Optimal Control Of A Company With Constant Debt Liability Under Bankrupt Probability Constraints

This paper considers an optimal control of a company with debt liability underbankrupt probability constraints. The company, which faces constant liability pay-ments and has choices to choose various production/business policies from an availableset of control policies with diferent expected profits and risks, controls the businesspolicy and dividend payout process to maximize the expected present value of the div-idends until the time of bankruptcy. However, if the dividend payout barrier is too lowto be acceptable, it may result in the company’s bankruptcy soon. In order to protectthe shareholders’ profits, the managements of the company impose a reasonable andnormal constraint on their dividend strategy, that is, the bankrupt probability associatedwith the optimal dividend payout barrier should be smaller than a given risk level withina fixed time horizon. This paper aims at working out the optimal control policy as wellas optimal return function for the company under bankrupt probability constraint bystochastic analysis, PDE methods and variational inequality approach. Moreover, weestablish a risk-based capital standard to ensure the capital requirement can cover thetotal given risk by numerical analysis, and give reasonable economic interpretation forthe results.