论文标题
通过凸优化的累积前景理论实用程序的投资组合优化
Portfolio Optimization with Cumulative Prospect Theory Utility via Convex Optimization
论文作者
论文摘要
我们考虑选择一种在资产回报的经验分布上最大化累积前景理论（CPT）实用程序的投资组合的问题。我们表明，尽管CPT实用程序不是投资组合权重的凹功能，但它可以表示为两个功能的差异。第一个术语是具有凹参数的凸函数的组成，第二项是带有凸参数的凸函数的组成。这种结构使我们能够在CPT实用程序上得出一个全局的下限或少数人，我们可以在较小的最大化（MM）算法中使用该结构，以最大化CPT实用程序。我们进一步表明，该问题适合一个简单的凸连接（CC）程序，该过程迭代地最大程度地提高了局部近似。这两种方法都可以处理中小型问题，以及复杂（但凸）的投资组合约束。我们还描述了一种更简单的方法，该方法扩展到更大的问题，但仅处理简单的投资组合约束。
We consider the problem of choosing a portfolio that maximizes the cumulative prospect theory (CPT) utility on an empirical distribution of asset returns. We show that while CPT utility is not a concave function of the portfolio weights, it can be expressed as a difference of two functions. The first term is the composition of a convex function with concave arguments and the second term a composition of a convex function with convex arguments. This structure allows us to derive a global lower bound, or minorant, on the CPT utility, which we can use in a minorization-maximization (MM) algorithm for maximizing CPT utility. We further show that the problem is amenable to a simple convex-concave (CC) procedure which iteratively maximizes a local approximation. Both of these methods can handle small and medium size problems, and complex (but convex) portfolio constraints. We also describe a simpler method that scales to larger problems, but handles only simple portfolio constraints.
