We analyze an algorithm for solving stochastic control problems, based on Pontrya-gin's maximum principle, due to Sakawa and Shindo in the deterministic case and extended to the stochastic setting by Mazliak. We assume that either the volatility is an affine function of the state, or the dynamics are linear. We obtain a monotone decrease of the cost functions as well as, in the convex case, the fact that the sequence of controls is minimizing, and converges to an optimal solution if it is bounded.

中文翻译：

---

关于 Sakawa-Shindo 算法在随机控制中的收敛性

我们分析了一种用于解决随机控制问题的算法，基于 Pontrya-gin 的最大值原理，由于 Sakawa 和 Shindo 在确定性情况下，并由 Mazliak 扩展到随机设置。我们假设波动率是状态的仿射函数，或者动态是线性的。我们获得了成本函数的单调递减，以及在凸情况下，控制序列最小化的事实，如果有界则收敛到最优解。