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.

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.

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.

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.

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.

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.

Risk-based Two-stage Optimal Scheduling of Energy Storage System with Second-life Battery Units

With the growing adoption of Electrical Vehicles(EVs),it is expected that a large number of on-board Li-ion batteries will be retired from EVs in the near future.Retired batteries will typically retain 80%of their initial capacities and can be recycled as second life batteries(SLBs).Although the capital costs of SLBs are much cheaper,their operational reliability is an important concern since used batteries may suffer from a higher failure rate.This paper aggregates brand new batteries and SLBs together to improve power system’s operating performance with renewable energy resources.In the context of a day-ahead and intra-day dispatch framework,a two-stage coordinated optimal scheduling method is proposed.Specifically,the energy cost of brand-new batteries and SLBs is calculated based on detailed battery degradation model,and the reliability of batteries is modeled based on the Weibull distribution.Moreover,Conditional value at risk(CVaR)criterion is applied to evaluate the risk induced by intermittent renewable power output,load demand variation and SLBs failure probability.Simulation tests demonstrate the effectiveness of the proposed method.

Bi-level Multi-leader Multi-follower Stackelberg Game Model for Multi-energy Retail Package Optimization

In the competitive energy market,energy retailers are facing the uncertainties of both energy price and demand,which requires them to formulate reasonable energy purchasing and selling strategies for improving their competitiveness in this market.Particularly,the attractive multi-energy retail packages are the key for retailers to increase their benefit.Therefore,combined with incentive means and price signals,five types of multi-energy retail packages such as peak-valley time-of-use(TOU)price package and day-night bundled price package are designed in this paper for retailers.The iterative interactions between retailers and end-users are modeled using a bi-level model of stochastic optimization based on multi-leader multi-follower(MLMF)Stackelberg game,in which retailers are leaders and end-users are followers.Retailers make decisions to maximize the profit considering the conditional value at risk(CVaR)while end-users optimize the satisfaction of both energy comfort and economy.Besides,a distributed algorithm is proposed to obtain the Nash equilibrium of above MLMF Stackelberg game model while the particle swarm optimization(PSO)algorithm and CPLEX solver are applied to solve the optimization model for each participant(retailer or end-user).Numeral results show that the designed retail packages can increase the overall profit of retailers,and the overall satisfaction of industrial users is the highest while that of residential users is the lowest after game interaction.

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].

Two-stage stochastic programming with robust constraints for the logistics network post-disruption response strategy optimization

Logistics networks (LNs) are essential for the transportation and distribution of goods or services from suppliers to consumers. However, LNs with complex structures are more vulnerable to disruptions due to natural disasters and accidents. To address the LN post-disruption response strategy optimization problem, this study proposes a novel two-stage stochastic programming model with robust delivery time constraints. The proposed model jointly optimizes the new-line-opening and rerouting decisions in the face of uncertain transport demands and transportation times. To enhance the robustness of the response strategy obtained, the conditional value at risk (CVaR) criterion is utilized to reduce the operational risk, and robust constraints based on the scenario-based uncertainty sets are proposed to guarantee the delivery time requirement. An equivalent tractable mixed-integer linear programming reformulation is further derived by linearizing the CVaR objective function and dualizing the infinite number of robust constraints into finite ones. A case study based on the practical operations of the JD LN is conducted to validate the practical significance of the proposed model. A comparison with the rerouting strategy and two benchmark models demonstrates the superiority of the proposed model in terms of operational cost, delivery time, and loading rate.

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.

The Odd Log-Logistic Weibull-G Family of Distributions with Regression and Financial Risk Models

A new generalization of the Weibull-G family is proposed with two extra shape parameters.The mathematical properties are derived in great detail.Using the Weibull and normal distributions as baseline distributions,two models are introduced.The first model is a location-scale regression model based on a new extension of the Weibull distribution.The second model is a new two-step financial risk model to forecast the daily value at risk.The flexibility and applicability of the proposed models are investigated by means of five real data sets on the lifetime and financial returns.Empirical findings of the study show that proposed models work well and produce better results than other well-known models for financial risk modeling and censored lifetime data analysis.

The sum of two independent polynomially-modified hyperbolic secant random variables with application in computational finance

In this paper,by reshaping the hyperbolic secant distribution using Hermite polynomial,we devise a polynomially-modified hyperbolic secant distribution which is more flexible than secant distribution to capture the skewness,heavy-tailedness and kurtosis of data.As a portfolio possibly consists of multiple assets,the distribution of the sum of independent polynomially-modified hyperbolic secant random variables is derived.In exceptional cases,we evaluate risk measures such as value at risk and expected shortfall(ES)for the sum of two independent polynomially-modified hyperbolic secant random variables.Finally,using real datasets from four international computers stocks,such as Adobe Systems,Microsoft,Nvidia and Symantec Corporations,the effectiveness of the proposed model is shown by the goodness of Gram–Charlier-like expansion of hyperbolic secant law,for performance of value at risk and ES estimation,both in and out of the sample period.

PRODUCTION PLANNING PROBLEM WITH PRICING UNDER RANDOM YIELD:CVAR CRITERION

In this paper, we address a basic production planning problem with price dependent demand and stochastic yield of production. We use price and target quantity as decision variables to lower the risk of low yield. The value of risk control becomes more important especially for products with short life cycle. This is because, the profit implications of low yield might be unbearable in the short run. We apply Conditional Value at Risk （CVaR） to model the, risk. CVaR measure is a coherent risk measure and thereby having nice conceptual and mathematical underpinnings. It is also widely used in practice. We consider the problem under general demand function and general distribution function of yield and find sufficient conditions under which the problem has a unique local maximum. We also both analytically and numerically analyze the impact of parameter change on the optimal solution. Among our results, we analytically show that with increasing risk aversion, the optimal price increases. This relation is opposite to that of in Newsvendor problem where the uncertainty lies in demand side.

Supply chain network design under uncertainty with new insights from contracts

In this paper, the classical problem of supply chain network design is reconsidered to emphasize the role of contracts in uncertain environments. The supply chain addressed consists of four layers: suppliers, manufacturers, warehouses, and customers acting within a single period. The single owner of the manufacturing plants signs a contract with each of the suppliers to satisfy demand from downstream. Available contracts consist of long-term and option contracts, and unmet demand is satisfied by purchasing from the spot market. In this supply chain, customer demand, supplier capacity, plants and warehouses, transportation costs, and spot prices are uncertain. Two models are proposed here: a risk-neutral two-stage stochastic model and a risk-averse model that considers risk measures. A solution strategy based on sample average approximation is then proposed to handle large scale problems. Extensive computational studies prove the important role of contracts in the design process, especially a portfolio of contracts. For instance, we show that long-term contract alone has similar impacts to having no contracts, and that option contract alone gives inferior results to a combination of option and long-term contracts. We also show that the proposed solution methodology is able to obtain good quality solutions for large scale problems.