Design of Efficient Investment Portfolios with a Shortfall Probability as a Measure of Risk

The paper presents a constructive description of the set of all efficient (Pareto-optimal) investment portfolios in a new setting, where the risk measure named “shortfall probability” (SP) is understood as the probability of a shortfall of investor’s capital below a prescribed level. Under a normali...

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Bibliographic Details
Published in:Automation and remote control 2023-04, Vol.84 (4), p.434-442
Main Authors: Gridin, V. N., Golubin, A. Y.
Format: Article
Language:English
Subjects:
CAE) and Design
Calculus of Variations and Optimal Control
Optimization
Computer-Aided Engineering (CAD
Confidence intervals
Control
Control in Social Economic Systems
Convexity
Mathematics
Mathematics and Statistics
Mean
Mechanical Engineering
Mechatronics
Normal distribution
Normality
Risk
Robotics
Statistical analysis
Systems Theory
Variance
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Summary:The paper presents a constructive description of the set of all efficient (Pareto-optimal) investment portfolios in a new setting, where the risk measure named “shortfall probability” (SP) is understood as the probability of a shortfall of investor’s capital below a prescribed level. Under a normality assumption, it is shown that SP has a generalized convexity property, the set efficient portfolios is constructed. Relations between the set of mean-SP and the set of mean-variance efficient portfolios as well as between mean-SP and mean-Value-at-Risk (VaR) sets of efficient portfolios are studied. It turns out that mean-SP efficient set is a proper subset of the mean-variance efficient set; interrelation with the mean-VaR efficient set is more complicated, however, mean-SP efficient set is proved to be a proper subset of mean-VaR efficient set under a sufficiently high confidence level. Besides a normal distribution, elliptic distributions are considered as an alternative for modeling the investor’s total return distribution. The obtained results provides the investor with a risk measure, that is more vivid than the variance and Value-at-Risk, and with determination of the corresponding set of effective portfolios.
ISSN:0005-1179
1608-3032
DOI:10.1134/S0005117923040070