Abstract
For some firms with large nonliquid assets, preferred shareholders can still get back a little bit of money when the firms finish disbursement of loans at the status of bankruptcy. For such a situation, to investigate the optimal dividend policy, a stochastic dynamic dividend model with nonzero terminal bankruptcy values is put forward in this paper. Moreover, an analytic solution for the optimal objective function of the discounted dividends is provided and verified. An important application of this result is that it can be employed to construct the solution for the optimal value function on the dividend problem with bailouts at bankruptcy. Further, the relationship for the solutions of these two different problems is demonstrated. In the end, some numerical examples are provided to support our theoretical results and the corresponding economic interpretations are illustrated.
Highlights
In the past decades, optimal dividend problems have been an important issue in financial and actuarial sciences
We refer the readers to Jeanblanc-Picqueand Shiryaev [2], Radner and Shepp [3], Taksar and Zhou [4], Højgaard and Taksar [5, 6], Hubalek and Schachermayer [7], Cadenillas et al [8], Paulsen [9, 10], Paulsen and Gjessing [11], Avanzi and Wong [12], Hunting and Paulsen [13], Chen et al [14], Eisenberg [15], Vierkotter and Schmidli [16], and so forth. In all of those works, the terminal value of a company is assumed to be equal to zero when there is a status of bankruptcy, where the bankruptcy is defined as the time when the liquid assets of the company vanish
The event and amounts of capital injections can be controlled by firms, Mathematical Problems in Engineering so the capital injections can be a controllable variable in the objective function of optimal dividends
Summary
Optimal dividend problems have been an important issue in financial and actuarial sciences. For firms at status of bankruptcy, sometimes they can get bailouts from governments or other firms with abundant cash flows In such a situation, the optimal dividend policy is an urgent problem for managers to analyze. That implies the firms are healthy in management and financial situation and they can attract much more capitals from externals to scale up their business In this case, the event and amounts of capital injections can be controlled by firms, Mathematical Problems in Engineering so the capital injections can be a controllable variable in the objective function of optimal dividends (see, e.g., Løkka and Zervos [22] and He and Liang [23, 24]).
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