Production, operating risk and market uncertainty: a valuation perspective on controlled policies

Abstract

This paper develops a contingent claims model of an optimally controlled production process characterized by financial and operational risks. Financial risk is depicted by the uncertainty in output prices as determined in competitive markets. Operational uncertainty is portrayed through the risk of system failures which we represent by a nonhomogeneous Poisson process. In the analysis, failure propensity is functionally specified by the system's age, rate of production, and system maintenance expenditures. In this environment, the model obtains an optimal production and maintenance policy maximizing the value of the production effort. Determination of the optimal policies results through the application of stochastic control techniques where production and maintenance expenditure rates are taken as adapted real-valued processes. Further extensions of the model include the analysis of an insurance option on failure repairs and the consequent moral hazard implications. We demonstrate that an appropriately established insurance premium must reflect the producer's operating policy in place and the extent to which operating policies may be modified to maintain the same level of operating risk, as in the absence of an insurance option. The framework presented provides insight into key strategic factors that affect the management of process operations, operating flexibility issues and their resulting economic value.