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
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
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
随着可再生能源占比的持续增长与负荷中心电网峰谷差日益显著,分布式资源的开发与利用已成为研究热点,催生了产消者及负荷聚合商等新兴主体的出现。鉴于各利益主体拥有差异化的优化目标,构建了以负荷聚合商作为售电主体参与电力市场的...随着可再生能源占比的持续增长与负荷中心电网峰谷差日益显著,分布式资源的开发与利用已成为研究热点,催生了产消者及负荷聚合商等新兴主体的出现。鉴于各利益主体拥有差异化的优化目标,构建了以负荷聚合商作为售电主体参与电力市场的双层优化模型。首先,引入产消者需求响应机制,形成主从博弈框架并利用Karush-Kuhn tucker(KKT)条件,将双层模型的下层目标及约束整合至上层,实现统一求解。其次,引入条件风险价值(conditional value at risk,CVaR)方法以量化电价不确定性对负荷聚合商购电策略的风险影响。最后,通过实证算例分析得出:该机制能有效激励用户侧可调资源参与系统灵活性调节,促进负荷聚合商与产消者间的双赢合作格局。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
为进一步提升综合能源系统环境效益,减少新能源出力不确定性所带来的潜在风险,提出了计及条件风险价值(conditional value at risk,CVaR)以及阶梯碳交易的综合能源系统优化调度模型。考虑到系统风电和光伏出力不确定性可能带来的影响,...为进一步提升综合能源系统环境效益,减少新能源出力不确定性所带来的潜在风险,提出了计及条件风险价值(conditional value at risk,CVaR)以及阶梯碳交易的综合能源系统优化调度模型。考虑到系统风电和光伏出力不确定性可能带来的影响,采用条件风险价值量度不确定性带来的潜在风险,并将碳捕获技术、电转气设备以及阶梯式碳交易机制引入系统调度模型,构建了综合考虑系统运行成本和碳交易成本的优化调度目标函数,由于所建立模型为混合整数规划问题,采用CPLEX求解器进行求解,设置4种场景进行验证分析,算例表明所提模型可有效减少二氧化碳排放,在兼顾经济性和环境性的同时引入CVaR,可避免由于忽略风光不确定性所带来的较为乐观的调度结果,使系统最终调度结果更为合理。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.
文摘随着可再生能源占比的持续增长与负荷中心电网峰谷差日益显著,分布式资源的开发与利用已成为研究热点,催生了产消者及负荷聚合商等新兴主体的出现。鉴于各利益主体拥有差异化的优化目标,构建了以负荷聚合商作为售电主体参与电力市场的双层优化模型。首先,引入产消者需求响应机制,形成主从博弈框架并利用Karush-Kuhn tucker(KKT)条件,将双层模型的下层目标及约束整合至上层,实现统一求解。其次,引入条件风险价值(conditional value at risk,CVaR)方法以量化电价不确定性对负荷聚合商购电策略的风险影响。最后,通过实证算例分析得出:该机制能有效激励用户侧可调资源参与系统灵活性调节,促进负荷聚合商与产消者间的双赢合作格局。
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.
文摘为进一步提升综合能源系统环境效益,减少新能源出力不确定性所带来的潜在风险,提出了计及条件风险价值(conditional value at risk,CVaR)以及阶梯碳交易的综合能源系统优化调度模型。考虑到系统风电和光伏出力不确定性可能带来的影响,采用条件风险价值量度不确定性带来的潜在风险,并将碳捕获技术、电转气设备以及阶梯式碳交易机制引入系统调度模型,构建了综合考虑系统运行成本和碳交易成本的优化调度目标函数,由于所建立模型为混合整数规划问题,采用CPLEX求解器进行求解,设置4种场景进行验证分析,算例表明所提模型可有效减少二氧化碳排放,在兼顾经济性和环境性的同时引入CVaR,可避免由于忽略风光不确定性所带来的较为乐观的调度结果,使系统最终调度结果更为合理。
