Strategy selection of inventory financing based on overconfident retailer

Weifan Jiang; Jian Liu; Hui Zhou; Miyu Wan

doi:10.3934/jimo.2021178

Article Contents

2023, Volume 19, Issue 1: 139-169. Doi: 10.3934/jimo.2021178

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Strategy selection of inventory financing based on overconfident retailer

1.
School of Business Administration, Nanchang Institute of Technology, Nanchang, 330099, Jiangxi, China
2.
School of Information Management, Jiangxi University of Finance and Economics, Nanchang, 330013, Jiangxi, China
3.
Modern Economics & Management College, Jiangxi University of Finance and Economics, Nanchang, 330013, Jiangxi, China
4.
School of Transportation and Logistics, East China Jiaotong University, Nanchang, 330013, Jiangxi, China

^* Corresponding author: Weifan Jiang
^* Corresponding author: Weifan Jiang

Received: April 2021

Revised: August 2021

Early access: October 2021

Published: January 2023

The first author is supported by Science and Technology Project (No.GJJ171003) founded by the Education Department of Jiangxi Province of China, the National Natural Science Foundation of China (No.71761015, No.71862014) and the Natural Science Foundation of Jiangxi Province of China (No.20202BABL201012)

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Abstract

Overconfidence of financing enterprises in market demand will have a significant impact on their business decision-making and banks' decision-making. This paper constructs the demand function based on the retailer's overconfidence and establishes the profit functions of the retailer and the bank respectively. Through Stackelberg game analysis, the influence of the retailer's overconfidence on each decision variable can be analyzed. The study has the following findings. Firstly, overconfidence makes decision-making deviate from rational decision-making. Secondly, the relationship between loan-to-value ratio and overconfidence is affected by different factors when the banks know the market or do not understand the market. Thirdly, the relationship between retailer's default probability and overconfidence is different when the bank doesn't know the market or knows the market. Fourthly, when the bank does not understand the market but listen to the overconfident retailer's market analysis, he should choose fixed loan-to-value ratio for financing. The overconfident retailer can ask the bank to give a higher loan-to-value ratio to reduce the capital pressure. Fifthly, when the bank conducts market research, the bank should choose the variable loan-to-value ratio contract for financing, while the retailer only needs to make decisions according to the bank's lending strategy.

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Mathematics Subject Classification: Primary: 91A80, 90B05; Secondary: 91A10, 91A35.

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Figure 1. Decision-making process

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Figure 2. Sales effort changes with overconfidence

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Figure 3. Order quantity changes with overconfidence

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Figure 4. Loan-to-value ratio changes with overconfidence

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Figure 5. Default probability changes with overconfidence

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Figure 6. Expected profits change with overconfidence ($ p = 9 $)

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Figure 7. Expected profits change with overconfidence ($ p = 11 $)

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Figure 8. Sales effort changes with overconfidence

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Figure 9. Order quantity changes with overconfidence

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Figure 10. Loan-to-value ratio changes with overconfidence

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Figure 11. Default probability changes with overconfidence

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Figure 12. Expected profits change with overconfidence ($ p = 9 $)

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Figure 13. Expected profits change with overconfidence ($ p = 11 $)

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Figure 14. The real total profits change with overconfidence in the case of BNCO

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Figure 15. The real total profits change with overconfidence in the case of BCO

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Figure 16. The real profits change with overconfidence in the case of BNCO ($ p = 9 $)

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Figure 17. The real profits change with overconfidence in the case of BCO ($ p = 9 $)

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Figure 18. The real profits change with overconfidence in the case of BNCO ($ p = 11 $)

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Figure 19. The real profits change with overconfidence in the case of BCO ($ p = 11 $)

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Table 1. Decision variables and model parameters

Decision variable of the bank
$ \omega $	the loan-to-value ratio, $ \omega_{o} $ is the loan-to-value ratio when the bank is not clear about the overconfidence of the retailer, $ \omega_{r} $ is the loan-to-value ratio when the bank is clear about the overconfidence of the retailer
Decision variable of the retailer
$ q_{o} $	the order quantity of the overconfident retailer, $ q_{o1} $ is the order quantity when the bank is not clear about the overconfidence of the retailer, $ q_{o2} $ is the order quantity when the bank is clear about the overconfidence of the retailer
$ e_{o} $	the sales effort of the overconfident retailer, $ e_{o1} $ is the sales effort when the bank is not clear about the overconfidence of the retailer, $ e_{o2} $ is the sales effort when the bank is clear about the overconfidence of the retailer
Parameters
$ r_{1} $	the annual deposit interest rate
$ r_{2} $	the annual loan interest rate which include all expenses incurred during the pledge period
$ p $	the sale price of the product
$ w $	the cost of the product of the retailer
$ v $	the buyback price of the product
$ T $	the period of the inventory pledge loan contract, the unit is year, $ 0<T\leq1 $

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