| Abstract: | 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, partial differential equation and variational inequality
approach. Moreover, we establish a riskbased capital standard to ensure the capital requirement can cover the total given
risk by numerical analysis, and give reasonable economic interpretation for the results. |
