Optimal Financing And Dividend Control Of The Insurance Company With Fixed And Proportional Transaction Costs For Lévy Process

This paper considers the optimal financing and dividend control problem of the in-surance company with fixed and proportional transaction costs. The risk process of theinsurance company is a spectrally negative Lévy process. The management of the com-pany controls the equity issuance process as well as dividends payout to maximize theexpected present value of the dividends payout minus the equity issuance until the timeof bankruptcy.This paper solves the mixed impulse control problem by constructing two categoriesof sub-optimal models, one is the classical model without equity issuance, the other withequity issuance. Our research shows that in the case of without equity issuance, theoptimal policy is a barrier strategy which keep the surplus below the barrier b and pay outas dividends all the amounts in excess of the barrier. In case of with equity issuance, theoptimal dividend policy is still a barrier strategy and the equity issuance happens when thesurplus process reached0continuously. Besides, there exists a optimal amount of equityissuance m. Furthermore, we investigate the relationship between the optimal returnfunction and model parameters as well as special Lévy process, the relationship betweendividend payout barrier, optimal amount of equity issuance and model parameters as wellas special Lévy process by numerical simulation. At last, we give reasonable economicinterpretation for both theoretical and numerical results.This paper makes use of knowledge of financial mathematics and actuarial etc. It usestochastic analysis, HJB variation, stochastic control and optimization as powerful toolsand a model which collects much more attention from researchers. It solves the problemwhich is relatively close to the actual economic life.