Uncertain random portfolio selection based on risk curve
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METHODOLOGIES AND APPLICATION
Uncertain random portfolio selection based on risk curve Rouhollah Mehralizade1 · Mohammad Amini2
· Bahram Sadeghpour Gildeh2 · Hamed Ahmadzade3
© Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This paper discusses the uncertain random portfolio selection problem when there are some existing risky securities which have enough historical data and some newly listed ones with insufficient data in the portfolio. So far, in the field of uncertain random portfolio selection, variance, skewness, and value-at-risk have been proposed as the risk criterion. This paper gives a new risk criterion for uncertain random portfolio selection and proposes a new type of mean-risk model based on this criterion to optimization. And in the end, a numerical example is presented for the sake of illustration. Keywords Uncertain random variable · Risk curve · Uncertain random portfolio selection · Mean-risk model · Optimization · Sensitivity analysis
1 Introduction The portfolio selection is concerned with the optimization of capital allocation to a large number of securities (see Huang 2011). The most salient feature of security returns is indeterminacy. Thus, how to describe the indeterminate return and handle the risk brought about by the indeterminacy can be the core of the portfolio selection problem. In practice, some candidate securities possess sufficient transaction data, and some others are newly listed and lack enough data. When we have enough data, the security returns are assumed to be random variables, and probability theory is the main tool for handling this indeterminacy. In portfolio theory based on probability theory, for the first-time, in 1952, Markowitz (1952) introduced the portfolio selection model. In that model, the investment return and risk were measured by the expected value and variance, respectively. Since the variance is sometimes not convenient to be used in practice, many researchers introCommunicated by V. Loia.
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Mohammad Amini [email protected]
1
Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
2
Department of Statistics, Ordered data, Reliability and Dependency Center of Excellence, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
3
Department of Mathematical Sciences, University of Sistan and Baluchestan, Zahedan, Iran
duced some other risk measures and formulated the related models such as mean-semivariance model (Markowitz 1959), mean-variance-skewness model (Konno and Suzuki 1995), the model based on value-at-risk (Krejic et al. 2011), the model based on conditional value-at-risk (Tong et al. 2010), mean-semivariance-CVaR model (Najafi and Mushakhian 2015), mean-risk curve model (Huang 2008), and so forth. When we have no enough data, the security returns can be assumed to be fuzzy variables or uncertain variables. Some deep researches (Huang and Zhao 2014; Liu 2012) have shown that if we use fuzzy variables to describe the subjective estimation of se
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