中文摘要：

将随机扰动和资产积累过程中资产之间的相互影响考虑到模型中，讨论了一类带有Fractional Brown运动和Markov调制的2种随机资产积累系统的最优逼近控制问题。采用最优控制的经典方法——最大值原理来对问题进行求解。利用Ito′s公式及一些基本不等式等证明了在利普希茨条件下，资产积累模型和其相对应的伴随方程的解都是有界的，并且给出了2种随机资产积累系统的最优逼近控制存在的必要条件是哈密顿函数的期望值无限逼近于其最大值。另一方面，利用Ekeland变分原理对哈密顿函数进行变分处理，得到当模型的最优逼近控制的期望值为哈密顿函数的上确界时，资产积累模型最优逼近控制是存在的。

英文摘要：

Considering stochastic disturbance and the interaction between the asset accumulations into the model, we introduce two competitive capital systems with Markovian switching and Fractional Brown motion; establish sufficient and necessary condition for near-optimality. The maximum principle is one of the classical methods that be used to solve the problem. Under the local Lipshitz condition, we prove the bound of the solution of the state equation and their corresponding adjoins equation by using Ito formula and some basic inequality. Then, we get the necessary condition for near-optimality is that the expectation of the Hamiltonian function approaching its maximum. On the other hand, Ekeland variational principle is used in Hamiltonian function to get the sufficient con dition for near-optimality of two competitive capital systems with Markovian switching and Fractional Brownian motion is that the expectation of the Hamiltonian function is equivalent to the supremum of Hamiltonian function.