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The present research proposes a novel methodology to solve the problems faced by investors who take into consideration different investment criteria in a fuzzy context. The approach extends the stochastic mean-variance model to a fuzzy multiobjective model where liquidity is considered to quantify portfolio’s performance, apart from the usual metrics like return and risk. The uncertainty of the future returns and the future liquidity of the potential assets are modelled employing trapezoidal fuzzy numbers. The decision process of the proposed approach considers that portfolio selection is a multidimensional issue and also some realistic constraints applied by investors. Particularly, this approach optimizes the expected return, the risk and the expected liquidity of the portfolio, considering bound constraints and cardinality restrictions. As a result, an optimization problem for the constraint portfolio appears, which is solved by means of the NSGA-II algorithm. This study defines the credibilistic Sortino ratio and the credibilistic STARR ratio for selecting the optimal portfolio. An empirical study on the S&P100 index is included to show the performance of the model in practical applications. The results obtained demonstrate that the novel approach can beat the index in terms of return and risk in the analyzed period, from 2008 until 2018. First published online 8 October 2020

Typically, point forecasting methods are compared and assessed by means of an error measure or scoring function, with the absolute error and the squared error being key examples. The individual scores are averaged over forecast cases, to result in a summary measure of the predictive performance, such as the mean absolute error or the mean squared error. I demonstrate that this common practice can lead to grossly misguided inferences, unless the scoring function and the forecasting task are carefully matched. Effective point forecasting requires that the scoring function be specified ex ante, or that the forecaster receives a directive in the form of a statistical functional, such as the mean or a quantile of the predictive distribution. If the scoring function is specified ex ante, the forecaster can issue the optimal point forecast, namely, the Bayes rule. If the forecaster receives a directive in the form of a functional, it is critical that the scoring function be consistent for it, in the sense that the expected score is minimized when following the directive. A functional is elicitable if there exists a scoring function that is strictly consistent for it. Expectations, ratios of expectations and quantiles are elicitable. For example, a scoring function is consistent for the mean functional if and only if it is a Bregman function. It is consistent for a quantile if and only if it is generalized piecewise linear. Similar characterizations apply to ratios of expectations and to expectiles. Weighted scoring functions are consistent for functionals that adapt to the weighting in peculiar ways. Not all functionals are elicitable; for instance, conditional value-at-risk is not, despite its popularity in quantitative finance.

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.

The maximum expert consensus model (MECM) with uncertain cost is a prominent area of research in group decision-making (GDM). The typical approach to addressing uncertain costs involves either possessing detailed information about its distribution or ensuring that the result is optimal under worst-case cost scenarios. In this paper, we assume that the probability of meeting the total uncertain consensus cost is not less than a given threshold at a specified level of confidence. Only the first- and second-order moments and the support of uncertain costs are used to construct the ambiguous probability distribution set. Building on distributionally robust optimization (DRO), we propose a novel distributionally robust chance-constrained MECM (DRCC-MECM) with incomplete information on uncertain costs. Additionally, by approximating the total uncertain consensus cost chance constraint with a worst-case conditional value-at-risk (CVaR) constraint, the DRCC-MECMs with different aggregation operators are transformed into tractable semi-definite programming models. Finally, the efficacy and advantages of the proposed models are demonstrated through an application to transboundary water pollution control in China. Sensitivity and comparative analyses further underscore the effectiveness of the proposed models in addressing uncertain costs in this context.

With the rapid development of microgrids (MGs) and electric vehicles (EVs), leveraging the flexibility of EVs in MG optimization scheduling has attracted significant attention. However, existing research does not consider the impact of EV scheduling potential on MG uncertainty or the avoidance of conflicts in EV users’ mobility needs and their charging/discharging activities. Therefore, this paper proposes a two-stage microgrid energy scheduling model integrated with the conditional value-at-risk (CVaR) and dynamic cooperative game theory. In addition, the aforementioned issues are specifically addressed by considering both EV scheduling potential and travel risk. The day-ahead model minimizes the MG’s operational costs, where a CVaR-based uncertainty model for MG net load is established to quantify risks from both renewable energy generation and load. The EV dispatchable potential is calculated using Minkowski summation theory. In the real-time stage, the adjustment of participating EVs and optimal incentive compensation costs are determined through the proposed EV travel risk model and dynamic cooperative game, aiming to minimizing the MG’s real-time adjustment costs. The simulation results validate the effectiveness of the proposed method, which can help to reduce the operational costs of MGs by 4%, reduce real-time adjustment costs by about 85%, and decrease load variability by 3%. For the main grid, the proposed method can avoid the “peak-on-peak” phenomenon. For EV users, travel demands can be fully satisfied, charging costs can be reduced for 34% of users, and 2.4% of users gain profits.

In today’s fast-paced world, delays or prolonged customer waiting times pose a threat to the firm’s profitability. This study utilizes the mean-CVaR metric to incorporate the risk associated with prolonged customer waiting times into the optimal trade-off decisions. For this purpose, we consider a single inventory system that faces Poisson demand and utilizes a base-stock policy to replenish its inventory, which takes a fixed amount of time. The firm implements a preorder strategy, encouraging customers to place their orders a fixed amount of time in advance of their actual needs, a period referred to as the commitment lead time. The firm rewards customers with a bonus termed the commitment cost, which increases with the length of the commitment lead time. We aim to determine the optimal control policy, including the optimal base-stock level and optimal commitment lead time, that minimizes the long-run average cost. The cost includes inventory holding, commitment, and customer waiting costs, with the latter adjusted for the firm’s degree of risk aversion. The optimal policy depends on the interdependence of the decisions, with the optimal commitment lead time following a “bang-bang” pattern, and the corresponding optimal base-stock level taking an “all-or-nothing” form. For linear commitment costs with a cost factor per time unit, we identify a threshold that increases with the firm’s risk aversion degree. Firms with greater risk aversion typically favor the buy-to-order strategy, while those with lower risk aversion may opt for either buy-to-stock or buy-to-order depending on their assessment of waiting costs.

This paper investigates the uncertain stochastic resource allocation problem in which the results of a given allocation of resources are described as probabilities and these probabilities are considered to be uncertain from practical aspects. Here uncertainties are introduced by assuming that these probabilities depend on random parameters which are impacted by various factors. The redundancy allocation problem (RAP) and the multi-stage weapon-target assignment (MWTA) problem are special cases of stochastic resource allocation problems. Bi-objective models for the uncertain RAP and MWTA problem in which the conditional value-at-risk measure is used to control the risk brought by uncertainties are presented in this paper. The bi-objective formulation covers the objectives of minimizing the risk of failure of completing activities and the resulting cost of resources. With the aim of determining referenced Pareto fronts, a linearized formulation and an approximated linear formulation are put forward for RAPs and MWTA problems based on problem-specific characteristics, respectively. Two state-of-the-art decomposition-based multi-objective evolutionary algorithms (i.e., MOEA/D-AWA and DMOEA-εC) are used to solve the formulated bi-objective problem. In view of differences between MOEA/D-AWA and DMOEA-εC, two matching schemes inspired by DMOEA-εC are proposed and embedded in MOEA/D-AWA. Numerical experiments have been performed on a set of uncertain RAP and MWTA instances. Experimental results demonstrate that DMOEA-εC outperforms MOEA/D-AWA on the majority of test instances and the superiority of DMOEA-εC can be ascribed to the ε-constraint framework.

The integration of advanced technology in smart homes has made the prevention of energy waste in the residential and building sectors a significant concern for both developed and developing nations in recent decades. This paper offers a thorough model for maximizing energy generation and consumption in smart homes with demand-responsive loads, energy storage systems (ESS), solar photovoltaic (PV) panels, bidirectional electric vehicles (EVs) that can communicate with both grid-to-vehicle (G2V) and vehicle-to-grid (V2G). The model uses a mixed-integer linear programming (MILP) framework to assess the technical and economic effects of these factors while accounting for the inherent uncertainties in outside temperatures, lighting loads, sun irradiation, and EV supply. Important situations include time-shifting deferrable loads (like washing machines), selling excess PV-generated energy to the grid, and putting price-based demand response (DR) techniques like real-time pricing (RTP) and day-ahead pricing (DAP) into practice. To manage uncertainties and adaptively schedule the operations of appliances, electric vehicles, and energy storage systems (ESS), the proposed HEMS uses a fuzzy programming technique supplemented by reinforcement learning. Harris Hawks Optimization (HHO) and Wild Horse Optimization (WHO) are two examples of metaheuristic algorithms used for optimization, whereas the conditional value at risk (CVaR) criterion is used for risk management. MATLAB simulations show that this adaptive technique can save up to 53% of home electricity expenses in tested scenarios while keeping computational efficiency under 60 s, which makes it suitable for real-time applications. The strategy opens the door for resilient and sustainable residential energy systems by highlighting new developments in smart grid integration, renewable energy use, and AI-driven optimization.

We study a multilocation newsvendor model with a retailer owning multiple retail stores, each of which is operated by a manager who decides the order quantity for filling random customer demand of a product. Store managers and the retailer are all risk averse, but managers are more risk averse than the retailer. We adopt conditional value-at-risk (CVaR) as the performance measure and consider two alternative strategies to improve the system’s performance. First, the retailer centralizes the ordering decisions. Second, managers still decide the order quantity for their own store, whereas their inventories are pooled together. We analyze and compare the optimal order quantities and the resultant CVaR values of the systems and study their comparative statistics. For centralization, we find that each store has a higher inventory level in the centralized system than in the decentralized system, and centralization positively benefits the retailer as long as some store managers are strictly more risk averse than the retailer. When there is inventory pooling, the ordering decisions in the decentralized system depend on how the additional profit from pooling is allocated among the stores. We consider a weighted proportional allocation rule and characterize the Nash equilibrium of the resultant ordering game among the store managers. Our key finding is that as long as the store managers are sufficiently more risk averse than the retailer or the demands are very heavy tailed, inventory pooling is less beneficial than centralization. We further derive a lower bound on the value of centralization and two upper bounds on the value of inventory pooling. Finally, our analytical results are illustrated using a data set from an online retailer in China, and various comparative statics are further examined via extensive numerical experiments. This paper was accepted by Charles Corbett, operations management .

Socially responsible investments represent the heart of a sustainable and inclusive economy. The goals set by the regulatory framework have encouraged the integration of responsible concerns into the corporate business strategy. In this paper, we present an operation research design under a risk management perspective that adjusts the portfolio selection problem for the ethical values of investors. We focus on the firms of the Euro Stoxx 50 during the years 2007–2019 and cluster the companies according to the Environmental Score (E). For each cluster, we build a portfolio that minimizes the Conditional Value-at-Risk (CVaR) introducing the constraint on the E into the optimization problem. We compute the Shapley Value for each portfolio using the minimized CVaR and the optimized E as the characteristic functions to yield, respectively, the contribution of the portfolios to the public welfare in terms of the exposure to the tail market risk and the required environmental commitment to mitigate it. The cluster analysis shows that the efforts of the firms to embrace environmental concerns are paid off with generally lower contribution to the tail market risk. From the two characterizations of the Shapley Value, the computation of well-known measures of financial performance (Sharpe, Sortino, and Calmar ratios) reveals that optimal portfolio choices should prioritize the environmental commitment of the companies.