Optimal Capital Structure in Depository Financial Institutions - A Dynamic Programming Approach
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We formulate a stochastic optimal control problem for the capital structure of depository financial institutions (DFIs), where the market value of equity is maximized in a dividend discount framework. The key objective is to study capital structure behavior of DFIs under uncertain market conditions when governmental capital regulations are imposed, in particular minimum requirements for the Core Tier 1 capital ratio given by the Basel III directive. We solve the problem by two distinct approaches based on dynamic programming: (1) by deriving and numerically solving the problem's Hamilton-Jacobi-Bellman partial differential equation, and (2) by an approximate dynamic programming approach using Q-learning with artificial neural networks. The model is calibrated and tested for DNB ASA. The results obtained suggest that there is a significant cost for equity holders associated with governmental capital regulations, seen from the reduction in market value of equity when these are imposed. We find the impact of regulations to be stronger in times of high economic growth than during downturns. Moreover, given the current regulatory requirements, our model suggests that DNB ASA could increase shareholder value substantially by lowering its capital adequacy ratio.