Conditional Value At Risk Research Articles

A multi-objective dispatching model for a novel virtual power plant considering combined heat and power units, carbon recycling utilization, and flexible load response

To optimize the energy supply potential and complementary advantages of distributed energy, this paper focuses on the dispatching optimization of cogeneration virtual power plant considering uncertainty. First of all, wind power, photovoltaic, combined heat and power (CHP) units, electric boilers, and controllable loads are integrated into a CHP virtual power plant. Then, carbon capture and electric-to-gas devices are introduced to realize carbon recycling. Furthermore, quantify the risk of real-time dispatching of virtual power plants through uncertainty scenario generation and conditional value at risk (CVaR) theory, and the multi-objective stochastic dispatching optimization model of virtual power plants is built with the aim at minimizing the operation cost, carbon emissions, and operation risk as the objectives, and the CRITIC weighting method is adopted to solve it. Finally, the calculation results show that: 1) the electric boiler can use wind and photovoltaic power to supply heat for the system, reduce the dependence of the virtual power plant (VPP) on the CHP unit, and make the electric output of the unit more flexible. 2) The risk quantification method proposed can fully measure the risk situation in real-time dispatching, arrange the wind and photovoltaic power generation plan and backup plan more reasonably, and enable the VPP to get more benefits while avoiding the risks in real-time dispatching.

Forecasting VaR and ES by using deep quantile regression, GANs-based scenario generation, and heterogeneous market hypothesis

Value at risk (VaR) and expected shortfall (ES) have emerged as standard measures for detecting the market risk of financial assets and play essential roles in investment decisions, external regulations, and risk capital allocation. However, existing VaR estimation approaches fail to accurately reflect downside risks, and the ES estimation technique is quite limited owing to its challenging implementation. This causes financial institutions to overestimate or underestimate investment risk and finally leads to the inefficient allocation of financial resources. The main purpose of this study is to use machine learning to improve the accuracy of VaR estimation and provide an effective tool for ES estimation. Specifically, this study proposes a VaR estimator by combining quantile regression with “Mogrifier” recurrent neural networks to capture the “long memory” and “clustering” properties of financial assets; while for estimating ES, this study directly models the quantile of assets and employs generative adversarial networks to generate future tail risk scenarios. In addition to the typical properties of financial assets, the model design is also consistent with heterogeneous market theory. An empirical application to four major global stock indices shows that our model is superior to other existing models.

Data-driven Wasserstein distributionally robust chance-constrained optimization for crude oil scheduling under uncertainty

Crude oil scheduling optimization is an effective method to enhance the economic benefits of oil refining. But uncertainties, including uncertain demands of crude distillation units (CDUs), might make the production plans made by the traditional deterministic optimization models infeasible. A data-driven Wasserstein distributionally robust chance-constrained (WDRCC) optimization approach is proposed in this paper to deal with demand uncertainty in crude oil scheduling. First, a new deterministic crude oil scheduling optimization model is developed as the basis of this approach. The Wasserstein distance is then used to build ambiguity sets from historical data to describe the possible realizations of probability distributions of uncertain demands. A cross-validation method is advanced to choose suitable radii for these ambiguity sets. The deterministic model is reformulated as a WDRCC optimization model for crude oil scheduling to guarantee the demand constraints hold with a desired high probability even in the worst situation in ambiguity sets. The proposed WDRCC model is transferred into an equivalent conditional value-at-risk (CVaR) representation and further derived as a mixed-integer nonlinear programming (MINLP) counterpart. Industrial case studies from a real-world refinery are conducted to show the effectiveness of the proposed method. Out-of-sample tests demonstrate that the solution of the WDRCC model is more robust than those of the deterministic model and the chance-constrained model.

Risk assessment in cryptocurrency portfolios: a composite hidden Markov factor analysis framework

In this paper, we deal with the estimation of two widely used risk measures such as Value-at-Risk (VaR) and Expected Shortfall (ES) in a cryptocurrency context. To face the presence of regime switching in the cryptocurrency volatilities and the dynamic interconnection between them, we propose a Monte Carlo-based approach using heteroskedastic factor analysis and hidden Markov models (HMM) combined with a structured variational Expectation-Maximization (EM) learning approach. This composite approach allows the construction of a diversified portfolio and determines an optimal allocation strategy making it possible to minimize the conditional risk of the portfolio and maximize the return. The out-of-sample prediction experiments show that the composite factorial HMM approach performs better, in terms of prediction accuracy, than some other baseline methods presented in the literature. Moreover, our results show that the proposed methodology provides the best performing crypto-asset allocation strategies and it is also clearly superior to the existing methods in VaR and ES predictions.

Forecasting value-at-risk and expected shortfall in emerging market: does forecast combination help?

PurposeThis paper investigates how various strategies for combining forecasts, both simple and optimised approaches, are compared with popular individual risk models in estimating value-at-risk (VaR) and expected shortfall (ES) in emerging market at alternative risk levels.Design/methodology/approachUsing the case study of the Vietnamese stock market, the author produced one-day-ahead VaR and ES forecast from seven individual risk models and ten alternative forecast combinations. Next, the author employed a battery of backtesting procedures and alternative loss functions to evaluate the global predictive accuracy of the different methods. Finally, the author investigated the relative performance over time of VaR and ES forecasts using fluctuation test.FindingsThe empirical results indicate that, although combined forecasts have reasonable predictive abilities, they are often outperformed by one individual risk model. Furthermore, the author showed that the complex combining methods with optimised weighting functions do not perform better than simple combining methods. The fluctuation test suggests that the poor performance of combined forecasts is mainly due to their inability to cope with periods of instability.Research limitations/implicationsThis study reveals the limitation of combining strategies in the one-day-ahead VaR and ES forecasts in emerging markets. A possible direction for further research is to investigate whether this finding holds for multi-day ahead forecasts. Moreover, the inferior performance of combined forecasts during periods of instability motivates further research on the combining strategies that take into account for potential structure breaks in the performance of individual risk models. A potential approach is to improve the individual risk models with macroeconomic variables using a mixed-data sampling approach.Originality/valueFirst, the authors contribute to the literature on the forecasting combinations for VaR and ES measures. Second, the author explored a wide range of alternative risk models to forecast both VaR and ES with recent data including periods of the COVID-19 pandemic. Although forecast combination strategies have been providing several good results in several fields, the literature of forecast combination in the VaR and ES context is surprisingly limited, especially for emerging market returns. To the best of the author’s knowledge, this is the first study investigating predictive power of combining methods for VaR and ES in an emerging market.

A conditional value at risk based stochastic allocation of SOP in distribution networks

Soft open points (SOPs) have been noticed to enhance the operation efficiency of distribution networks due to their capability of exchanging power between feeders as well as reactive power compensation. The uncertainty of distributed renewable energy sources (DRESs) and load demands make its optimal allocation and active power flow settings difficult. Uncertainties should be modeled through appropriate techniques to give more reliable schemes for SOPs allocation and regulation. However, in the probabilistic environment, decreasing the risk of violations from objectives and constraints is also important to guarantee confident solutions.This paper finds the optimal location of an SOP and its power flow setpoints, considering the uncertainty of DRESs and load demands. The mentioned uncertainties are handled by the efficient K-medoids data clustering technique. In addition to considering the expected value of losses and voltage deviation as objective functions, the conditional value at risk (CVaR) of voltage deviation is considered, too. This ensures that in the final solution, the probability of voltage deviation in most worst scenarios will not be considerable. The proposed optimization model is implemented in a multi-objective optimization frame and solved by the multi-objective particle swarm optimization (MOPSO) algorithm and tested on the modified IEEE 33-bus test distribution system and the effect of considering the CVaR index on results is comprehensively discussed.

Optimal product and after-sales service decisions considering risk attitudes under price-dependent uncertain demand

In this paper, we investigate a service-oriented manufacturer that provides fashionable products with after-sales services to customers. Before the selling season, the manufacturer invests in service capacity in advance and then decides on the production quantity and selling price based on updated demand information. Interestingly, it is found that the manufacturer’s production and pricing decisions will not be affected by the unit production cost when the market base exceeds a threshold. We investigate and compare the manufacturer’s decisions in two cases: imperfect and perfect demand information updates. The selling price in the imperfect demand updates case is always set lower than that in the perfect demand updates case when the service capacity is sufficient but may not be under insufficient service capacity. The possibility that the prepared service capacity limits the production quantity may decrease with the unit production cost in the imperfect demand updates case. In contrast, this possibility is invariant with the unit production cost in the case of perfect demand updates. The effects of risk aversion are also investigated. It is found that under the conditional value-at-risk (CVaR) criterion, the manufacturer with a higher risk-averse degree establishes a lower service capacity and sets a lower selling price.

Adjusted higher-order expected shortfall

How to detect different tail behaviors of two risk random variables with the same mean is an important task. In this paper, motivated by Burzoni et al. (2022), a class of convex risk measures, referred to as adjusted higher-order Expected Shortfall (ES), is introduced and studied. The adjusted risk measure quantifies risk as the minimum amount of capital that has to be raised and injected into a financial position to ensure that its higher-order ES does not exceed a pre-specified threshold for every probability level. This new risk measure is intimately linked to dual higher-order increasing convex order by choosing the risk threshold to be the higher-order ES of a special benchmark random loss. The dual representation for (adjusted) higher-order Expected Shortfall is also given.

A distributionally robust energy management of microgrid problem with ambiguous chance constraints and its tractable approximation method

As the penetration of intermittent renewable energy increases in microgrid systems, flexible power generation resources cause the power imbalance problem. To improve the absorption of renewable energy and to deal with its uncertainty more effectively, this paper proposes a distributionally robust approximate model for microgrid with ambiguous chance constraints (DR-CCP). First, the distributionally robust model with ambiguous chance constraints is a semi-infinite chance constrained planning problem, which is computationally difficult and inefficient, so the use of Chernoff's inequality to derive a safe tractable approximation form for the ambiguous chance constraint on the basis of a probability distribution for ambiguous sets including bounded perturbations with mean zero, transforms it into a mixed integer linear programming problem that can be directly solved using CPLEX to solve it. Then, the optimal value of the proposed model is used to approximate equivalent conditional value at risk (CVaR), and the relationship with CVaR is established. The optimal solution of our model is employed to construct multiple sets of comparison models, enhancing the richness of numerical experiments. Finally, to validate the feasibility and effectiveness of our proposed model, a series of diverse tests are performed on the IEEE 33-bus power distribution system.

Risk-Based Hosting Capacity Analysis in Distribution Systems

Solar hosting capacity analysis (HCA) assesses the ability of a distribution network to host distributed solar generation without seriously violating distribution network constraints. In this paper, we consider risk-sensitive HCA that limits the risk of network constraint violations with a collection of scenarios of solar irradiance and nodal power demands, where risk is modeled via the conditional value at risk (CVaR) measure. First, we consider the question of maximizing aggregate installed solar capacities, subject to risk constraints and solve it as a second-order cone program (SOCP) with a standard conic relaxation of the feasible set of the power flow equations. Second, we design an incremental algorithm to decide whether a configuration of solar installations has acceptable risk of constraint violations, modeled via CVaR. The algorithm circumvents explicit risk computation by incrementally constructing inner and outer polyhedral approximations of the set of acceptable solar installation configurations from prior such tests conducted. Our numerical examples study the impact of risk parameters, the number of scenarios and the scalability of our framework.

Risk-Averse Optimal Combining Forecasts for Renewable Energy Trading Under CVaR Assessment of Forecast Errors

Renewable energy producer is often exposed to huge financial losses in some imbalance hours (meaning that the contracted energy in day-ahead market is not equal to the actual output in real time) caused by extremely large forecast error. To address this challenge, this paper integrates the forecast end-user's risk profile into the development of risk-averse combining forecast approach for renewable energy trading. First, the conditional value-at-risk (CVaR) is applied to evaluate the extreme prediction error of combined forecasts. Then, convex optimization models are formulated with the objective of minimizing the mean square error plus the CVaR of large error. Solving our proposed models determines the optimal weights for individual models participating in the combined forecasts. Finally, the value of risk-averse combined forecasts is verified through examining the financial performance of using risk-averse forecasts as inputs of the bidding strategy in renewable energy trading. Case studies on real-world datasets present that our proposed method not only reduces the mean error but also lowers the extreme error. More importantly, it decreases the imbalance energy and cost in renewable energy trading, thus being less exposed to the risk of large financial losses under extreme prediction errors.

A systematic approach for risk assessment and mitigation of wind integrated electricity markets

A risk-based double auction mechanism with dispatchable loads is one of the most cost-efficient trading mechanisms in the modern real-time electricity markets. Risks in the system due to various uncertainties, such as line failure, generator failure, load changes and other severe contingencies causes non-systematic execution of real-time electricity markets. This paper presents a simple and systematic procedure for reducing system risks in deregulated power markets considering wind power integrations. For maximizing the considerable system social welfare and minimizing the system’s economic risk, the optimal placement and operation of wind power producers (WPP) have been suggested. The critical buses have been identified by accessing the different assessment tools e.g., Value at Risk (VaR), Conditional Value at Risk (CVaR), and locational marginal pricing (LMP) based Marginal Pricing Index (MPI). The presented approach has been evaluated and validated on modified IEEE 30-bus system.

Fusion of multifactor modeling and supervised learning algorithms in quantitative finance: a comparative analysis of predictive and explanatory power

Abstract Finance serves as the lifeblood of the real economy’s development, fundamentally aimed at bolstering the real economy and mitigating financial risks. This paper investigates the application of machine learning technologies in finance, organizing a detailed classification and analysis of associated risks within the sector. Specifically, the study employs the Conditional Value at Risk (CoVaR) to quantify systemic financial risks. It introduces both the Fama-French three-factor and five-factor models for constructing multifactor financial models. It assesses the significance and regression coefficients of risk factors within these models to provide a comparative analysis. Moreover, this research develops an early warning model for financial risk by incorporating financial risk measurement indices into the XGBoost machine learning framework. It utilizes the SHAP (Shapley Additive exPlanations) explanatory framework to elucidate the key features influencing financial risk. This comprehensive approach not only enhances the understanding of financial risk dynamics but also advances the predictive capabilities of financial risk management. It was found that the modified R² increased from 36.52% to 56.25% after adding the IMU factor to the three-factor model, and the coefficient of SMB decreased from 0.135 to −0.215 the larger the size of the enterprise. The accuracy of the financial risk early warning model was 96.35%, and the probability of being predicted by the model to be a high-risk sample was lower when the value of the characteristic INDI was taken as [0,0.125]. Financial institutions can enhance their risk prevention ability by combining the financial risk factors obtained from the multifactor model with the supervised learning algorithm.

A Market Strategy for Joint Profitability of Electric Vehicle Charging Stations and Retailers: Considering Electricity Price Fluctuations and Users’ Service Fee Response

With the introduction of the “carbon peaking and carbon neutralizing” initiative, China is undergoing a positive energy transition, emphasizing the replacement of traditional fossil fuels with clean energy sources. As part of this transition, numerous megacities are progressively endorsing electric vehicles (EVs) as substitutes for traditional fuel‐based vehicles. The expanding use of EVs, however, has presented challenges related to the randomness and volatility of EV charging. In response to this, many regions in China have mandated the implementation of the time‐of‐use (ToU) scheme. This scheme divides the day into distinct periods such as “valley,” “flat,” “peak,” and “critical peak,” each associated with varying charging prices. According to the management regulations, the fees collected from vehicle owners at the charging station are divided into two parts: ToU electricity value and service fees. The former is jointly determined by the power company and the government, while the latter is set by the charging station operator. To overcome the limitation on profitability, this paper proposes a scheme enabling charging stations and retailers to participate in the day‐ahead (DA) market. The proposed approach involves a two‐stage decision‐making method. By analyzing the charging habits of local residents, the paper constructs a quadratic curve for dynamic service fees and charging rates. The objective function is then utilized to adjust the anticipated charging load curve. Prior to the DA‐bidding process, an uncertain set of scenarios for electricity prices and charging loads is generated. The conditional value‐at‐risk (C‐VaR) method is employed to balance expected benefits and risks amid uncertain scenarios.

Research on Power Investment and Expansion Planning Considering Coal-fired Power Capacity and Electricity Price in Market-Driven Environment

The market-oriented environment and the shift away from the coal-fired power are inevitable trends in the future development of electric power energy. Based on this, this article establishes a dual-level model for power investment expansion planning with wind power system in an oligopoly competitive electricity market. In the upper-level model, power generation companies make investment decisions and formulate their bidding strategies in market transactions, while the lower-level model simulates the day-ahead market clearing process under the centralized bidding and trading mode. To encourage the transition from coal-fired power plants, a model for expected annual operating revenue of coal-fired power companies under a dual pricing system is proposed, and the conditional value-at-risk (CVaR) is used to measure the investment risk brought by the uncertainty of competitors in the investment planning game for power generation companies. The numerical results verify the effectiveness of the proposed model and method.

CVaR-Constrained Policy Optimization for Safe Reinforcement Learning.

Current constrained reinforcement learning (RL) methods guarantee constraint satisfaction only in expectation, which is inadequate for safety-critical decision problems. Since a constraint satisfied in expectation remains a high probability of exceeding the cost threshold, solving constrained RL problems with high probabilities of satisfaction is critical for RL safety. In this work, we consider the safety criterion as a constraint on the conditional value-at-risk (CVaR) of cumulative costs, and propose the CVaR-constrained policy optimization algorithm (CVaR-CPO) to maximize the expected return while ensuring agents pay attention to the upper tail of constraint costs. According to the bound on the CVaR-related performance between two policies, we first reformulate the CVaR-constrained problem in augmented state space using the state extension procedure and the trust-region method. CVaR-CPO then derives the optimal update policy by applying the Lagrangian method to the constrained optimization problem. In addition, CVaR-CPO utilizes the distribution of constraint costs to provide an efficient quantile-based estimation of the CVaR-related value function. We conduct experiments on constrained control tasks to show that the proposed method can produce behaviors that satisfy safety constraints, and achieve comparable performance to most safe RL (SRL) methods.

Inventory management and delivery of perishable products with stochastic demands and risks consideration

In the agri-food supply chain, the perishable nature of the commodities opens a series of challenges at all decision levels: strategical, tactical and operational. This paper presents an age-based model for the inventory-routing problem of perishable commodities with stochastic demands. To deal with this source of uncertainty, the conditional value-at-risk (CVaR) has been adopted as a risk measure, and then the model has been applied to the agri-food supply chain under investigation. The model is the core of a dynamic approach for the optimal distribution and inventory planning over a short-medium horizon. To address a problem as realistic as possible, we assume that the demand for products of each age is unknown and we model this uncertainty by means of random variables with a probability distribution that can be estimated from historical data. Computational experiments on test cases based on a real-life agri-food company located in Italy show the effectiveness of the proposed approach for evaluating different risk attitudes.

Risk-Averse Decision Making Under Uncertainty

A large class of decision making under uncertainty problems can be described via Markov decision processes (MDPs) or partially observable MDPs (POMDPs), with application to artificial intelligence and operations research, among others. In this paper, we consider the problem of designing policies for MDPs and POMDPs with objectives and constraints in terms of dynamic coherent risk measures rather than the traditional total expectation, which we refer to as the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">constrained risk-averse problem</i> . Our contributions can be described as follows: For MDPs, under some mild assumptions, we propose an optimization-based method to synthesize Markovian policies. We then demonstrate that such policies can be found by solving difference convex programs (DCPs). We show that our formulation generalize linear programs for constrained MDPs with total discounted expected costs and constraints; For POMDPs, we show that, if the coherent risk measures can be defined as a Markov risk transition mapping, an infinite-dimensional optimization can be used to design Markovian belief-based policies. For POMDPs with stochastic finite-state controllers (FSCs), we show that the latter optimization simplifies to a (finite-dimensional) DCP. We incorporate these DCPs in a policy iteration algorithm to design risk-averse FSCs for POMDPs. We demonstrate the efficacy of the proposed method with numerical experiments involving conditional-value-at-risk (CVaR) and entropic-value-at-risk (EVaR) risk measures.

Impact assessment of shared storage and peer-to-peer trading on industrial buildings in the presence of electric vehicle parking lots: A hybrid robust-CVaR analysis

Local power markets and peer-to-peer (P2P) power transaction plans between the clients have lately received attractions as a cost-effective approach to encourage flexible energy options and sharing the internal power resources. For the integration of industrial consumers (ICs) in the presence of electric vehicle parking lot, this study modeled local power markets to share the surplus power of ICs between each other. Other hands, shared storage is modeled in the proposed system to benefit consumers. In order to investigate the proposed system under uncertain conditions, a hybrid optimization method is proposed for uncertainty modeling. In this paper, the well-known uncertainty modeling tools, including the robust optimization and Conditional Value at Risk (CVaR) embedded stochastic optimization approach, are proposed to model the uncertainties. The markets price uncertainty is one of the important uncertain parameters assumed as an unknown-distribution parameter due to insufficient historical data or not following a specific distribution; thus, the risks of this parameter are modeled by robust optimization, which has no need for big historical data of uncertain parameter. The other uncertain parameter is solar irradiation. The corresponding risks of solar irradiation is modeled by CVaR modeling because of the following Beta distribution. Thus, the financial risks of different uncertain parameters can be modeled effectively using the proposed hybrid optimization framework. According to obtained results, using peer-to-peer trading reduces the operation cost by 7.94%, while using the shared storage along with peer-to-peer trading reduces the operation cost by 21.49%.

Efficiency gains in value-at-risk and expected shortfall estimation by using copulas and full maximum likelihood

We provide Monte Carlo evidence on the efficiency gains obtained in GARCH-based estimations of value-at-risk (VaR) and expected shortfall (ES) by incorporating dependence information through copulas and subsequently using full maximum likelihood (FML) estimates. First, we consider an individual returns series; in this case, the efficiency gain stems from exploiting the relationship with another returns series using a copula model. Second, we consider a portfolio returns series obtained as a linear combination of returns series related through a copula model; in this case, the efficiency gain stems from using FML estimates instead of two-stage ML estimates. We consider three copulas models in order to analyze the effect of the type and degree of tail dependence on the results. Our results show that, in these situations, using copula models and FML leads to a substantial reduction in the mean squared error of the VaR and ES estimates when there is a relatively high degree of dependence between returns (up to 70% in the presence of lower-tail dependence) and a notable improvement in the performance of backtesting procedures.