Abstract：On the assumption that the fund follows the standard brownian motion,the insurer buys the proportional reinsurance in order to reduce the risk,choosing the exponential utility function as the optimal standard,the corresponding Hamilton-Jacobi-Bellman equation is gotten and the model of the optimal reinsurance is created,by solving the equation,the optimal proportion of the proportional reinsurance is given,which can make the expected exponential utility of terminal wealth maximum.

Keyword：Brownian motion;hamilton-jacobi-bellman equation;exponential utility;proportional reinsurance;