Your insurance company will pay the damage if your insurance company believes you. His insurance(not yours) will go up. It is good that you got his insurance info. Otherwise, it is difficult for your insurance company to pay your damage. It is also true that the police will not bother to come for a small accident.
如果警察没有出具事故报告,你的保险公司会调查。结果如果是他的责任,保险公司会认定你为无责方,你不会涨保险。如果无法证明是他就是hit and run,就等同于是你自己的责任。一般保险公司是两次责任事故以后会涨保险。具体细节可能也看不同的保险公司,和损坏程度。无论谁是责任方都是由各自的保险公司负责赔偿各自的损失。