Downside Risk Constraints Research Articles

Risk evaluation and retail electricity pricing using downside risk constraints method

Electricity in the retail market has a different value for different types of consumers. Therefore, different retail prices are usually determined for various consumers in the retail market. However, imposed risks from uncertain parameters are a big challenge in the real-time retail market pricing process. This paper proposed a real-time pricing (RTP) framework for various users including residential, commercial, and industrial consumers by the electricity retailer. In addition, uncertainties of various input parameters such as output power of renewable energy resources, electricity demand, and pool market price are modeled using scenario-based stochastic approach while downside risk constraints method is proposed to model risk associated with uncertainties. By implementing this method, electricity retailer will be able to select various risk-based strategies. Furthermore, numerical results illustrate the various risks versus various profits by the occurring of each scenario which helps the retailer for decisions-making in different scenarios. According to obtained results, retailer by choosing of zero risk strategy can reduce its risk by 100% while expected profit is reduced by 2.07%. In addition, offered RTP by the retailer is higher for industrial, commercial, and residential customers, respectively. Finally, risk-averse and risk-neutral strategies of electricity retailer are determined in the power procurement problem.

RETRACTED: Risk-involved stochastic performance of hydrogen storage based intelligent parking lots of electric vehicles using downside risk constraints method

Today, the utilizations of hydrogen storage systems (HSS), renewable generation units (PV and wind generation) and distributed energy units are increased in the intelligent parking lots (IPL) in order to charge the electric vehicles (EVs) with clean energy sources. In this work, the uncertainties of upstream grid price, the demand of IPL, wind speed, solar irradiation and temperature are modeled via scenario approach based on stochastic programing. Furthermore, the downside risk constraints method (DRCM) is applied to consider risk related to uncertainties to get risk-involved stochastic performance of hydrogen storage based intelligent parking lots of electric vehicles. The proposed risk-based formulation is modeled using mixed-integer linear programming (MIP) which is implemented under GAMS software and solved via CPLEX solver. Two cases namely risk-averse and risk-neutral strategies are studied and compared to show the effects of DRCM implementation. The obtained results demonstrate the expected performance cost (EPC) of IPL is slowly raised while risk-in-cost (RIC) is significantly reduced due to model of risk related to uncertainties.

RETRACTED: Risk-averse stochastic operation of a power system integrated with hydrogen storage system and wind generation in the presence of demand response program

Wind generation (WG) units as renewable energy sources (RESs) are increasing in the world due to environmental functions and lack of conventional energy sources. Also, hydrogen storage system (HSS) as an energy storage system (ESS) is used to cope with variable nature of RESs in which the concepts of power to hydrogen (P2H) and hydrogen to power (H2P) are defined. In this work, a risk-averse stochastic operation of HSS and WG is modeled using a scenario-based stochastic approach by considering price-responsive demand response (DR) program. All uncertainties are modeled via a scenario-based stochastic approach while the risk related uncertainties are modeled via the downside risk constraints (DRC) to capture the risk-averse operation of the HSS and WG. In order to investigate the impact of DRC implementation, a risk-averse strategy is compared versus risk-neutral strategy. Compared results show that the risk-in-cost (RIC) is reduced while the expected operation cost (EOC) is raised to deal with the risk of the uncertainty.

Risk-Constrained Stochastic Optimization of a Concentrating Solar Power Plant

A central concentrating solar power (CSP) plant is increasing in the power systems as novel technology in the solar energy sources. Also, solar thermal storage unit is combined with the CSP plant to increase flexibility and decrease the dependence on the instantaneous solar radiation. Furthermore, the CSP plant can be obtained the optimal offering strategies to submit to the electricity market in order to sell the produced power and increase the expected profit. In this paper, the uncertainty modeling of solar irradiation and electricity market price is a big challenge for a CSP plant. Therefore, the scenario-based stochastic framework is proposed for optimal scheduling of a CSP plant in the presence of uncertainties to obtain optimal offering curves in order to sell to power market. Also, the risk related to uncertainties is considered via the downside risk constraints (DRC), which leads to obtain risk-constrained stochastic optimization of a CSP plant. The proposed model is formulated as mixed-integer linear programming, which is solved via CPLEX solver under GAMS optimization software. Risk-averse strategy is introduced in comparison with risk-neutral strategy to investigate the impacts of DRC implementation, which leads to decrease the expected profit while the expected risk-in-profit reduced.

RETRACTED: Risk-based stochastic scheduling of energy hub system in the presence of heating network and thermal energy management

Energy hub as the future’s energy technology has discussed a new point of view in the energy consumption optimization field. The heating market as a new energy market, which is recently in some countries, presents a new venue for an energy hub operation. Heat demand side management is another control variable that makes the hub’s management more active and flexible. Providing heat from the heating market and utilization heat demand response features can influence the hub’s operational cost because of adding new degrees of freedom to the problem. In this paper, risk-based stochastic scheduling of energy hub is formulated via scenario-based stochastic programming by considering a wind turbine, electricity market, electrical and heat storage systems, electrical and heat demand response programs (DRP), and the heating market as the new found energy market. The downside risk constraints (DRC) are proposed to minimize the risk associated with uncertainties in order to obtain the risk-based scheduling of energy hub. Simulation results have been presented in different cases to show the impact of DRC implementation which the expected cost is increased while the risk-in-cost (RIC) is decreased. Finally, the effect of the DRP on the problem is investigated and the results show that the expected cost and RIC are decreased.

Impact of the downside risk of retailer on the supply chain coordination

This paper analyzes the coordinating mechanisms for a single-period supply chain comprising of one supplier and one retailer. The later is constrained by downside risk. We model the decision problems with the newsvendor model, and then analytically derive the optimal order policies of the retailer. We have analyzed several often used coordinating mechanisms under retailer downside risk constraint. We find that none of the price-only contract, returns policies contract and revenue sharing contract can coordinate a supply chain with retailer’s downside risk constraint. However, by integrating the transfer payment contract with returns policy contract and the revenue sharing contract, perfect coordination is possible. For optimal decisions of the supplier, we use the numerical method to analyze the effect of the retailer downside risk on decision variables, and profits of the supplier and the retailer. Compared with the case of no risk constraints, the study has shown that the splitting of the expected channel profits between the supplier and the retailer is dependent on the retailer’s risk attitude. The more risk-reverse the retailer is, the lower are the profits earned by the retailer and, of course, the more are the profits of the supplier. We close with a discussion of contract implementation issues and future research.

A dynamic Stackelberg game model for portfolio procurement

Purpose – The purpose of this paper is to propose a portfolio procurement framework to response to uncertain customer demand and purchasing price volatility in a simultaneous manner. Then it aims to obtain optimal procurement and production decisions under the portfolio framework to maximize profit. Design/methodology/approach – The portfolio procurement problem is modeled as a dynamic Stackelberg game and Nash equilibrium solutions are obtained. The portfolio procurement framework is analyzed in the settings, with both risk-neutral objective and downside risk constraints measure of contract prices. Findings – By obtaining the Nash equilibrium solutions for both the buyer’s ordering decisions and the supplier’s optimum production decisions, Stackelberg game model for portfolio procurement is proved to be feasible. Additionally, downside risk constrains are proposed to help supply chain participants’ to evaluate the profitability and risk probabilities of the designed procurement contracts under the uncertain customer demand and spot market. Research limitations/implications – This paper assumes the supplier is risk averse and the buyer is risk neutral, and it would be interesting to examine the performances of portfolio procurement strategy with different risk attitudes participants. Practical implications – This research could help the buyer respond to not only demand uncertainty but also the volatile spot price in the procurement process. Related optimal portfolio procurement strategy can be carried out to improve the enterprise’ procurement plan by adjusting the order of long-term contract, option contract and the spot market. The proposed framework could also help suppliers design and evaluate contracts for buyers with different risk preference, and on the other hand help the buyers decide if she should accept the contracts from the supplier. Social implications – This research should also increase awareness in both academia and industry on the opportunities of using the dynamic portfolio procurement approach to enhance flexibility and to mitigate the inventory as well as price risks in the procurement process. Effective downside risk constrains on contract prices could also help to protect the bottom line of companies with different risk preference. Originality/value – The portfolio procurement framework proposed in this research can mitigate inventory and price risks simultaneously. Also, instead of solving the portfolio procurement planning problem in computational simulation experiments as in previous research, this paper proposed a dynamic game model for this portfolio-based procurement problem and obtained its Nash equilibrium solutions for both the buyer’s ordering decisions and the supplier’s optimum production decisions. Finally, an innovative and simple downside risk constraints has been designed to help the buyer evaluate supplier’s contract prices according to their individual risk preference.

Tail Risk Constraints and Maximum Entropy

Portfolio selection in the financial literature has essentially been analyzed under two central assumptions: full knowledge of the joint probability distribution of the returns of the securities that will comprise the target portfolio; and investors’ preferences are expressed through a utility function. In the real world, operators build portfolios under risk constraints which are expressed both by their clients and regulators and which bear on the maximal loss that may be generated over a given time period at a given confidence level (the so-called Value at Risk of the position). Interestingly, in the finance literature, a serious discussion of how much or little is known from a probabilistic standpoint about the multi-dimensional density of the assets’ returns seems to be of limited relevance. Our approach in contrast is to highlight these issues and then adopt throughout a framework of entropy maximization to represent the real world ignorance of the “true” probability distributions, both univariate and multivariate, of traded securities’ returns. In this setting, we identify the optimal portfolio under a number of downside risk constraints. Two interesting results are exhibited: (i) the left- tail constraints are sufficiently powerful to override all other considerations in the conventional theory; (ii) the “barbell portfolio” (maximal certainty/ low risk in one set of holdings, maximal uncertainty in another), which is quite familiar to traders, naturally emerges in our construction.

The effect of risk aversion on a supply chain with postponed pricing

We consider a supply chain consisting of a supplier and a risk-averse retailer operating under endogenous demand in retail pricing. The demand potential is uncertain and is revealed at the beginning of the selling season when it is too late to order products. The product price, on the other hand, is not determined in advance and can be postponed until the demand is revealed. The goal is to study the effect of risk-aversion and postponed pricing on both the retailer’s decisions and the overall supply chain. We find that the risk-averse retailer does not necessarily order less than the risk-neutral one and may introduce a bias by choosing a specific demand distribution. We contrast two specific choices. One is symmetric (balanced) with respect to the mean demand potential. The other is skewed (pessimistic) with most observations expected below the mean demand potential. Our numerical results show that the binding downside risk constraint deteriorates the supply chain performance when the forecast is balanced and improves it when the forecast is pessimistic.

A Numerical Study for Robust Active Portfolio Management with Worst-Case Downside Risk Measure

Recently, active portfolio management problems are paid close attention by many researchers due to the explosion of fund industries. We consider a numerical study of a robust active portfolio selection model with downside risk and multiple weights constraints in this paper. We compare the numerical performance of solutions with the classical mean-variance tracking error model and the naive1/Nportfolio strategy by real market data from China market and other markets. We find from the numerical results that the tested active models are more attractive and robust than the compared models.

Adjusting service performance criteria based on categorised information from previous reports

This paper uses non-linear least square method for developing stochastic models to fit the historical ordinal data for evaluating service performances. This paper then provides formula to adjust current criteria to a future point, to set criteria to promote performance, and determine criteria to hedge risks. This paper shows that current criteria can be adjusted for a future point by incorporating the trend f and time factors. By evaluating the benefit of achieving the criterion and the loss of missing the criterion, this paper develops the equations to adjust current criteria under different conditions. By setting a downside risk constraint, companies can exclude the criterion choices which are very risky even if the returns are extremely high when they succeed. The paper further describes, by using numerical examples, the impacts of parameters to the downside risk.

The Effect of Risk Aversion on Manufacturer Advertising in a Two-Stage Supply Chain

Abstract We consider a supply chain system with a risk-neutral manufacturer as the leader and a risk-averse retailer as the follower with uncertain demand. At the beginning of the game, the manufacturer makes efforts on advertising and then the retailer decides its order quantity before demand realization. The retailer's risk aversion is modeled by the Value-at-Risk (VaR) approach with the downside risk constraint. The analysis of equilibrium strategies indicates some characteristics of the game are different from those under risk-neutral assumptions. We find that the manufacturer can effectively prevent the risk-averse retailer from downsizing the order quantity through advertising. In order to explain the difference, we investigate the impacts of risk aversion on the manufacturer's advertising decision and the retailer's ordering decision. We find that the retailer with moderate degree of risk aversion orders a larger volume and receives greater advertising support from the manufacturer. Moreover, the feasible combinations of target profit and downside risk for moderate risk aversion are discussed to derive the relationship of the two parameters. In addition, we make a simple analysis of the situation with two independent retailers who have heterogeneous degrees of risk aversion.

Risk Averse Members Coordination with Extended Buy-Back Contract

This paper considers how to coordinate a supply chain (SC) consisted of one supplier and one retailer who possess different risk aversion preference with a contract. Based on the classical buy-back contract, this paper presents an extended buy-back contract. In addition to the member’s objective of maximizing his expected profit, downside risk constraint is used to represent the SC member’s risk aversion preference. Under different risk aversion preference combination, the SC perfect solution existence conditions are identified and the specific contract is provided accordingly. This research finds out that, with a low risk aversion supplier and a high risk aversion retailer, the supplier as the SC coordinator can give the retailer incentive to increase the order quantity so as to reach SC perfect coordination. Finally a numerical analysis verifies the effectiveness of the extended buy-back contract.

Multi-product newsvendor problem with value-at-risk considerations

We consider the single period stochastic inventory (newsvendor) problem with downside risk constraints. The aim in the classical newsvendor problem is maximizing the expected profit. This formulation does not take into account the risk of earning less than a desired target profit or losing more than an acceptable level due to the randomness of demand. We utilize Value at Risk (VaR) as the risk measure in a newsvendor framework and investigate the multi-product newsvendor problem under a VaR constraint. To this end, we first derive the exact distribution function for the two-product newsvendor problem and develop an approximation method for the profit distribution of the N-product case ( N>2). A mathematical programming approach is used to determine the solution of the newsvendor problem with a VaR constraint. This approach allows us to handle a wide range of cases including the correlated demand case that yields new results and insights. The accuracy of the approximation method and the effects of the system parameters on the solution are investigated numerically.

Utility maximization under a shortfall risk constraint

The article analyzes optimal portfolio choice of utility maximizing agents in a general continuous-time financial market model under a joint budget and downside risk constraint. The risk constraint is given in terms of a class of convex risk measures. We do not impose any specific assumptions on the price processes of the underlying assets. We analyze under which circumstances the risk constraint is binding. We provide a closed-form solution to the optimization problem in a general semimartingale framework. For a complete market, the wealth maximization problem is equivalent to a dynamic portfolio optimization problem.

Revisiting the home bias puzzle: Downside equity risk

Deviations from normality in financial return series have led to the development of alternative portfolio selection models. One such model is the downside risk model, whereby the investor maximizes his return given a downside risk constraint. In this paper, we empirically observe the international equity allocation for the downside risk investor using nine international markets' returns over the last 34 years. The results hold for both daily and monthly data; and also from an international perspective. Due to greater downside risk, investors may think globally, but instead act locally. The model's results therefore provide an alternative view of the home bias puzzle.

Downside risk-aversion analysis for a single-stage newsvendor problem

We extend the classical newsvendor problem by introducing a downside risk constraint from the perspective of inventory control. At the beginning of a replenishment period the newsvendor will place an order, then he will review the inventory level at the end of the period. If the inventory level is positive then he will bear the holding cost and if the inventory level is negative then he will bear the backorder cost. The optimal order quantity has a simple form. We analyze the form of the optimal order quantity when we restrict that the probability that the cost level is larger than or equal to a fixed cost constant is less than a fixed value of probability. At last, we analyze the case that the fixed cost constant is equal to the expected cost.

Portfolio selection with heavy tails

Consider the portfolio problem of choosing the mix between stocks and bonds under a downside risk constraint. Typically stock returns exhibit fatter tails than bonds corresponding to their greater downside risk. Downside risk criteria like the safety first criterion therefore often select corner solutions in the sense of a bonds only portfolio. This is due to a focus on the asymptotically dominating first order Pareto term of the portfolio return distribution. We show that if second order terms are taken into account, a balanced solution emerges. The theory is applied to empirical examples from the literature.

Coordination of Supply Chains with Risk‐Averse Agents

The extant supply chain management literature has not addressed the issue of coordination in supply chains involving risk‐averse agents. We take up this issue and begin with defining a coordinating contract as one that results in a Pareto‐optimal solution acceptable to each agent. Our definition generalizes the standard one in the risk‐neutral case. We then develop coordinating contracts in three specific cases: (i) the supplier is risk neutral and the retailer maximizes his expected profit subject to a downside risk constraint; (ii) the supplier and the retailer each maximizes his own mean‐variance trade‐off; and (iii) the supplier and the retailer each maximizes his own expected utility. Moreover, in case (iii), we show that our contract yields the Nash Bargaining solution. In each case, we show how we can find the set of Pareto‐optimal solutions, and then design a contract to achieve the solutions. We also exhibit a case in which we obtain Pareto‐optimal sharing rules explicitly, and outline a procedure to obtain Pareto‐optimal solutions.

Portfolio Selection with Heavy Tails

Consider the portfolio problem of choosing the mix between stocks and bonds under a downside risk constraint. Typically, stock returns exhibit fatter tails than bonds corresponding to their greater downside risk. Downside risk criteria like the safety first criterion, therefore, of ten select corner solutions in the sense of a bonds only portfolio. This is due to a focus on the asymptotically dominating first order Pareto term of the portfolio return distribution. We show that if second order terms are taken into account, a balanced solution emerges. The theory is applied to empirical examples from the literature.