scholarly journals Kelly's Criterion in Portfolio Optimization: A Decoupled Problem

2017 ◽  
Author(s):  
Zachariah Peterson
Keyword(s):  
Differential Evolution ◽  
Portfolio Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Stock Exchange ◽  
Differential Evolution Algorithm ◽  
Monte Carlo Calculations ◽  
Evolution Algorithm ◽  
Portfolio Optimization Problem ◽  
Single Objective

Kelly's Criterion is well known among gamblers and investors as a method for maximizing the returns one would expect to observe over long periods of betting or investing. These ideas are conspicuously absent from portfolio optimization problems in the financial and automation literature. This paper will show how Kelly's Criterion can be incorporated into standard portfolio optimization models. The model developed here combines risk and return into a single objective function by incorporating a risk parameter. This model is then solved for a portfolio of 10 stocks from a major stock exchange using a differential evolution algorithm. Monte Carlo calculations are used to verify the accuracy of the results obtained from differential evolution. The results show that evolutionary algorithms can be successfully applied to solve a portfolio optimization problem where returns are calculated by applying Kelly's Criterion to each of the assets in the portfolio.

scholarly journals Cardinality Constrained Portfolio Optimization Using Bee Colony Algorithm (Case Study: Tehran Stock Exchange)

2018 ◽  
Author(s):  
Masomeh Mansourinia ◽  
Alireza Momeni
Keyword(s):  
Quadratic Programming ◽  
Portfolio Optimization ◽  
Programming Problem ◽  
Efficient Solution ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Stock Exchange ◽  
Cardinality Constraints ◽  
Bee Colony ◽  
Portfolio Optimization Problem

One of the most studied variant of portfolio optimization problems is with cardinality constraints that transform classical mean-variance model from a convex quadratic programming problem into a mixed integer quadratic programming problem which brings the problem to the class of NP-Complete problems. Therefore, the computational complexity is significantly increased since cardinality constraints have a direct influence on the portfolio size. In order to overcome arising computational difficulties, for solving this problem, researchers have focused on investigating efficient solution algorithms such as metaheuristic algorithms since exact techniques may be inadequate to find an optimal solution in a reasonable time and are computationally ineffective when applied to large-scale problems. In this paper, our purpose is to present an efficient solution approach based on an artificial bee colony algorithm with feasibility enforcement and infeasibility toleration procedures for solving cardinality constrained portfolio optimization problem. Computational results confirm the effectiveness of the solution methodology. In this study, the ABC-I algorithm and the ABC-II algorithm, which are the modern meta-innovative models for solving optimization problems, have been used to optimize the investment portfolio with the goal of increasing returns and reducing risk. Of the 591 companies listed on the Tehran Stock Exchange, 150 companies were selected during the period from 2014 to 2018 using a systematic elimination method with limitation as the final sample. The data from these companies were analyzed using the algorithms used in the research and their performance was compared. The results of the research indicate that the ABC-II algorithm is more efficient than ABC-I for solving the stock portfolio optimization problem.

scholarly journals Cardinality Constrained Portfolio Optimization Using bee Colony Algorithm (Case Study: Tehran Stock Exchange)

2018 ◽  
Author(s):  
Masomeh Mansourinia ◽  
Alireza Momeni
Keyword(s):  
Quadratic Programming ◽  
Portfolio Optimization ◽  
Programming Problem ◽  
Efficient Solution ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Stock Exchange ◽  
Cardinality Constraints ◽  
Bee Colony ◽  
Portfolio Optimization Problem

One of the most studied variant of portfolio optimization problems is with cardinality constraints that transform classical mean-variance model from a convex quadratic programming problem into a mixed integer quadratic programming problem which brings the problem to the class of NP-Complete problems. Therefore, the computational complexity is significantly increased since cardinality constraints have a direct influence on the portfolio size. In order to overcome arising computational difficulties, for solving this problem, researchers have focused on investigating efficient solution algorithms such as metaheuristic algorithms since exact techniques may be inadequate to find an optimal solution in a reasonable time and are computationally ineffective when applied to large-scale problems. In this paper, our purpose is to present an efficient solution approach based on an artificial bee colony algorithm with feasibility enforcement and infeasibility toleration procedures for solving cardinality constrained portfolio optimization problem. Computational results confirm the effectiveness of the solution methodology. In this study, the ABC-I algorithm and the ABC-II algorithm, which are the modern meta-innovative models for solving optimization problems, have been used to optimize the investment portfolio with the goal of increasing returns and reducing risk. Of the 591 companies listed on the Tehran Stock Exchange, 150 companies were selected during the period from 2014 to 2018 using a systematic elimination method with limitation as the final sample. The data from these companies were analyzed using the algorithms used in the research and their performance was compared. The results of the research indicate that the ABC-II algorithm is more efficient than ABC-I for solving the stock portfolio optimization problem.

scholarly journals A Memetic Differential Evolution Algorithm Based on Dynamic Preference for Constrained Optimization Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Ning Dong ◽  
Yuping Wang
Keyword(s):  
Differential Evolution ◽  
Constrained Optimization ◽  
Reference Point ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Fitness Function ◽  
Differential Evolution Algorithm ◽  
Feasible Region ◽  
Weighting Vector ◽  
Evolution Algorithm

The constrained optimization problem (COP) is converted into a biobjective optimization problem first, and then a new memetic differential evolution algorithm with dynamic preference is proposed for solving the converted problem. In the memetic algorithm, the global search, which uses differential evolution (DE) as the search scheme, is guided by a novel fitness function based on achievement scalarizing function (ASF). The novel fitness function constructed by a reference point and a weighting vector adjusts preference dynamically towards different objectives during evolution, in which the reference point and weighting vector are determined adapting to the current population. In the local search procedure, simplex crossover (SPX) is used as the search engine, which concentrates on the neighborhood embraced by both the best feasible and infeasible individuals and guides the search approaching the optimal solution from both sides of the boundary of the feasible region. As a result, the search can efficiently explore and exploit the search space. Numerical experiments on 22 well-known benchmark functions are executed, and comparisons with five state-of-the-art algorithms are made. The results illustrate that the proposed algorithm is competitive with and in some cases superior to the compared ones in terms of the quality, efficiency, and the robustness of the obtained results.

The Genetic Algorithm

2019 ◽  
pp. 154-178
Author(s):  
Burcu Adıguzel Mercangöz ◽  
Ergun Eroglu
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Models ◽  
Portfolio Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Biological Evolution ◽  
Research Field ◽  
Risk Level ◽  
Important Research ◽  
Portfolio Optimization Problem

The portfolio optimization is an important research field of the financial sciences. In portfolio optimization problems, it is aimed to create portfolios by giving the best return at a certain risk level from the asset pool or by selecting assets that give the lowest risk at a certain level of return. The diversity of the portfolio gives opportunity to increase the return by minimizing the risk. As a powerful alternative to the mathematical models, heuristics is used widely to solve the portfolio optimization problems. The genetic algorithm (GA) is a technique that is inspired by the biological evolution. While this book considers the heuristics methods for the portfolio optimization problems, this chapter will give the implementing steps of the GA clearly and apply this method to a portfolio optimization problem in a basic example.

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