运筹与管理2024，Vol.33Issue(12)：165-171,7.DOI:10.12005/orms.2024.0401
Knight不确定下银行存款价值与资本结构优化
Bank Deposit Value and Capital Structure Optimization under Knightian Uncertainty
摘要
Abstract
The optimization of capital structure is an important guarantee to maximize the value of commercial banks and shareholders'returns,as well as a key to controlling liquidity risks,enhancing competitive advantages and promoting sustainable development.As commercial banks are affected by their own capital structure,financial market fluctuations,macroeconomic policies their deposit scale,capital access methods,and financial market investment returns are all faced with uncertainties.Such uncertainties come from both random factors such as the objective environment,and Knightian uncertainties from the psychological subjective judgment of commercial banks'economic subjects.Commercial banks face the stochastic modeling problem of the Knightian uncertainty.Therefore,in the dynamic optimization adjustment of capital structure,commercial banks must solve the Knightian uncertainty and probabilistic uncertainty. As a relatively cheap source of bank loans and financing,deposit is the premise of ensuring the safety and liquidity of bank operation,and has an important impact on the capital structure of banks.The client's deposit and withdrawal in the bank are random,and due to the complexity of the real world and the incompleteness of information acquisition,it is difficult to use a model to fully describe financial problems.Probability theory is capable of solving situations in which the corresponding probability model can be determined by mathematical statistics and data analysis.However,sublinear expectations can be used for the robust quantitative analysis and calculation of various risks in situations where the probability model itself cannot be determined.Many scholars have analyzed the optimal investment,entrepreneurial behavior and optimal contract under the Knightian uncertain-ty,but little literature has considered the Knightian uncertainty of bank deposits and loans.In an uncertain envi-ronment,the mechanism of the influence of deposit flow on bank capital structure,deposit marginal value,optimal deposit interest rate and shareholder return rate has been analyzed.The relevant research has an important theoreti-cal and practical value for optimizing the capital structure of commercial banks and improving the value of banks. This paper attempts to use stochastic differential equation and stochastic control to conduct a dynamic modeling of bank deposits and loans and bank capital under the Knightian uncertainty environment.With the ex-pected value maximization of bank shareholders as the goal and principle of dynamic programming,this paper discusses the optimization of bank deposit value and capital structure.Firstly,the G-Brownian motion under the sub-linear expectation framework is used to describe the impact of bank risk assets,deposits and short-term debt,and the Hamilton-Jacobi-Bellman equation satisfied by the bank shareholder value function is derived.Secondly,the analytical formula of bank franchise value,marginal value of bank deposits,short-term debt and deposit ratio,loan weight,loan capital ratio and optimal deposit interest rate is obtained.Finally,the results of the model are simulated and analyzed.The results show that,faced with an increase in the Knightian uncertainty,when the bank capital is insufficient,its deposit marginal value will be negative,the franchise value will decrease,the low interest rate will be maintained for a short time,and the bank will be more willing to hold risk-free assets.When the bank has sufficient capital,the marginal value of its deposit will be positive,the franchise value will increase,the adjustable space of the optimal deposit interest rate will become larger,and the bank will take short-term debt as the main source of loan funds. In this paper,we systematically analyze the value of bank deposits and the optimization of capital structure under the Knightian uncertainty,and take G-Brownian motion as the noise of deposit,loan and bank capital shock.When considering the optimal decision-making behavior of ambiguity aversion commercial banks,we can further use the Choque-Brownian motion to depict the noise impact of deposits and loans.When considering the influence of a sudden change in the international and domestic economic environment on the investment decision of commercial banks,the jump-diffusion process can be used to describe the dynamic characteristics of deposit,loan and bank capital.In addition,as an inflation risk is an important factor affecting asset value,a comprehen-sive consideration of the Knightian uncertainty and bank capital structure optimization for random inflation will be worthy of further study.关键词
Knight不确定/银行存款/银行资产/资本结构/动态规划原理Key words
Knightian uncertainty/bank deposits/bank assets/capital structure/dynamic programming principle分类
数理科学引用本文复制引用
潘海峰,黄玉喜,费为银..Knight不确定下银行存款价值与资本结构优化[J].运筹与管理,2024,33(12):165-171,7.基金项目
国家自然科学基金资助项目(62273003) （62273003）
安徽省自然科学基金项目(1608085MA02) （1608085MA02）
安徽省高校自然科学基金重点项目(KJ2020A0369) （KJ2020A0369）
