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This paper considers an optimal control of a big financial company with debtliability under bankrupt probability constraints. The company, which facesconstant liability payments and has choices to choose variousproduction/business policies from an available set of control policies withdifferent expected profits and risks, controls the business policy and dividendpayout process to maximize the expected present value of the dividends untilthe time of bankruptcy. However, if the dividend payout barrier is too low tobe acceptable, it may result in the company's bankruptcy soon. In order toprotect the shareholders' profits, the managements of the company impose areasonable and normal constraint on their dividend strategy, that is, thebankrupt probability associated with the optimal dividend payout barrier shouldbe smaller than a given risk level within a fixed time horizon. This paper aimsat working out the optimal control policy as well as optimal return functionfor the company under bankrupt probability constraint by stochastic analysis,PDE methods and variational inequality approach. Moreover, we establish arisk-based capital standard to ensure the capital requirement of can cover thetotal given risk by numerical analysis and give reasonable economicinterpretation for the results.

Optimal control of a big financial company with debt liability under bankrupt probability constraints