跳扩散分数布朗运动的随机最大值原理*1

摘要

目的：对于一类带有泊松跳过程的分数布朗控制系统，研究随机最优控制输入的存在性问题。方法分数布朗运动的伊藤公式和随机微积分理论。结果证明这类系统的随机最大值原理，控制输入是最优控制输入的充分条件。结论这一理论结果可用于金融数学领域的投资最优控制问题中。%Objective- To study the stochastic optimal control problem for a class of control system which is driven by fractional Brownian motion.Methods- Employ Ito equation and stochastic calculus for fractional Brownian processes.Results- Prove a stochastic maximum principle for this kind of sys-tems.Conclusion- The results can be used in the field of financial engineering.