Optimal Dividend Policies with Random Profitability

Abstract

We study an optimal dividend problem under a bankruptcy constraint. Firms face a trade-off between potential bankruptcy and extraction of profits. In contrast to previous works, general cash flow drifts, including Ornstein-Uhlenbeck and CIR processes, are considered. We provide rigorous proofs of continuity of the value function, whence dynamic programming, as well as comparison between the sub-and supersolutions of the Hamilton-Jacobi-Bellman equation, and we provide an efficient and convergent numerical scheme for finding the solution. The value function is given by a nonlinear PDE with a gradient constraint from below in one dimension. We find that the optimal strategy is both a barrier and a band strategy and that it includes voluntary liquidation in parts of the state space. Finally, we present and numerically study extensions of the model, including equity issuance and credit lines.

Deep Stochastic Optimization in Finance

“…We use this assumption to show that the stopping region has a certain geometric structure which we exploit. The following result is already proved in [8] and more generaly in [32]. We provide its proof for completeness.…”

“…In look-back type options, the minimum or the maximum of the stock process must be included in the state. We refer to [32] for the details of these extensions.…”

“…An important step in our approach is to replace the stopping rule given by the sharp interface by a relaxed stopping rule given by a fuzzy boundary as described in the subsection 4.4. Further analysis and the results of our free-boundary methodology are given in our future manuscript [32].…”

Analysis of the Bank Specific Factors, Macroeconomics and Oil Price on Dividend Policy

“…The more investors in the company's stock are risk averse, the lower the dividends to be paid (Akyildirim et al, 2014). Other studies consider company profitability factors, company growth, and investment growth opportunities in the future (Hagen, 1973;Décamps and Villeneuve, 2007;Reppen et al, 2020).…”