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

Abstract

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 εBBO. In order to test the computing power of εBBO, 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 εBBO 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 εBBO, 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 εBBO 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 εBBO algorithm has great potential in the field of financial decision-making, it also shows that εBBO algorithm has a better performance in optimization problem.

Whale Optimization Algorithm for Multiconstraint Second-Order Stochastic Dominance Portfolio Optimization

“…Unlike the above risk measures, the SD constraint is not an indicator, which establishes relative risk advantages by comparison between the k-order distribution function of any two portfolios. Assuming that the utility function of all investors is monotonically increasing, the portfolio Y stochastically dominates the portfolio Y in the first order when all the investors prefer portfolio X to portfolio X or that there is no difference between a part of them [37]. Let x and x 0 be the decision vectors and ξ be a random variable; then…”

“…Unlike the above risk measures, the SD constraint is not an indicator, which establishes relative risk advantages by comparison between the k -order distribution function of any two portfolios. Assuming that the utility function of all investors is monotonically increasing, the portfolio Y stochastically dominates the portfolio Y in the first order when all the investors prefer portfolio X to portfolio X or that there is no difference between a part of them [ 37 ]. Let x and x 0 be the decision vectors and ξ be a random variable; then g ( x , ξ ) is preferred to g ( x 0 , ξ ) weakly in E [( η − X ) + ] ≤ E [( η − X 0 ) + ], ∀ η ∈ ℝ , first-order stochastic dominance, denoted by , if and only if where g ( x , ξ ) is the returns of the portfolio x ∈ R n , which is a concave continuous function both in x and ξ , and F ( g ( x , ξ ); η ) is the cumulative distribution function of g ( x , ξ ).…”

Predicting DNA Motifs by Using Multi-Objective Hybrid Adaptive Biogeography-Based Optimization

“…We will try to combine NSGA-III or MOEA/D with the BBO algorithm for motif discovery problem. Additionally, in our earlier work, we discussed the portfolio optimization problem in second-order stochastic dominance constraint based on the BBO algorithm [46], and we will try to apply the multi-objective BBO algorithm to the multi-objective portfolio optimization problem [47,48] in the future.…”

Application and Effect Analysis of Financial Engineering Tools in Portfolio Optimization

“…In order to strike a balance between risk and return, portfolio optimization has become a crucial task. With the continuous development and innovation in the field of financial engineering, various advanced tools and technologies have emerged, providing more refined and effective solutions for portfolio management (Silva, Pinheiro, & Poggi, 2017;Ye, Yang, & Feng, 2017).…”