Multi-period portfolio selection problem under uncertain environment with bankruptcy constraint

Abstract

The complexity of financial markets leads to different types of indeterminate asset returns. For example, asset returns are considered as random variables, when the available data is enough. When the available data is too small or even no available data to estimate a probability distribution, we have to invite some domain experts to evaluate the belief degrees of asset returns. Then, asset returns can be described as uncertain variables. In this paper, we discuss a multi-period portfolio selection problem under uncertain environment, which maximizes the final wealth and minimizes the risk of investment. Unlike the common method to describe the multi-period portfolio selection problem as a bi-objective optimization model, we formulate this uncertain multi-period portfolio selection problem by a new method in three steps with two single objective optimization models. And, we consider the influence of transaction cost and bankruptcy of investor. Then, the proposed uncertain optimization models are transformed into the corresponding crisp optimization models and we use the genetic algorithm combined with penalty function method to solve them. Finally, a numerical example is given to show the effectiveness and practicability of proposed models and method.

Uncertain Portfolio Selection with Borrowing Constraint and Background Risk

“…e chance-mean model can be transformed to a deterministic linear programming model and then it can be easily solved by Table 4: Optimal solution of model (46). Mathematical Problems in Engineering optimization software.…”

“…For example, Huang and Qiao [45] discussed the multiperiod portfolio selection problem and proposed a risk index model. Li et al [46] further discussed uncertain multiperiod portfolio selection with a bankruptcy constraint. Zhang et al [47] proposed two innovative uncertain portfolio selection models, the expected-variance-chance model and chanceexpected-variance model and designed a hybrid intelligent algorithm to solve the models.…”

An Effective League Championship Algorithm for the Stochastic Multi-Period Portfolio Optimization Problem

“…Wang et al [35] studied MPPO problem with returns considered as fuzzy random variables and proposed a fuzzy simulation-based PSO algorithm for solving the problem. Li et al [36] considered an uncertain multiperiod portfolio selection problem with the in uence of transaction cost and bankruptcy. They solved the problem using GA with penalty function.…”

A Single Machine Scheduling with Periodic Maintenance and Uncertain Processing Time

“…To deal with the involved human uncertainty, the uncertainty theory was founded by Liu [12] in 2007 and refined it in 2010 [13]. The uncertainty theory is a branch of axiomatic mathematics for modeling human uncertainty, which has been deeply developed in many fields such as uncertain programming [14][15][16], uncertain scheduling [17][18][19][20][21][22], uncertain risk analysis [23][24][25], uncertain calculus [26][27][28] and uncertain optimal control [29][30][31][32][33][34].…”