  This paper considers nonlinear regular-singular stochastic optimal control of
large insurance company. The company controls the reinsurance rate and dividend
payout process to maximize the expected present value of the dividend pay-outs
until the time of bankruptcy. However, if the optimal dividend barrier is too
low to be acceptable, it will make the company result in bankruptcy soon.
Moreover, although risk and return should be highly correlated, over-risking is
not a good recipe for high return, the supervisors of the company have to
impose their preferred risk level and additional charge on firm seeking
services beyond or lower than the preferred risk level. These indeed are
nonlinear regular-singular stochastic optimal problems under ruin probability
constraints. This paper aims at solving this kind of the optimal problems, that
is, deriving the optimal retention ratio,dividend payout level, optimal return
function and optimal control strategy of the insurance company. As a
by-product, the paper also sets a risk-based capital standard to ensure the
capital requirement of can cover the total given risk, and the effect of the
risk level on optimal retention ratio, dividend payout level and optimal
control strategy are also presented.
