模糊厌恶下银行最优存款利率与资本结构优化

Optimal Deposit Interest Rate and Capital Structure Optimization Under Ambiguity Aversion

基于动态银行理论,研究模糊厌恶下银行最优存款利率与资本结构优化。首先运用肖-布朗运动刻画银行风险资产、银行存款的随机干扰,其次利用动态规划原理构建银行股东价值所满足的HJB方程,推导出银行的特许经营权价值、银行存款的边际价值、短期债务与存款比例、贷款权重、贷款资本比率和最优存款利率的解析式。最后对结果进行了数值模拟,从经济学的角度分析了模糊厌恶下银行最优存款利率与资本结构的特征。模拟结果发现,随着模糊厌恶程度的增加,银行的特许经营价值和存款边际价值增加、存款的最优利率可调节的空间增加;银行通过持有无风险资产和下调存款利率来控制杠杆,从而减少了股票发行成本,维持银行股东的价值。

Based on dynamic banking theory,this paper studies the optimal deposit interest rate and capital structure of banks under ambiguity aversion.Firstly,the Choquet-Brownian motion is used to describe the random interference of bank risk assets and bank deposits.Secondly,the HJB equation satisfied by bank shareholder value is constructed by using the principle of dynamic programming,and deduces the analytical formulas of the bank franchise value,the marginal value of bank deposits,the ratio of short-term debt to deposits,the loan weight,the loan capital ratio and the optimal deposit interest rate.Finally,the obtained analytic results are numerically simulated,and the characteristics of bank optimal deposit interest rate and capital structure under ambiguity aversion are analyzed from the perspective of economics.The simulation results show that with the increase of the degree of ambiguity aversion,the franchise value and the marginal value of deposits increase,the adjusted space of the optimal deposit interest rate will increase.The bank leverage can be restrained by holding risk-free assets and cutting deposit rates,value for bank shareholders can be maintained by reducing the cost of equity issuance.