论文标题
凸随机优化中的二元性
Duality in convex stochastic optimization
论文作者
论文摘要
本文研究了Rockafellar和Wets在1976年提出的一般凸的随机优化问题中的二元性和最佳条件。我们从两个双重变量方面提出了一个明确的双重问题，其中一个是信息的阴影价格，而另一个是一个偶然的偶然性变量，而在经典的Lagrangian Lagrangangangangangangangangian clangangian clangangian偶然的偶然性上产生了极大的影响。存在原始解决方案和缺乏双重性差距，没有紧凑或有限性假设。在金融数学的背景下，在众所周知的无责任条件和公用事业函数的合理渐近弹性条件下，满足了轻松的假设。我们将经典的投资组合优化双重性理论扩展到最佳半静态对冲问题。除了金融数学外，我们还获得了几个新的框架，以随机编程和随机最佳控制。
This paper studies duality and optimality conditions in general convex stochastic optimization problems introduced by Rockafellar and Wets in 1976. We derive an explicit dual problem in terms of two dual variables, one of which is the shadow price of information while the other one gives the marginal cost of a perturbation much like in classical Lagrangian duality. Existence of primal solutions and the absence of duality gap are obtained without compactness or boundedness assumptions. In the context of financial mathematics, the relaxed assumptions are satisfied under the well-known no-arbitrage condition and the reasonable asymptotic elasticity condition of the utility function. We extend classical portfolio optimization duality theory to problems of optimal semi-static hedging. Besides financial mathematics, we obtain several new frameworks in stochastic programming and stochastic optimal control.
