PROFIT MAXIMIZATION WITH BANKRUPTCY AND VARIABLE SCALE

In a diffusion model of an enterprise with variable scale, conditions are given for the maximization of 'profit' (expected total discounted withdrawals) to lead to bankruptcy almost surely. The optimal withdraw al policy is an 'overflow policy': the withdrawal rate is zero if the asset level is below a 'barrier', and equal to the maximum rate if the asset level is at least equal to the barrier. The optimal policy for the control of the drift (yield) and volatility (risk) of the earnings is the solution of an explicit differential equation, and a formula i s given for the corresponding value function. (C) 1998 Elsevier Scienc e B.V. All rights reserved.