跳跃—扩散过程的最优投资消费

Optimal investment and consumption of jump-diffusion process

针对连续时间资产组合模型,在证券价格服从跳跃—扩散过程的假设下,研究了在通货膨胀率影响下,不完备金融市场上有随机收入和红利支付情况下的最优投资和消费问题.通过离散时间模型对财富过程的模型作逼近,给出了财富过程的最优投资消费解的形式,并讨论了HARA效用函数,得到了具体的最优投资消费解.

As to the continuous time portfolios model, a question on optimal investment and consumption whichis affected by inflation is researched with dividend payment and stochastic income in incomplete markets under the assumption that securities processes are jump-diffusion processes. The model of wealth process was drew up by using discrete time model and the form of solution to optimal investment and consumption of wealth process was acquired. Finally, the optimum solution for hara function was given.