论文标题
两种Quasiconvex风险度量的投资组合优化
Portfolio optimization with two quasiconvex risk measures
论文作者
论文摘要
我们通过两种风险措施研究了一个静态投资组合优化问题：目标函数中的主要风险度量和次要风险措施，其价值在约束中受到控制。当有必要同时考虑两方的风险偏好，例如投资组合经理和监管机构时，这个问题就很有趣。最近在作者的共同工作中研究了假定风险措施相干的特殊情况（正同质性）。本文通过假设两种风险度量仅是准认证，将分析扩展到更通用的环境。首先，我们研究主要风险度量为凸的情况。我们引入了双重问题，表明投资组合优化问题与双重问题之间存在零二元性差距，并最终确定了与最优性相关的Lagrange乘数与双重问题相关联的条件。接下来，我们研究一般情况没有凸度假设，并表明通过使用众所周知的一分双分配算法与我们证明的双重性结果相结合，可以实现具有规定的最佳差距的近似最佳解决方案。
We study a static portfolio optimization problem with two risk measures: a principle risk measure in the objective function and a secondary risk measure whose value is controlled in the constraints. This problem is of interest when it is necessary to consider the risk preferences of two parties, such as a portfolio manager and a regulator, at the same time. A special case of this problem where the risk measures are assumed to be coherent (positively homogeneous) is studied recently in a joint work of the author. The present paper extends the analysis to a more general setting by assuming that the two risk measures are only quasiconvex. First, we study the case where the principal risk measure is convex. We introduce a dual problem, show that there is zero duality gap between the portfolio optimization problem and the dual problem, and finally identify a condition under which the Lagrange multiplier associated to the dual problem at optimality gives an optimal portfolio. Next, we study the general case without the convexity assumption and show that an approximately optimal solution with prescribed optimality gap can be achieved by using the well-known bisection algorithm combined with a duality result that we prove.
