVaR）is put forward.Firstly,it makes use of SV model to forecast the volatility of return.Secondly,the Markov chain Monte Carlo（MCMC）simulation and Gibbs sampling have been used to estimate the parameters in the SV model.Thirdly,in this model,CVaR calculation is immediate.In this way,the SV-CVaR model overcomes the drawbacks of the generalized autoregressive conditional heteroscedasticity value at risk（GARCH-VaR）model.Empirical study suggests that this model is better than GARCH-VaR model in this field.
基金supported by the National Key R&D Program of China(Grant No.2019YFA0308700)the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0301500)。
文摘The subset sum problem is a combinatorial optimization problem,and its complexity belongs to the nondeterministic polynomial time complete(NP-Complete)class.This problem is widely used in encryption,planning or scheduling,and integer partitions.An accurate search algorithm with polynomial time complexity has not been found,which makes it challenging to be solved on classical computers.To effectively solve this problem,we translate it into the quantum Ising model and solve it with a variational quantum optimization method based on conditional values at risk.The proposed model needs only n qubits to encode 2ndimensional search space,which can effectively save the encoding quantum resources.The model inherits the advantages of variational quantum algorithms and can obtain good performance at shallow circuit depths while being robust to noise,and it is convenient to be deployed in the Noisy Intermediate Scale Quantum era.We investigate the effects of the scalability,the variational ansatz type,the variational depth,and noise on the model.Moreover,we also discuss the performance of the model under different conditional values at risk.Through computer simulation,the scale can reach more than nine qubits.By selecting the noise type,we construct simulators with different QVs and study the performance of the model with them.In addition,we deploy the model on a superconducting quantum computer of the Origin Quantum Technology Company and successfully solve the subset sum problem.This model provides a new perspective for solving the subset sum problem.
基金Supported by the Social Science Foundation of the Ministry of Education of China (07JA630015)
文摘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.
文摘The global financial crisis （GFC） has placed the creditworthiness of banks under intense scrutiny. In particular, capital adequacy has been called into question. Current capital requirements make no allowance for capital erosion caused by movements in the market value of assets. This paper examines default probabilities of Swiss banks under extreme conditions using structural modeling techniques. Conditional Value at Risk （CVaR） and Conditional Probability of Default （CPD） techniques are used to measure capital erosion. Significant increase in Probability of Default （PD） is found during the GFC period. The market asset value based approach indicates a much higher PD than external ratings indicate. Capital adequacy recommendations are formulated which distinguish between real and nominal capital based on asset fluctuations.
文摘随着能源系统互联化和能源交易市场化的高度发展,通过多综合能源系统(Multi-Integrated Energy System,MIES)的区域互联使综合能源系统(Integrated Energy System,IES)的能源利用率更高效、经济收益更可观。首先,文中构建多能源市场背景下的MIES合作联盟的能量共享架构,建立MIES之间的电能和备用点对点(Point To Point,P2P)交易模型;其次,对新能源出力的不确定性,电价及备用价格波动风险进行分析,文中采用条件风险价值(Conditional Value-at-Risk,CVaR)理论,构建风险成本函数,并将其纳入综合运行成本模型;最后,选择交替方向乘子法(Alternating Direction Method Of Multipliers,ADMM)进行分布式求解,并通过算例分析验证模型的正确性与合理性,实现MIES运行成本的最小化和支付收益最大化,体现不同条件风险厌恶系数对MIES的影响。
文摘针对当前省内分时电价机制忽略省级以上电力市场交易成本影响且忽视代理购电商购电成本传导风险的问题,提出一种考虑多级市场代理购电成本传导风险的分时电价定价模型。首先,基于购电成本最小化目标,设计多级市场购电决策模型;然后,采用概率场景描述现货市场价格预测偏差和用户响应预测偏差,并以条件风险价值(conditional value at risk,CVaR)作为传导风险评估指标,建立最大化传导上级市场购电成本变动和最小化代理购电商传导风险为目标的分时电价模型;最后,采用k-means和粒子群算法进行求解。算例分析结果表明,所提出的分时电价模型能更准确传导多级市场的成本与风险,向用户释放多级电力市场的综合价格信号,并能够为代理购电商提供多级市场交易情境下的风险分析。
