Stochastic optimal control on dividend policies with bankruptcy

• Published in: Optimization Vol. 68; no. 12; pp. 2317 - 2337
• Main Authors: Chen, Peimin, Luo, Xiankang
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 02.12.2019; Taylor & Francis LLC
• Subjects: bailout; Bailouts; Bankruptcy; Dividend policy; Dividends; Exact solutions; Expected values; HJB equation; Optimal control; Optimal dividend; proportional reinsurance; terminal value
• ISSN: 0233-1934; 1029-4945
• DOI: 10.1080/02331934.2019.1582049

When a firm is at the edge of bankruptcy, it would endeavour to attract bailouts from governments or financial institutions to cast off bad situation. If this effort fails, then the firm would face to sell off their properties to pay their debts to loaners or shareholders. In this paper, from these two cases of bankruptcy, two optimal dividend policies are considered and analysed, respectively. In the case of unrestricted dividend payment rate, a terminal bankruptcy model with non-zero terminal value is put forward. An analytic solution for the optimal objective function, which maximizes the expected value of total discounted dividends before bankruptcy and the residual value at bankruptcy, is provided and verified. As a significant application, a non-terminal bankruptcy problem with bailouts is considered, an explicit solution and the corresponding control policies are also obtained. In the end, some numerical examples are listed and the influence of the recovery rate on the optimal strategies is also discussed.