Optimal Option Purchasing Decisions for the Risk-Averse Retailer with Shortage Cost

2019 ◽  
Vol 36 (02) ◽  
pp. 1940005 ◽  
Author(s):  
Xin-Sheng Xu ◽  
Felix T. S. Chan
Keyword(s):  
Confidence Level ◽  
Value At Risk ◽  
Expected Profit ◽  
Conditional Value At Risk ◽  
Risk Averse ◽  
Purchasing Decisions ◽  
Shortage Cost ◽  
High Return ◽  
Potential Risks ◽  
Purchase Quantity

To hedge against potential risks, this paper introduces the conditional value-at-risk (CVaR) measure into the option purchasing for the risk-averse retailer with shortage cost. We introduce two models for the risk-averse retailer to select the optimal option purchase quantity. It is found that both two optimal option purchase quantities to two models can be decreasing in the retail price and increasing in the option executing price under certain conditions. This is different from the optimal option purchase quantity for a risk-neutral retailer to maximize the expected profit. It is found that both two optimal option purchase quantities may be increasing or decreasing in the confidence level, which implies a retailer who becomes more risk-averse may purchase more or fewer options to hedge against potential risks. Under both two optimal option purchase quantities, it is proven that the retailer’s expected profit is decreasing in the confidence level. This confirms the fact that high return implies high risk while low risk comes with low return.

Coordinating Supply Chain with Buy-Back Contracts in the Presence of Risk Aversion

2018 ◽  
Vol 35 (02) ◽  
pp. 1840008 ◽  
Author(s):  
Chunlin Luo ◽  
Xin Tian ◽  
Xiaobing Mao ◽  
Qiang Cai
Keyword(s):  
Supply Chain ◽  
Risk Aversion ◽  
Value At Risk ◽  
Performance Measure ◽  
Expected Profit ◽  
Conditional Value At Risk ◽  
Allocation Rule ◽  
Risk Averse ◽  
Buy Back ◽  
The Impact

This paper addresses the operational decisions and coordination of the supply chain in the presence of risk aversion, where the risk averse retailer’s performance is measured by a combination of the expected profit and conditional value-at-risk (CVaR). Such performance measure reflects the desire of the retailer to maximize the expected profit on one hand and to control the downside risk of the profit on the other hand. The impact of risk aversion on the supply chain’s decision and performance is also explored. To overcome the inefficiency due to the double marginalization and the aggravation resulting from risk aversion, we investigate the buy-back contract to coordinate the supply chain. Such contract can largely increase the supply chain’s profit, especially when the retailer is more risk averse. Lastly, we extend such risk measure to the widely-used business model nowadays — platform selling model, and explore the impact of the allocation rule on the manufacturer’s decision.

scholarly journals Optimal Procurement Strategy for Supply Chain with Trade Credit and Backorder under CVaR Criterion

2021 ◽  
Vol 13 (18) ◽  
pp. 10201
Author(s):  
Gaoke Wu ◽  
Bo Feng ◽  
Libin Guo
Keyword(s):  
Supply Chain ◽  
Confidence Level ◽  
Value At Risk ◽  
Trade Credit ◽  
Wholesale Price ◽  
Conditional Value At Risk ◽  
Risk Averse ◽  
Financial Pressure ◽  
Strategy Model ◽  
Credit Financing

Some capital-constrained and risk-averse retailers may unable to obtain financing from banks due to insufficient collateral and high loan costs, so some retailers tend to use trade credit financing to ease their financial pressure. For the two echelon supply chain composed of a well-funded supplier and a capital-constrained retailer with risk-averse preference, a trade credit strategy model with the supplier-led is established in this paper. By analyzing both parties’ benefits, we derive the model solution and provide optimal decisions to all petitioners. The results obtained in this paper show that the optimum order quantity under the Conditional Value-at-Risk (CVaR) criterion declines w.r.t. the confidence level, and the wholesale price of the supplier increases w.r.t. the confidence level. The reason is that when the retailer makes fewer orders, the supplier will correspondingly increase the wholesale price to maximize their profit. On the other hand, the ordering policy with allowing backorder will make the retailer place fewer orders. Finally, the proposed model is indicated by the given numerical experiments.

scholarly journals A Deep Peak Regulation Auxiliary Service Bidding Strategy for CHP Units Based on a Risk-Averse Model and District Heating Network Energy Storage

Energies ◽  
2019 ◽  
Vol 12 (17) ◽  
pp. 3314 ◽  
Author(s):  
Liang Tian ◽  
Yunlei Xie ◽  
Bo Hu ◽  
Xinping Liu ◽  
Tuoyu Deng ◽  
...  
Keyword(s):  
Energy Storage ◽  
Electricity Market ◽  
Value At Risk ◽  
District Heating ◽  
Expected Profit ◽  
Conditional Value At Risk ◽  
Bidding Strategy ◽  
Energy Market ◽  
Risk Averse ◽  
Service Market

With the advance of China’s power system reform, combined heat and power (CHP) units can participate in multi-energy market. In order to maximize CHP profit in a multi-energy market, a bidding strategy for deep peak regulation auxiliary service of a CHP based on a two-stage stochastic programming risk-averse model and district heating network (DHN) energy storage was proposed. The quotation set of competitors and load uncertainty was modeled with a Latin hypercube sampling (LHS) method. A dynamic queuing method was used to clear the market for the deep peak regulation auxiliary service to determine the bidding capacities of CHPs in the electricity market and the deep peak regulation auxiliary service market, respectively. Finally, the conditional value-at-risk (CVaR) indicator is used to measure the risk brought by the system uncertainty to the CHP, and the quotation coefficient is determined after considering the expected profit and risk profit comprehensively. The results of the example show that the profits produced by simultaneous participation in both electricity market and the deep peak regulation auxiliary service market are increased by approximately 9.5% compared with the profits produced by only participation in a single market. In addition, the use of DHN energy storage led to a profit increase of approximately 4.6%. As the risk aversion coefficient increases, the expected profit will be further reduced.

scholarly journals Risk-Averse Multi-Stage Stochastic Programming to Optimizing Vaccine Allocation and Treatment Logistics for Effective Epidemic Response

2021 ◽  
Author(s):  
Xuecheng Yin ◽  
Esra Buyuktahtakin
Keyword(s):  
Value At Risk ◽  
Virus Disease ◽  
Risk Measure ◽  
Adverse Outcomes ◽  
Mixed Integer ◽  
Conditional Value At Risk ◽  
Risk Averse ◽  
Expected Number ◽  
Multi Stage ◽  
Stochastic Mixed Integer Programming

Existing compartmental-logistics models in epidemics control are limited in terms of optimizing the allocation of vaccines and treatment resources under a risk-averse objective. In this paper, we present a data-driven, mean-risk, multi-stage, stochastic epidemics-vaccination-logistics model that evaluates various disease growth scenarios under the Conditional Value-at-Risk (CVaR) risk measure to optimize the distribution of treatment centers, resources, and vaccines, while minimizing the total expected number of infections, deaths, and close contacts of infected people under a limited budget. We integrate a new ring vaccination compartment into a Susceptible-Infected-Treated-Recovered-Funeral-Burial epidemics-logistics model. Our formulation involves uncertainty both in the vaccine supply and the disease transmission rate. Here, we also consider the risk of experiencing scenarios that lead to adverse outcomes in terms of the number of infected and dead people due to the epidemic. Combining the risk-neutral objective with a risk measure allows for a trade-off between the weighted expected impact of the outbreak and the expected risks associated with experiencing extremely disastrous scenarios. We incorporate human mobility into the model and develop a new method to estimate the migration rate between each region when data on migration rates is not available. We apply our multi-stage stochastic mixed-integer programming model to the case of controlling the 2018-2020 Ebola Virus Disease (EVD) in the Democratic Republic of the Congo (DRC) using real data. Our results show that increasing the risk-aversion by emphasizing potentially disastrous outbreak scenarios reduces the expected risk related to adverse scenarios at the price of the increased expected number of infections and deaths over all possible scenarios. We also find that isolating and treating infected individuals are the most efficient ways to slow the transmission of the disease, while vaccination is supplementary to primary interventions on reducing the number of infections. Furthermore, our analysis indicates that vaccine acceptance rates affect the optimal vaccine allocation only at the initial stages of the vaccine rollout under a tight vaccine supply.

scholarly journals ESTIMASI NILAI CONDITIONAL VALUE AT RISK MENGGUNAKAN FUNGSI GAUSSIAN COPULA

2015 ◽  
Vol 4 (4) ◽  
pp. 188
Author(s):  
HERLINA HIDAYATI ◽  
KOMANG DHARMAWAN ◽  
I WAYAN SUMARJAYA
Keyword(s):  
At Risk ◽  
Confidence Level ◽  
Value At Risk ◽  
Risk Measure ◽  
Copula Function ◽  
Gaussian Copula ◽  
Nonlinear Dependence ◽  
Conditional Value At Risk ◽  
Dependence Structure ◽  
Measurement Tools

Copula is already widely used in financial assets, especially in risk management. It is due to the ability of copula, to capture the nonlinear dependence structure on multivariate assets. In addition, using copula function doesn’t require the assumption of normal distribution. There fore it is suitable to be applied to financial data. To manage a risk the necessary measurement tools can help mitigate the risks. One measure that can be used to measure risk is Value at Risk (VaR). Although VaR is very popular, it has several weaknesses. To overcome the weakness in VaR, an alternative risk measure called CVaR can be used. The porpose of this study is to estimate CVaR using Gaussian copula. The data we used are the closing price of Facebook and Twitter stocks. The results from the calculation using 90%  confidence level showed that the risk that may be experienced is at 4,7%, for 95% confidence level it is at 6,1%, and for 99% confidence level it is at 10,6%.

SUPPLY CHAIN COORDINATION WITH CVaR CRITERION

2009 ◽  
Vol 26 (01) ◽  
pp. 135-160 ◽  
Author(s):  
LEI YANG ◽  
MINGHUI XU ◽  
GANG YU ◽  
HANQIN ZHANG
Keyword(s):  
Supply Chain ◽  
Value At Risk ◽  
Supply Chain Coordination ◽  
Revenue Sharing ◽  
Retail Price ◽  
Conditional Value At Risk ◽  
Risk Averse ◽  
Mild Conditions ◽  
Quantity Flexibility ◽  
Buy Back

We study the coordination of supply chains with a risk-neutral supplier and a risk-averse retailer. Different from the downside risk setting, in a conditional value-at-risk (CVaR) framework, we show that the supply chain can be coordinated with the revenue-sharing, buy-back, two-part tariff and quantity flexibility contracts. Furthermore the revenue-sharing contracts are still equivalent to the buy-back contracts when the retail price is fixed. At the same time, it is shown that the risk-averse retailer of the coordinated supply chain can increase its profit by raising its risk-averse degree under mild conditions.

scholarly journals Single-stage gradient-based stellarator coil design: stochastic optimization

2021 ◽  
Author(s):  
Florian Wechsung ◽  
Andrew Giuliani ◽  
M. Landreman ◽  
Antoine J Cerfon ◽  
Georg Stadler
Keyword(s):  
Stochastic Optimization ◽  
Value At Risk ◽  
Optimization Problems ◽  
Numerical Study ◽  
Single Stage ◽  
Conditional Value At Risk ◽  
Risk Averse ◽  
Coil Design ◽  
Risk Neutral ◽  
Gradient Based

Abstract We extend the single-stage stellarator coil design approach for quasi-symmetry on axis from [Giuliani et al, 2020] to additionally take into account coil manufacturing errors. By modeling coil errors independently from the coil discretization, we have the flexibility to consider realistic forms of coil errors. The corresponding stochastic optimization problems are formulated using a risk-neutral approach and risk-averse approaches. We present an efficient, gradient-based descent algorithm which relies on analytical derivatives to solve these problems. In a comprehensive numerical study, we compare the coil designs resulting from deterministic and risk-neutral stochastic optimization and find that the risk-neutral formulation results in more robust configurations and reduces the number of local minima of the optimization problem. We also compare deterministic and risk-neutral approaches in terms of quasi-symmetry on and away from the magnetic axis, and in terms of the confinement of particles released close to the axis. Finally, we show that for the optimization problems we consider, a risk-averse objective using the Conditional Value-at-Risk leads to results which are similar to the risk-neutral objective.

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