Bank Deposit Value And Capital Structure Optimization Under Uncertain Environment

In the dynamic theory of banking where the role of deposit is akin to that of productive capital in the classical q-theory of investment for non-financial firms.As the key source of leverage,deposits create value for well-capitalized banks.However,unlike productive capital of non-financial companies usually has a positive marginal q,the deposit q can turn negative for under-capitalized banks.Demand deposit accounts commit banks to allow holders to withdraw or deposit funds at will,so banks cannot perfectly control leverage.Therefore,for banks with insufficient equity-capital to buffer risk,deposit inflow and the associated uncertainty in future leverage can destroy value.The main work of this paper is to consider the optimization of bank deposit value and capital structure under Knight uncertainty,ambiguity aversion and inflation uncertainty.The main research contents are as follows:1.We study the problem of optimizing of bank deposit value and optimal capital structure under Knight uncertainty,using the G-Brownian motion in the sublinear expectation framework to carve out shocks to banks’ risky assets,deposits and short-term debt,obtaining the HJB equation satisfied by the bank’s shareholder value function,simulating the results numerically and analyzing the impact of bank deposit value and capital structure from an economic perspective.2.We study the problem of optimizing the value of bank deposits and capital structure under ambiguity aversion.Firstly,the Choquet-Brownian motion is applied to carve out the stochastic disturbance of the bank’s risky assets and bank deposits.Secondly,the dynamic programming principle is used to construct the HJB equation satisfied by the bank’s shareholder value and derive the analytical equations for the bank’s franchise value,the marginal value of bank deposits,the short-term debt to deposit ratio,the loan weights,the loan capital ratio and the optimal deposit interest rate.Finally,the results are numerically simulated and the characteristics of the optimal deposit rate and capital structure of banks under ambiguity aversion are analyzing from an economic perspective.3.We study the problem of optimizing the value of bank deposits and optimal capital structure under inflation uncertainty.Firstly,stochastic analysis is used to obtain the real value process of bank shareholders,secondly,the dynamic programming principle is used to construct the HJB equation satisfied by the real value of bank shareholders,and finally,the results are numerically simulated to analyse the impact of inflation risk,leverage constraint,deposit volatility risk and risk-free interest rate on the value of bank deposits and capital structure from an economic perspective.