摘要翻译：
一个期望效用最大化的连续时间金融投资组合选择模型通常归结为在预算约束下求解一个以最终财富为单位的（静态）凸随机优化问题。在文献中，后者是通过假定{\It先验}问题是适定的（即上确界值是有限的）并且存在一个拉格朗日乘子（因此最优解是可获得的）来解决的。本文首先通过各种反例证明了这两个假设都不成立，最优解也不一定存在。这些异常反过来又对投资组合选择模型和解决方案有重要的解释和影响。然后研究了拉格朗日乘子的不存在性、问题的不适定性和最优解的不可达性之间的关系。最后，给出了能找到唯一最优解的显式且易于验证的条件。
---
英文标题：
《A Convex Stochastic Optimization Problem Arising from Portfolio
  Selection》
---
作者：
Hanqing Jin, Zuo Quan Xu and Xun Yu Zhou
---
最新提交年份：
2007
---
分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Portfolio Management        项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
--
一级分类：Mathematics        数学
二级分类：Numerical Analysis        数值分析
分类描述：Numerical algorithms for problems in analysis and algebra, scientific computation
分析和代数问题的数值算法，科学计算
--
一级分类：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
--
一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
--

---
英文摘要：
  A continuous-time financial portfolio selection model with expected utility maximization typically boils down to solving a (static) convex stochastic optimization problem in terms of the terminal wealth, with a budget constraint. In literature the latter is solved by assuming {\it a priori} that the problem is well-posed (i.e., the supremum value is finite) and a Lagrange multiplier exists (and as a consequence the optimal solution is attainable). In this paper it is first shown, via various counter-examples, neither of these two assumptions needs to hold, and an optimal solution does not necessarily exist. These anomalies in turn have important interpretations in and impacts on the portfolio selection modeling and solutions. Relations among the non-existence of the Lagrange multiplier, the ill-posedness of the problem, and the non-attainability of an optimal solution are then investigated. Finally, explicit and easily verifiable conditions are derived which lead to finding the unique optimal solution.
---
PDF链接：
https://arxiv.org/pdf/0709.4467