We consider an optimal control problem of a property insurance company with proportional reinsurance strategy. The insurance business brings in catastrophe risk, such as earthquake and flood. The catastrophe risk could be partly reduced by reinsurance. The management of the company controls the reinsurance rate and dividend payments process to maximize the expected present value of the dividend...

For a class of uncertain nonlinear chaotic systems with unknown control gain signs and saturated input, by means Nussbaum function, scheme finite-time prescribed performance synchronization is proposed. Here, function used to eliminate the influence signs, fuzzy logic are estimate functions. Lyapunov theory prove that all errors converge predefined small range under designed method. Finally, si...