论文标题
凸随机优化中的动态编程
Dynamic programming in convex stochastic optimization
论文作者
论文摘要
本文研究了Rockafellar和Wets在[30]中引入的一般凸的随机优化问题的动态编程原理。我们通过放松的紧凑性和有限性假设来扩展理论的适用性。在金融数学的背景下，在众所周知的无肢体条件和效用函数的合理渐近弹性条件下，满足了放松的假设。除了金融数学外，我们还获得了线性和非线性随机编程和随机最佳控制的几个新结果。
This paper studies the dynamic programming principle for general convex stochastic optimization problems introduced by Rockafellar and Wets in [30]. We extend the applicability of the theory by relaxing compactness and boundedness assumptions. In the context of financial mathematics, the relaxed assumption are satisfied under the well-known no-arbitrage condition and the reasonable asymptotic elasticity condition of the utility function. Besides financial mathematics, we obtain several new results in linear and nonlinear stochastic programming and stochastic optimal control.
