  This paper considers an optimal control of a big financial company with debt
liability under bankrupt probability constraints. The company, which faces
constant liability payments and has choices to choose various
production/business policies from an available set of control policies with
different expected profits and risks, controls the business policy and dividend
payout process to maximize the expected present value of the dividends until
the time of bankruptcy. However, if the dividend payout barrier is too low to
be acceptable, it may result in the company's bankruptcy soon. In order to
protect the shareholders' profits, the managements of the company impose a
reasonable and normal constraint on their dividend strategy, that is, the
bankrupt probability associated with the optimal dividend payout barrier should
be smaller than a given risk level within a fixed time horizon. This paper aims
at working out the optimal control policy as well as optimal return function
for the company under bankrupt probability constraint by stochastic analysis,
PDE methods and variational inequality approach. Moreover, we establish a
risk-based capital standard to ensure the capital requirement of can cover the
total given risk by numerical analysis and give reasonable economic
interpretation for the results.
