Dividends, safety and liquidation when liabilities are long-term and stochastic

This paper investigates the optimal management of a firm faced with a long-term liability that occurs at a random date. Three issues are analysed: The optimal dividend policy; optimal expenditure on safety to delay the occurrence of the liability; and the optimal liquidation date of the firm. An owner faced with dynamic unlimited liability never liquidates and therefore accumulates capital to the golden rule level. For long-term liabilities, dividend payments and safety expenditure are non-decreasing over time. The owner protected by limited liability may liquidate the firm in finite time in order to avoid paying the liability. If this is the case, then it accumulates less capital than the dynamic unlimited liability owner; and may decrease dividend payments and safety expenditure over time. The paper shows that a finite liquidation date is more likely to be optimal when the arrival rate of the liability occurrence increases over time.