Solving the subset sum problem by the quantum Ising model with variational quantum optimization based on conditional values at risk

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.

Supply chain coordination with participators' risk bias under buy-back contract

Considering participators' risk bias,which is measured by the method of value at risk,the risk constraints in a two-echelon supply chain coordination under buy-back contract is equal to giving the order of an upper bound.With a risk-averse dominant enterprise(M)and a risk-neutral non-dominant one(R),the coordination which optimizes the supply chain under the risk constraints is achieved by a penalty mechanism L to reduce R's order.With risk-neutral M and risk-averse R,M can motivate R to increase his order by providing a risk subsidy K,and two cases are discussed.If the risk constraints of R cannot satisfy M's participation constraint to offer K,M will prefer to accept R's order to obtain a sub-optimization solution of the supply chain.Or else,with M's K,R's optimal order just coordinates the supply chain,which is equal to the case without risk bias,and in this situation R's risk bias only affects the profit distribution between the participators.

Operational risk assessment of third-party payment platforms:a case study of China

Operational risk events have severely impacted the development of third-party payment(TPP)platforms,and have even led to a discussion on the operational risk capital charge settlement by relevant international regulators.However,prior studies have mostly focused on qualitative mechanism analysis,and have rarely examined quantitative risk assessment based on actual operational risk events.Therefore,this study attempts to assess the operational risk on TPP platforms in China by constructing a systematic framework incorporating database construction and risk modeling.First,the operational risk database that covers 202 events between Q1,2014,and Q2,2020 is constructed.Then,specific causes are clarified,and the characteristics are analyzed from both the trend and loss severity perspectives.Finally,the piecewise-defined severity distribution based-Loss Distribution Approach(PSD-LDA)with double truncation is utilized to assess the operational risk.Two main conclusions are drawn from the empirical analysis.First,legal risk and external fraud risk are the two main causes of operational risk.Second,the yearly Value at Risk and Expected Shortfall are 724.46 million yuan and 1081.98 million yuan under the 99.9%significance level,respectively.Our results are beneficial for both TPP platform operators and regulators in managing and controlling operational risk.

Multi scale risk measurement in electricity market:a wavelet based value at risk approach

Value at risk (VaR) is adopted to measure the risk level in the electricity market. To estimate VaR at higher accuracy and reliability, the wavelet variance decomposed approach for value at risk estimates (WVDVaR) is proposed. Empirical studies conduct in five Australian electricity markets, which evaluate the performances of both the proposed approach and the traditional ARMA-GARCH approach using the Kupiec backtesting procedure. Experimental results suggest that the proposed approach measures electricity market risks at higher accuracy and reliability than the bench mark ARMA-GARCH approach, as indicated by the higher p values during the Kupiec backtesting procedure. In addition, the new approach also provides more insight into the risk evolution process over time and helps in adjusting VaR estimates to the time horizons that best suit investor interests. The distribution of risk according to investor preferences is shown by decomposing VaR across different time horizons. This also provides important information for the appropriate aggregation of risk measures based on investor investment preferences.

Market Risk Evaluation on Single Futures Contract:SV-CVaR Model and Its Application on Cu00 Data

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.

STUDY ON THE INTERRELATION OF EFFICIENT PORTFOLIOS AND THEIR FRONTIER UNDER t DISTRIBUTION AND VARIOUS RISK MEASURES

In order to study the effect of different risk measures on the efficient portfolios （fron- tier） while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper that the joint return distribution of risky assets obeys the multivariate t-distribution. Under the mean-risk analysis framework, the interrelationship of efficient portfolios （frontier） based on risk measures such as variance, value at risk （VaR）, and expected shortfall （ES） is analyzed and compared. It is proved that, when there is no riskless asset in the market, the efficient frontier under VaR or ES is a subset of the mean-variance （MV） efficient frontier, and the efficient portfolios under VaR or ES are also MV efficient; when there exists a riskless asset in the market, a portfolio is MV efficient if and only if it is a VaR or ES efficient portfolio. The obtained results generalize relevant conclusions about investment theory, and can better guide investors to make their investment decision.

On the factors of Bitcoin’s value at risk

This study investigates the factors of Bitcoin’s tail risk,quantified by Value at Risk(VaR).Extending the conditional autoregressive VaR model proposed by Engle and Manganelli(2004),I examine 30 potential drivers of Bitcoin’s 5%and 1%VaR.For the 5%VaR,quantity variables,such as Bitcoin trading volume and monetary policy rate,were positively significant,but these effects were attenuated when new samples were added.The 5%VaR responds positively to the Internet search index and negatively to the fluctuation of returns on commodity variables and the Chinese stock market index.For the 1%VaR,variables related to the macroeconomy play a key role.The consumer sentiment index exerts a strong positive effect on the 1%VaR.I also find that the 1%VaR has positive relationships with the US economic policy uncertainty index and the fluctuation of returns on the corporate bond index.

A Value-at-Risk Based Approach for PMU Placement in Distribution Systems

With the application of phasor measurement units(PMU)in the distribution system,it is expected that the performance of the distribution system state estimation can be improved obviously with the PMU measurements into consideration.How to appropriately place the PMUs in the distribution is therefore become an important issue due to the economical consideration.According to the concept of efficient frontier,a value-at-risk based approach is proposed to make optimal placement of PMU taking account of the uncertainty of measure errors,statistical characteristics of the pseudo measurements,and reliability of the measurement instrument.The reasonability and feasibility of the proposed model is illustrated with 12-node system and IEEE-33 node system.Simulation results indicated that uncertainties of measurement error and instrument fault result in more PMU to be installed,and measurement uncertainty is the main affect factor unless the fault rate of PMU is quite high.

Loan Loss Reserves （LLR）, Expected Loss （EL）, and Value at Risks （VaR）

This paper clarifies the distinctions between loan loss reserves （LLR）, expected loss （EL）, and loan loss provisions （LLP）. The paper also includes information on individual and collective impairment assessment of local commercial banks in Malaysia collected from their annual reports. Most banks have maintained collective assessment （CA） allowance ratio of lower than 1.2% of gross total loans.

Three Methods to Calculate the Financial Risk Measurement: Value- At-Risk and Expected Shortfall

This paper analyzes the relationship between the risk factor of each stock and the portfolio’s risk based on a small portfolio with four U.S.stocks,and the reason why these risk factors can be regarded as a market invariant.Then,it evaluates the properties of the convex and coherent risk indicators of the capital requirement index composed of VaR and ES,and use three methods(the historical estimation method,boudoukh’s mixed method and Monte Carlo method)to estimate the risk measurement indicators VaR and ES respectively based on the assumption of multivariate normal distribution’risk factors and multivariate student t-copula distribution’s one,finally it figures out that these three calculation results are very close.

Risk Constrained Self-scheduling of AA-CAES Facilities in Electricity and Heat Markets:A Distributionally Robust Optimization Approach

Advanced adiabatic compressed air energy storage(AA-CAES)has the advantages of large capacity,long service time,combined heat and power generation(CHP),and does not consume fossil fuels,making it a promising storage technology in a low-carbon society.An appropriate self-scheduling model can guarantee AA-CAES’s profit and attract investments.However,very few studies refer to the cogeneration ability of AA-CAES,which enables the possibility to trade in the electricity and heat markets at the same time.In this paper,we propose a multimarket self-scheduling model to make full use of heat produced in compressors.The volatile market price is modeled by a set of inexact distributions based on historical data through-divergence.Then,the self-scheduling model is cast as a robust risk constrained program by introducing Stackelberg game theory,and equivalently reformulated as a mixed-integer linear program(MILP).The numerical simulation results validate the proposed method and demonstrate that participating in multienergy markets increases overall profits.The impact of uncertainty parameters is also discussed in the sensibility analysis.

预测央行脆弱性的VaR模型

本文旨在研究可将两代货币危机模型有机地结合在一起的用于预测央行脆弱性的VaR模型,这一模型为央行提供了一个预警指标,同时也为市场参与者提供了一个判断央行是否具有偿付能力的依据。

基于期望损失对中国股票市场风险的返回检验

基于风险估价和期望损失的返回检验存在一定缺陷。为此,将一种新的返回检验方法——鞍点技术应用于3种中国股票指数的日收益率。然后,使用3种不同的模型进行预测,与真实数据相比较进行返回检验。研究结果表明:简单的GARCH-N orm al模型无法捕捉股票市场风险,对实践中相当普遍的基于正态分布的风险建模提出了一种警示。同时,鞍点技术的优点在于,允许基于每年的股指收益率数据进行返回检验。

股票市场风险计量中的损失分布法与价值分布法研究

股票市场是一个稳定性极差的平台,需要学术界对其损失与价值进行科学全面的分析,才有利于全球经济的持续健康发展。文章借助VaR方法,对我国股票市场风险计量中的损失与价值分布进行了科学全面的分析。

SV-t模型下人民币汇率VaR和ES的动态度量与分析

人民币汇率的风险度量是汇率风险管理的关键环节。本文首先用SV-t模型对人民币对美元、日元及欧元汇率收益的波动率进行分析,在此基础上分别运用VaR和ES方法对其风险进行动态的度量与分析比较。结果表明:SV-t模型能够刻画出人民币汇率收益率序列的波动特征;人民币对美元的VaR基本反映出其最大可能的损失;人民币对日元及欧元的Va R则低估了实际的风险水平,相应的ES虽保守却比较准确地估计出尾部风险。文章最后也对中国汇率市场的风险管理及风险监管提出了一些政策建议。

应用极值理论和EGARCH模型对深圳股市VAR测量

精确度量风险是金融风险管理的关键问题。本文用随机波动模型将ARCH类模型和极值理论有机的结合起来,用来描述金融资产收益率尾部特征,从而计算VaR的值并用深圳成份指数进行实证分析,经过研究我们发现用随机波动模型调整估计出来VaR值比未经调整出来的值明显偏大,这说明在收益率序列不是独立同分布的情况下直接用POT模型,用GPD模型对超过阈值的数据进行拟合低估了真实的市场风险。

Application of intelligent algorithms in Down syndrome screening during second trimester pregnancy

BACKGROUND Down syndrome(DS)is one of the most common chromosomal aneuploidy diseases.Prenatal screening and diagnostic tests can aid the early diagnosis,appropriate management of these fetuses,and give parents an informed choice about whether or not to terminate a pregnancy.In recent years,investigations have been conducted to achieve a high detection rate(DR)and reduce the false positive rate(FPR).Hospitals have accumulated large numbers of screened cases.However,artificial intelligence methods are rarely used in the risk assessment of prenatal screening for DS.AIM To use a support vector machine algorithm,classification and regression tree algorithm,and AdaBoost algorithm in machine learning for modeling and analysis of prenatal DS screening.METHODS The dataset was from the Center for Prenatal Diagnosis at the First Hospital of Jilin University.We designed and developed intelligent algorithms based on the synthetic minority over-sampling technique(SMOTE)-Tomek and adaptive synthetic sampling over-sampling techniques to preprocess the dataset of prenatal screening information.The machine learning model was then established.Finally,the feasibility of artificial intelligence algorithms in DS screening evaluation is discussed.RESULTS The database contained 31 DS diagnosed cases,accounting for 0.03%of all patients.The dataset showed a large difference between the numbers of DS affected and non-affected cases.A combination of over-sampling and undersampling techniques can greatly increase the performance of the algorithm at processing non-balanced datasets.As the number of iterations increases,the combination of the classification and regression tree algorithm and the SMOTETomek over-sampling technique can obtain a high DR while keeping the FPR to a minimum.CONCLUSION The support vector machine algorithm and the classification and regression tree algorithm achieved good results on the DS screening dataset.When the T21 risk cutoff value was set to 270,machine learning methods had a higher DR and a lower FPR than statistical methods.

VAR AND CTE BASED OPTIMAL REINSURANCE FROM A REINSURER'S PERSPECTIVE

In this article,we study optimal reinsurance design.By employing the increasing convex functions as the admissible ceded loss functions and the distortion premium principle,we study and obtain the optimal reinsurance treaty by minimizing the VaR(value at risk)of the reinsurer's total risk exposure.When the distortion premium principle is specified to be the expectation premium principle,we also obtain the optimal reinsurance treaty by minimizing the CTE(conditional tail expectation)of the reinsurer's total risk exposure.The present study can be considered as a complement of that of Cai et al.[5].

Measuring Real Capital Adequacy in Extreme Economic Conditions： An Examination of the Swiss Banking Sector

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.

Management of a Complex Portfolio of Assets with Stochastic Drifts and Volatilities

In financial analysis risk quantification is essential for efficient portfolio management in a stochastic framework. In this paper we study the value at risk, the expected shortfall, marginal expected shortfall and value at risk, incremental value at risk and expected shortfall, the marginal and discrete marginal contributions of a portfolio. Each asset in the portfolio is characterized by a trend, a volatility and a price following a three-dimensional diffusion process. The interest rate of each asset evolves according to the Hull and White model. Furthermore, we propose the optimization of this portfolio according to the value at risk model.