Biogeography-Based Optimization of the Portfolio Optimization Problem with Second Order Stochastic Dominance Constraints

Tao Ye,Siling Feng,Ziqiang Yang

doi:10.3390/a10030100

Abstract

The portfolio optimization problem is the central problem of modern economics and decision theory; there is the Mean-Variance Model and Stochastic Dominance Model for solving this problem. In this paper, based on the second order stochastic dominance constraints, we propose the improved biogeography-based optimization algorithm to optimize the portfolio, which we called ε BBO. In order to test the computing power of ε BBO, we carry out two numerical experiments in several kinds of constraints. In experiment 1, comparing the Stochastic Approximation (SA) method with the Level Function (LF) algorithm and Genetic Algorithm (GA), we get a similar optimal solution by ε BBO in [ 0 , 0 . 6 ] and [ 0 , 1 ] constraints with the return of 1.174% and 1.178%. In [ - 1 , 2 ] constraint, we get the optimal return of 1.3043% by ε BBO, while the return of SA and LF is 1.23% and 1.26%. In experiment 2, we get the optimal return of 0.1325% and 0.3197% by ε BBO in [ 0 , 0 . 1 ] and [ - 0 . 05 , 0 . 15 ] constraints. As a comparison, the return of FTSE100 Index portfolio is 0.0937%. The results prove that ε BBO algorithm has great potential in the field of financial decision-making, it also shows that ε BBO algorithm has a better performance in optimization problem.

Highlights

In solving the problem of uncertainty, the Expected Utility Theory describes the rational people how to determine the optimal decisions and take action when faced with the uncertainty of risk and return
Aiming at the portfolio optimization problem based on stochastic dominance (SSD) constraints, drawn on the experience of mutation operator of the Differential Evolution (DE) algorithm, we propose the εBBO algorithm
In model (28) we do not consider the transaction cost, if we take it into account, in order to weaken the contribution of small transactions we propose the following model: min

Summary

Introduction

In solving the problem of uncertainty, the Expected Utility Theory describes the rational people how to determine the optimal decisions and take action when faced with the uncertainty of risk and return. The Expect Utility Theory assumes that the individual is risk aversion, that is, its utility function is concave. How to choose the optimal portfolio is one of its central problems. Based on the relationship between the risk of assets and the return on assets, Markowitz [1] solve the portfolio optimization problem through mathematic statistic method and propose the Mean-Variance model. The Mean-Variance model measures the expected revenue at the required rate of return, and measures the risk size with the variance of required rate of return. The model gets poor applications because of its harsh assumptions

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Conclusion