Stochastic optimal control on dividend policies with bankruptcy

ABSTRACT

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.

KEYWORDS:

• Optimal dividend
• proportional reinsurance
• terminal value
• bailout
• HJB equation

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was jointly supported by the Scientific Research Fund of Sichuan Provincial Department of Education [grant number 11ZA220] and the Funds for 1000 Talents Plan of Sichuan Province [grant number 221410001003040002].