Portfolio choice and optimal hedging with general risk functions: A simplex-like algorithm

详细信息    查看全文

• 作者：Alej ; ro Balb&#xe1 ; s ; Raquel Balb&#xe1 ; s ; Silvia Mayoral
• 关键词：Risk measure ; Deviation measure ; Portfolio selection ; Infinite-dimensional linear programming ; Simplex-like method
• 刊名：European Journal of Operational Research
• 出版年：2009
• 出版时间：16 January 2009
• 年：2009
• 卷：192
• 期：2
• 页码：603-620
• 全文大小：285 K

文摘

The minimization of general risk functions is becoming more and more important in portfolio choice theory and optimal hedging. There are two major reasons. Firstly, heavy tails and the lack of symmetry in the returns of many assets provokes that the classical optimization of the standard deviation may lead to dominated strategies, from the point of view of the second order stochastic dominance. Secondly, but not less important, many institutional investors must respect legal capital requirements, which may be more easily studied if one deals with a risk measure related to capital losses.

This paper proposes a new method to simultaneously minimize several general risk or dispersion measures. The representation theorems of risk functions are applied to transform the general risk minimization problem in a minimax problem, and later in a linear programming problem between infinite-dimensional Banach spaces. Then, new necessary and sufficient optimality conditions are stated and a simplex-like algorithm is developed. The algorithm solves the dual problem and provides both optimal portfolios and their sensitivities.

The approach is general enough and does not depend on any particular risk measure, but some of the most important cases are specially analyzed. A final real data numerical example illustrates the practical performance of the proposed methodology.