Abstract
Investors are concerned about the reliability and safety of their capital, especially its liquidity, when investing. This paper sets up a possibilistic portfolio selection model with liquidity constraint. In this model, the asset return and liquidity are fuzzy variables which follow the normal possibility distributions. Liquidity is measured as the turnover rate of the asset. On the basis of possibility theory, we transform the model into a quadratic programming problem to obtain its solution. We illustrate that, in the process of investment, investors can make better use of capital by choosing their investment portfolios according to their expected return and asset liquidity.
Highlights
Portfolio selection has received extensive attentions [1,2,3,4]. e portfolio selection model studies how to allocate investment funds among different assets to guarantee profits and disperse investment risk
Markowitz [5] proposed a mean-variance model (MVM) for portfolio selection, which played an important role in the development of modern portfolio selection theory. e MVM uses mean and variance to describe, respectively, the expected return and risk of a portfolio. e basic rule is the investors’ tradeoff between expected return and risk
If the return rate of asset k, k 1, 2, . . . , n, is a normally distributed fuzzy variable denoted as rk ∼ FN(μk, σ2k) and the turnover rate of asset k, k 1, 2, . . . , n, is a normally distributed fuzzy variable denoted as lk ∼ FN(ak, b2k), the model (PL2) can be transformed into min Var(R) 1⎛⎝n 2 k 1 n s.t. xkμk ≥ μ, k 1 xk σ
Summary
Portfolio selection has received extensive attentions [1,2,3,4]. e portfolio selection model studies how to allocate investment funds among different assets to guarantee profits and disperse investment risk. In order to better integrate an uncertain decision environment with vagueness and ambiguity, in 2009, Zhang et al [37] proposed a possibilistic mean-variance portfolio selection model based on the definitions of the possibilistic return and possibilistic risk. In this model, the returns of assets were fuzzy variables with LR-type possibility distributions. Liu and Zhang [40] defined the product of multiple fuzzy numbers’ possibilistic mean and variance, and, based on these definitions, they developed three multiperiod fuzzy portfolio optimization models.
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