Development of an efficient method to approximate the risk measure of Lower Partial Moment of the first order

• Published in: Computers & industrial engineering 2019-09, Vol.135, p.326-332
• Main Authors: Jasemi, Milad, Monplaisir, Leslie, Amini Jam, Pegah
• Format: Article
• Language: English
• Subjects: Approximation methods; Downside risk; Financial risk measures; Lower Partial Moments; Risk management
• ISSN: 0360-8352; 1879-0550
• DOI: 10.1016/j.cie.2019.06.018

•Dealing with computational difficulties of Lower Partial Moment of the first order.•Development of a new methodology to approximate LPM of the first order.•Designing an innovative evaluation system based on a comprehensive set of simulations. In this paper after a review on the best known risk measures, the focus is on a particular shape of Lower Partial Moments (LPM). The measure in spite of its practical definition, has not been applied in portfolio optimization models as was expected. The main reason is its computational complexity. This is the challenge this paper is about to meet. After considering some statistical facts, several distinct relations for estimation of LPM of the first order are developed. Then for performance assessment of the methods, a simulation-based evaluation system is designed. The evaluation system concentrates on both the general efficiency of the methods individually, and their comparative performances versus each other. Among 3 approaches of 1, 2 and 3, along with a bunch of medial approaches, Approach 1 proves to be the best, while all of them are found reliable for use.