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中国管理科学 ›› 2025, Vol. 33 ›› Issue (9): 312-324.doi: 10.16381/j.cnki.issn1003-207x.2023.0256

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CVaR条件下考虑授信额度的报童模型

林强1, 单镇杰1, 李文卓2()   

  1. 1.广东工业大学管理学院,广东 广州 510520
    2.华南理工大学工商管理学院,广东 广州 510641
  • 收稿日期:2023-02-20 修回日期:2023-06-14 出版日期:2025-09-25 发布日期:2025-09-29
  • 通讯作者: 李文卓 E-mail:liwenzhuo03@163.com
  • 基金资助:
    国家自然科学基金项目(72102080);国家自然科学基金项目(72001048);国家自然科学基金项目(72002046);广东省基础与应用基础研究基金项目(2019A1515011767);广东省基础与应用基础研究基金项目(2019A1515110848);广东省基础与应用基础研究基金项目(2021A1515011969);广东省基础与应用基础研究基金项目(2021A1515011876);广东省哲学社会科学规划项目(GD19YGL12)

A Newsboy Model Considering Credit Line Based on CVaR

Qiang Lin1, Zhenjie Shan1, Wenzhuo Li2()   

  1. 1.School of Management,Guangdong University of Technology,Guangzhou 510520,China
    2.School of Business Administration,South China University of Technology,Guangzhou 510641,China
  • Received:2023-02-20 Revised:2023-06-14 Online:2025-09-25 Published:2025-09-29
  • Contact: Wenzhuo Li E-mail:liwenzhuo03@163.com

摘要:

中小企业是国民经济和社会发展的主力军,但在生产经营过程中却面临资金短缺的难题。作为中小企业融资的主要渠道,银行等金融机构往往在评估中小企业的信用和还款能力后,为其提供授信额度内的资金支持。基于此,本文构建银行为资金短缺的风险规避零售商(中小企业)提供授信额度内贷款时的报童模型,并利用条件风险价值(conditional value-at-risk, CVaR)刻画零售商的风险规避特性,探讨零售商的风险规避和银行的授信额度对零售商的订购与贷款决策的影响。研究发现:①零售商的最优订购量将随其风险规避程度的增大而减小,而银行为零售商提供贷款可缓解其风险规避特性的负向影响,使得风险规避程度较高的零售商的最优订购量高于无资金约束时的订购量。②银行设定授信额度既可以限制风险规避程度较低的零售商的采购决策,也可以减弱因风险规避程度较高的零售商过度贷款而带来的损失。此外,当银行基于风险价值(value-at-risk, VaR)决策授信额度时,同样可得上述结论。与此同时,数值结果不仅证实了上述结论,还发现市场需求的不确定性将放大零售商的风险规避特性和银行的授信额度对零售商的订购与贷款决策的影响。

关键词: 零售商融资, 授信额度, 报童模型, CVaR

Abstract:

Small and medium-sized retailers are the main force of national economic and social development, but they often face the problem of capital shortage in their production and operation processes. Small and medium-sized retailers mainly obtain loans from financial institutions such as banks to solve their capital shortage problems. After evaluating the credit and repayment ability of small and medium-sized retailers, banks provide funds within the credit line for small and medium-sized retailers in need. Based on these, the impact of bank credit constraints and retailer risk aversion characteristics is considered, and Conditional value-at-risk (CVaR) is used to characterize the risk aversion features of retailers. Three models are constructed: the newsboy model without funding constraints, the full credit exposure model provided by banks, and the newsboy model with credit constraints. The impact of bank credit line and retailer risk aversion characteristics on joint decision-making for retailer ordering and loan procurement is explored.The main results suggest that (i) Providing loans to the retailer can share some market uncertainty risks and stimulate the retailer to increase product orders, mitigating the negative impact of retailer risk aversion characteristics. Specifically, when the degree of risk aversion of the retailer is high, their optimal ordering quantity is higher than the optimal ordering quantity without funding constraints. (ii) A risk-neutral retailer only applies for gap funding loans from banks, while a risk-averse retailer may apply for high-value loans to transfer bankruptcy risks to banks in order to obtain more stable returns. (iii) A risk-neutral retailer will not over-borrow, and their optimal ordering decisions will be determined by market factors and credit line. For a risk-averse retailer, when the bank's credit line is high, they may choose credit line loans and the optimal ordering quantity is consistent with that without funding constraints. It should be noted that when the bank endogenously determines the credit line, the above research conclusions can still be obtained. Moreover, the numerical analysis indicate that although increasing market uncertainty may reduce the utility of the retailer, it does not necessarily lead to a decrease in their ordering quantity. In addition, when banks provide lower credit line and the retailer have a higher degree of risk aversion, the impact of market uncertainty on the optimal ordering quantity of the retailer is more significant, which will also significantly affect their utility. In other words, market demand uncertainty will amplify the impact of bank credit line and retailer risk aversion characteristics on the decision-making of retailer ordering and loan amounts.The management implications are as follows. First, retailers need to develop reasonable financing and ordering strategies based on their own risk aversion characteristics and market demand uncertainty. With the support of a certain credit line provided by banks, retailers can adjust their ordering decisions to achieve the optimal ordering quantity. Second, banks should flexibly adjust credit line based on factors such as retailer risk aversion characteristics and market demand uncertainty to meet retailers’ funding needs. At the same time, banks need to consider risk control to avoid losses caused by retailers’ inability to repay loans.

Key words: retailer financing, credit line, newsboy model, CVaR

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