The paper discusses the economic model of the Geometric Brownian motion with Poisson jumps. In the case of the reward function R(x)=ax~2-b, we seek the average optimum solutions of the reward by Ito formula.

• 本文讨论了带泊松过程的几何布朗运动的经济模型；在收益函数R(x)=ax2-b的情形下；利用伊藤公式；求得平均收益的最优解.