Profit Maximization with Bankruptcy and Variable Scale

In a diffusion model of an enterprise with variable scale, sufficientconditions are given for the maximization of expected profit (expectedtotal discounted withdrawals) to lead to eventual bankruptcy with probabilityone. The optimal withdrawal policy is an quot;overflow policy,quot; in which the withdrawalrate is equal to zero if the asset level is below a quot;barrier,quot; and equalto the maximum rate if the asset level is greater than or equal to the barrier.The optimal policy for the control of the drift (yield) and volatility (risk) ofthe earnings process is derived as the solution of a differential equation, and aformula is given for the corresponding value function. The optimality of theconstructed policy is demonstrated using the standard quot;Bellman Conditions.quot