中文摘要：

从系统的观点出发，把保险公司的赔付情况与投资收益相结合，对比例再保险和超额损失再保险，建立了在投资背景下它们应满足的线性正倒向随机微分方程．根据一类特殊线性倒向随机微分方程的显式解，给出了基于投资的再保险定价公式，为保险公司厘订再保险保费提供了新的方法．

英文摘要：

Starting from systematic view, the paper integrates compensations that insuers will be up against with its return on investment and establishes linear forwardbackward stochastic differential equations for proportional and excess-of-loss reinsurance premiums. The reinsurance pricing formulas are obtained on the basis of the explicit solution of a special class of their linear backward stochastic differential equations. The results have a directly helpful role for insuers to make reinsurance premiums.