Search Results (37)

The volatility and uncertainty of wind power output pose significant challenges to the safe and stable operation of power systems. To enhance the economic efficiency and reliability of day-ahead scheduling in wind farms, this paper proposes a day-ahead planning and scheduling method for wind/storage systems based on multi-scenario generation and Conditional Value-at-Risk (CVaR). First, based on the statistical characteristics of historical wind power forecasting errors, a kernel density estimation method is used to fit the error distribution. A Copula-based correlation model is then constructed to generate multi-scenario wind power output sequences that account for spatial correlation, from which representative scenarios are selected via K-means clustering. An objective function is subsequently formulated, incorporating electricity sales revenue, energy storage operation and maintenance cost, initial state-of-charge (SOC) cost, peak–valley arbitrage income, and penalties for schedule deviations. The initial SOC of the storage system is introduced as a decision variable to enable flexible and efficient coordinated scheduling of the wind/storage system. The storage system is implemented using a 1500 kWh/700 kW lithium iron phosphate (LiFePO₄) battery to enhance operational flexibility and reliability. To mitigate severe profit fluctuations under extreme scenarios, the model incorporates a CVaR-based risk constraint, thereby enhancing the reliability of the day-ahead plan. Finally, simulation experiments under various initial SOC levels and confidence levels are conducted to validate the effectiveness of the proposed method in improving economic performance and risk management capability. Full article

Carbon emissions from human activities such as production and consumption have exacerbated climate deterioration. A common worldwide objective is to create a low-carbon economy by implementing carbon reduction measures in production, consumption, and other processes. To this end, this paper explores the production, price, carbon reduction rate, and profit or utility for a dual-channel low-carbon supply chain network (DLSCN) that includes numerous competing suppliers, manufacturers, risk-averse retailers, and demand markets under carbon trading. In order to create an equilibrium model for the DLSCN, risk-averse retailers are characterized using the mean-CVaR method, and each member’s optimal decision-making behavior is described using variational inequalities. A projection contraction algorithm is used to solve the model, and numerical analysis is presented to investigate how risk aversion, carbon abatement investment cost coefficients, and carbon trading prices affect network equilibrium. The results indicate that increasing retailers’ risk aversion can enhance supply chain members’ profits and carbon reduction rates. Retailers prioritize expected profits, while other members prefer them to focus more on CVaR profits. When retailers are more risk-averse and value CVaR, traditional retail channels become more popular. Increasing the carbon reduction investment cost coefficients for suppliers and manufacturers can boost their profits, and retailers also support this move to charge more for low-carbon products and enhance utility. When carbon trading prices rise, suppliers and manufacturers opt to increase carbon reduction rates to generate more profits from selling carbon allowances. This study provides decision-making references for achieving both economic and environmental benefits for members of DLSCN. Full article

The paper demonstrates the nonsense of using Bitcoin in financial investments. By using mean-variance financial analysis, stochastic dominance, CVaR, and the Shapley value theory as analytical statistical models, I show how Bitcoin performs poorly by comparing it against other traded assets. The conclusion is reached by analyzing daily freely available market data for the period 2018–2023. Full article

This paper introduces a mean profit- conditional value-at-risk (CVaR) model for purchasing electricity on the day-ahead market (DA) by electric vehicles fleet aggregator (EVA). EVA controls electric vehicles (EVs) during their workplace parking, enabling smart charging and cost savings by accessing market prices that are potentially lower than flat rates available during home charging. The proposed stochastic linear programming model leverages market price scenarios to optimize aggregated charging schedules, which serve as templates for constructing effective DA bidding curves. It integrates an aspiration/reservation-based formulation of the mean profit-risk criteria, specifically Conditional Value at Risk (CVaR) to address the EVA’s risk aversion. By incorporating interactive analysis, the framework ensures adaptive and robust charging schedules and bids tailored to the aggregator’s risk preferences. Its ability to balance profitability with risk is validated in case studies. This approach provides a practical and computationally efficient tool for EV aggregators of global companies that can benefit from the workplace charging their fleets thanks to buying energy in the DA market. Full article

This study examines the impact of risk models and investors’ risk aversion on the selection of community solar portfolios. Various risk models to account for the volatility in the electrical power output of community solar, namely variance (Var), SemiVariance (SemiVar), mean absolute deviation (MAD), and conditional value at risk (CVaR), were considered. A statistical model based on modern portfolio theory was employed to simulate investors’ risk aversion in the context of community solar portfolio selection. The results of this study showed that the choice of risk model that aligns with investors’ risk-aversion level plays a key role in realizing more return and safeguarding against volatility in power generation. In particular, the findings of this research revealed that the CVaR model provides higher returns at the cost of greater volatility in power generation compared to other risk models. In contrast, the MAD model offered a better tradeoff between risk and return, which can appeal more to risk-averse investors. Based on the simulation results, a new approach was proposed for optimizing the portfolio selection process for investors with divergent risk-aversion levels by averaging the utility functions of investors and identifying the most probable outcome. Full article

Downside risk measures play a very interesting role in risk management problems. In particular, the value at risk (VaR) and the conditional value at risk (CVaR) have become very important instruments to address problems such as risk optimization, capital requirements, portfolio selection, pricing and hedging issues, risk transference, risk sharing, etc. In contrast, expectile risk measures are not as widely used, even though they are both coherent and elicitable. This paper addresses the bidual representation of expectiles in order to prove further important properties of these risk measures. Indeed, the bidual representation of expectiles enables us to estimate and optimize them by linear programming methods, deal with optimization problems involving expectile-linked constraints, relate expectiles with VaR and CVaR by means of both equalities and inequalities, give VaR and CVaR hyperbolic upper bounds beyond the level of confidence, and analyze whether co-monotonic additivity holds for expectiles. Illustrative applications are presented. Full article

This paper reviews 17 studies addressing dynamic option hedging in frictional markets through Deep Reinforcement Learning (DRL). Specifically, this work analyzes the DRL models, state and action spaces, reward formulations, data generation processes and results for each study. It is found that policy methods such as DDPG are more commonly employed due to their suitability for continuous action spaces. Despite diverse state space definitions, a lack of consensus exists on variable inclusion, prompting a call for thorough sensitivity analyses. Mean-variance metrics prevail in reward formulations, with episodic return, VaR and CvaR also yielding comparable results. Geometric Brownian motion is the primary data generation process, supplemented by stochastic volatility models like SABR (stochastic alpha, beta, rho) and the Heston model. RL agents, particularly those monitoring transaction costs, consistently outperform the Black–Scholes Delta method in frictional environments. Although consistent results emerge under constant and stochastic volatility scenarios, variations arise when employing real data. The lack of a standardized testing dataset or universal benchmark in the RL hedging space makes it difficult to compare results across different studies. A recommended future direction for this work is an implementation of DRL for hedging American options and an investigation of how DRL performs compared to other numerical American option hedging methods. Full article

The reduced cumulative distribution function (rCDF) is the maximal lower bound for the cumulative distribution function (CDF). It is equivalent to the inverse of the conditional value at risk (CVaR), or one minus the buffered probability of exceedance (bPOE). This paper introduces the reduced probability density function (rPDF), the derivative of rCDF. We first explore the relation between rCDF and other risk measures. Then we describe three means of calculating rPDF for a distribution, depending on what is known about the distribution. For functions with a closed-form formula for bPOE, we derive closed-form formulae for rPDF. Further, we describe formulae for rPDF based on a numerical bPOE when there is a closed-form formula for CVaR but no closed-form formula for bPOE. Finally, we give a method for numerically calculating rPDF for an empirical distribution, and compare the results with other methods for known distributions. We conducted a case study and used rPDF for sensitivity analysis and parameter estimation with a method similar to the maximum likelihood method. Full article

The objective of this study is to evaluate assets’ performance by considering the exit time within the risk measurement framework alongside Shannon entropy and, alternatively, excluding these factors, which can be used to create a portfolio aligned with short- or long-term objectives. This portfolio effectively balances the potential risks and returns, guiding investors to make decisions that are in line with their financial goals. To assess the performance, we used data envelopment analysis (DEA), whereby we utilized the risk measure as an input and the mean return as an output. The stop point probability–CVaR (SPP-CVaR) was the risk measurement used when considering the exit time. We calculated the SPP-CVaR by converting the risk-neutral density to the real-world density, calibrating the parameters, running simulations for price paths, setting the stop-profit points, determining the exit times, and calculating the SPP-CVaR for each stop-profit point. To account for negative data and to incorporate the exit time, we have proposed a model that integrates the mean return and SPP-CVaR, utilizing DEA. The resulting inefficiency scores of this model were compared with those of the mean-CVaR model, which calculates the risk across the entire time horizon and does not take the exit time and Shannon entropy into account. To accomplish this, an analysis was conducted on a portfolio that included a variety of stocks, cryptocurrencies, commodities, and precious metals. The empirical application demonstrated the enhancement of asset selection for both short-term and long-term investments through the combined use of Shannon entropy and the exit time. Full article

Taking into account both market benefits and power grid demand is one of the main challenges for cascade hydropower stations trading on electricity markets and secluding operation plan. This study develops a multi-objective optimal operation model for the long-term operation of cascade hydropower in different markets. Two objectives were formulated for economics benefits and carryover energy storage. One was to maximize the market utility value based on portfolio theory, for which conditional value at risk (CVaR) was applied to measure the risk of multi-markets. Another was the maximization of energy storage at the end of a year. The model was solved efficiently through a multi-objective particle swarm optimization (MOPSO). Under the framework of the MOPSO, the chaotic mutation search mechanism and elite individual retention mechanism were introduced to diversify and accelerate the non-inferior solution sets. Lastly, a dynamic updating of archives was established to collect the non-inferior solution. The proposed model was implemented on the hydropower plants on the Lancang River, which traded on the Yunnan Electricity Market (YEM). The results demonstrated non-inferior solution sets in wet, normal and dry years. A comparison in solution sets revealed an imbalanced mutual restriction between objectives, such that a 2.65 billion CNY increase in market utility costs a 13.96 billion kWh decrease in energy storage. In addition, the non-inferior solution provided various schemes for actual demands based on other evaluating indexes such as the minimum output, power generation and spillage. Full article

Reverse logistics is attracting attention due to the increasing concerns over environmental issues and the important economic impacts. The design of a reverse logistics network is a major strategic problem in the field of reverse logistics. As cost pressures in product returns continue to mount, a growing number of manufacturers have begun to outsource reverse logistics operations to third-party logistics (3PL) providers. On the other hand, considering disruption risks caused by natural or man-made factors in the reverse logistics network design is inevitable. This paper studies third-party reverse logistics network designs under uncertain disruptions. The problem is formulated as a risk-averse two-stage stochastic programming model with a mean risk objective. Two types of risk measures, value at risk (VaR) and conditional value at risk (CVaR), were examined, respectively. Finally, the sensitivity analysis of the model was carried out. The validity of the mean risk criteria is proved by comparison with risk-neutral approach. Moreover, the performance of the proposed model was examined by stochastic measures. Full article

Portfolio optimisation aims to efficiently find optimal proportions of portfolio assets, given certain constraints, and has been well-studied. While portfolio optimisation ascertains asset combinations most suited to investor requirements, numerous real-world problems impact its simplicity, e.g., investor preferences. Trading restrictions are also commonly faced and must be met. However, in adding constraints to Markowitz’s basic mean-variance model, problem complexity increases, causing difficulties for exact optimisation approaches to find large problem solutions inside reasonable timeframes. This paper addresses portfolio optimisation complexities by applying the Worst Case GARCH-Copula Conditional Value at Risk (CVaR) approach. In particular, the GARCH-copula methodology is used to model the portfolio dependence structure, and the Worst Case CVaR (WCVaR) is considered as an alternative risk measure that is able to provide a more accurate evaluation of financial risk compared to traditional approaches. Copulas model the marginal of each asset separately (which may be any distribution) and also the interdependencies between assets This allows an accurate risk to investment assessment to be applied in order to compare it with traditional methods. In this paper, we present two case studies to evaluate the performance of the WCVaR and compare it against the VaR measure. The first case study focuses on the time series of the closing prices of six major market indexes, while the second case study considers a large dataset of share prices of the Gulf Cooperation Council’s (GCC) oil-based companies. Results show that the values of WCVaR are always higher than those of VaR, demonstrating that the WCVaR approach provides a more accurate assessment of financial risk. Full article

Risk management is very important for individual investors or companies. There are several ways to measure the risk of investment. Prices of risky assets vary rapidly and randomly due to the complexity of finance market. Random interval is a good tool to describe uncertainty including both randomness and imprecision. Considering the uncertainty of financial market, we employ random intervals to describe returns of a risk asset and define an interval-valued risk measurement, which considers the tail risk. It is called the interval-valued conditional value-at-risk (ICVaR, for short). Similar to the classical conditional value-at-risk, ICVaR satisfies the sub-additivity. Under the new risk measure ICVaR, as a manner similar to the classical Mean-CVaR portfolio model, two optimal interval-valued portfolio selection models are built. The sub-additivity of ICVaR guarantees the global optimal solution to the Mean-ICVaR portfolio model. Based on the real data from mainland Chinese stock markets and international stock markets, the case study shows that our models are interpretable and consistent with the practical scenarios. Full article

Investors always pay attention to the two factors of return and risk in portfolio optimization. There are different metrics for the calculation of the risk factor, among which the most important one is the Conditional Value at Risk (CVaR). On the other hand, Data Envelopment Analysis (DEA) can be used to form the optimal portfolio and evaluate its efficiency. In these models, the optimal portfolio is created by stocks or companies with high efficiency. Since the search space is vast in actual markets and there are limitations such as the number of assets and their weight, the optimization problem becomes difficult. Evolutionary algorithms are a powerful tool to deal with these difficulties. The automotive industry in Iran involves international automotive manufacturers. Hence, it is essential to investigate the market related to this industry and invest in it. Therefore, in this study we examined this market based on the price index of the automotive group, then optimized a portfolio of automotive companies using two methods. In the first method, the CVaR measurement was modeled by means of DEA, then Particle Swarm Optimization (PSO) and the Imperial Competitive Algorithm (ICA) were used to solve the proposed model. In the second method, PSO and ICA were applied to solve the CVaR model, and the efficiency of the portfolios of the automotive companies was analyzed. Then, these methods were compared with the classic Mean-CVaR model. The results showed that the automotive price index was skewed to the right, and there was a possibility of an increase in return. Most companies showed favorable efficiency. This was displayed the return of the portfolio produced using the DEA-Mean-CVaR model increased because the investment proposal was basedon the stock with the highest expected return and was effective at three risk levels. It was found that when solving the Mean-CVaR model with evolutionary algorithms, the risk decreased. The efficient boundary of the PSO algorithm was higher than that of the ICA algorithm, and it displayed more efficient portfolios.Therefore, this algorithm was more successful in optimizing the portfolio. Full article

This paper focuses on the selection and optimisation of a cryptoasset portfolio, using the K-means clustering algorithm and GARCH C-Vine copula model combined with the differential evolution algorithm. This integrated approach allows the construction of a diversified portfolio of eight cryptocurrencies and determines an optimal allocation strategy making it possible to minimize the conditional value-at-risk of the portfolio and maximise the return. Our results show that stablecoins such as True-USD are negatively correlated to the other cryptoassets in the portfolio and could therefore be a safe haven for crypto-investors during market turmoil. Our findings are in line with previous studies exhibiting stablecoins as potential diversifiers. Full article