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The covariance matrix for 4 projects (%)
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The mean-variance technique has played an important role in the development of modern portfolio selection theory. In comparison with the single objective optimization, the utilization of multi-objective optimization is increased, to solve the complex multiple-objective functions. Applications of portfolio are usually observed in the stock markets;...
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Citations
... In this situation, variance can not adequately describe the risk of portfolio return. As a result, many scholars point out that the higher moments of asset return should be considered when constructing portfolio selection model (Harvey et al. 2010;Maringer et al. 2009;Liu et al. 2003Liu et al. , 2018Samuelson 1970;Wilcox 2020). For instance, Samuelson (1970) proved the limitations of mean-variance model and the correlation between portfolio decisions and higher moments (skewness and kurtosis). ...
... As is known to all, skewness and kurtosis are important statistical indicators, which represent the characteristics of asymmetry and steepness of data, respectively. As a result, more and more scholars consider the higher moments of asset returns, i.e., adding skewness and kurtosis into meanvariance portfolio models (Konno et al. 1993;Liu et al. 2018Liu et al. , 2003Li and Sun 2022). Diversification is the practice of reducing risk by allocating investments among various financial instruments, industries and other categories. ...
The complexity of the financial systems inevitably leads to the uncertain information and random information simultaneously. Because asset returns frequently show excessive kurtosis and tend to be skewed, we consider an uncertain random higher moments portfolio optimization problem in this paper, in which uncertain and random return rates exist simultaneously. First, the concept of kurtosis for uncertain random variable is defined and the deterministic expressions of kurtosis under three kinds of distributions are derived. Then, an uncertain random mean-variance-skewness-kurtosis-entropy model is formulated with two auxiliary models for portfolio optimization problem. After solving the equivalent deterministic model with NSGA-II algorithm, we propose a new optimal solution criterion for finding a single optimal solution in Pareto optimal solution set. Finally, we present a numerical simulation and obtain the following results: (i) the practicability and the validity of the proposed model, the NSGA-II algorithm and the optimal selection criterion have verified; (ii) the size of population has an obvious influence on the single optimal solution; (iii) the parameter adjustment has a significant impact on the results, and the results are in perfect agreement with the actual situation.
... where ζ l and ζ r contain all the left and right endpoints of candidate intervals. Variances and kurtosis are often the indexes of the dispersion degree of numeric values [36,37]. However, they only consider the numerical distribution characteristics and fail to reflect the overlapping part of the intervals. ...
Due to evaluation performance limits and compatibility problems with PDP (Policy Decision Point) in practical information systems, some established schemes have limits in handling massive complex requests. To address the existing challenges of fast rule match on interval values, we propose a novel policy evaluation engine, namely Poliseek with three desired modules. A preprocessing module of Poliseek is equipped with a static encoding strategy and converts the XACML rules and requests into four-dimensional numeric vectors in an attribute space. Owing to a novel optimization object of minimizing interval collisions, a dimensionality reducer and diffuser module can generate candidate values related to each rule vector in the identification space. These values and requests are handled by a fast policy evaluation module using well-constructed hash buckets and a characterized search algorithm. The experimental results show that if the number of requests reaches 10,000, Poliseek can find the target rule approximately 1090, 15, and 15 times faster than the Sun PDP, XEngine, and SBA-XACML, respectively. Poliseek also offers a fast evaluation progress of handling 10,000 complex policy rules with interval attribute values in 275.9 ms, which shows its strong robustness and practicality.
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