Optimal Operating Strategies Under Stochastic Cash Flows

We solve a series of four stochastic control problems for a firm whose cash flows are a diffusion process that includes (individually): (i) Financial distress costs; (ii) Costs of company politics; (iii) Agency costs of free cash flow and; (iv) Physical asset upgrades. Amongst other things, our results show that: (a) There are conditions for which asset substitution (risk¿taking when close to broke) is optimal, with financial distress costs; (b) When politicking amongst employees exists, it is optimal to keep the firm extremely small by downsizing frequently; (c) Increasing the free cash boundary (or equivalently increasing cash obligations) would reduce the agency costs associated with free cash flow from overly negligent managers; (d) It is optimal to have a buffer cash zone before upgrading technologies, rather than upgrade immediately. We solve for the optimal operating strategy using an algorithm that includes applying Itô calculus, the use of martingale theory and linear programming. We use sparse matrix techniques, a manageable number of constraints and the MOSEK solver embedded into Matlab; this technique is a quick and easy way to solve this class of stochastic problems.