Duality in convex stochastic optimization
研究一般凸随机优化问题的对偶性和最优性条件，推导出显式对偶问题，在无紧性或界性假设下得到原问题解的存在性和无对偶间隙，并将经典投资组合对偶理论扩展到最优半静态对冲问题。
Abstract This paper studies duality and optimality conditions in general convex stochastic optimization problems introduced by Rockafellar and Wets in (Math Programm Stud 6:170-187, 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 results in stochastic programming and stochastic optimal control.