scholarly journals A comparison of the Normal and Laplace distributions in the models of fuzzy probability distribution for portfolio selection

2020 ◽  
Vol 8 (5) ◽  
pp. 183-198
Author(s):  
Marcus Pinto da Costa da Rocha ◽  
Lucelia M. Lima ◽  
Valcir J. C. Farias ◽  
Benjamin Bedregal ◽  
Heliton R. Tavares
Keyword(s):  
Probability Distribution ◽  
Normal Distribution ◽  
Portfolio Selection ◽  
Real Data ◽  
Laplace Distribution ◽  
Fuzzy Probability ◽  
Variance Model ◽  
Risk Rate ◽  
Mean Variance ◽  
Fuzzy Normal Distribution

The propose of this work is applied the fuzzy Laplace distribution on a possibilistic mean-variance model presented by Li et al which appliehe fuzzy normal distribution. The theorem necessary to introduce the Laplace distribution in the model was demonstrated. It was made an analysis of the behavior of the fuzzy normal and fuzzy Laplace distributions on the portfolio selection with VaR constraint and risk-free investment considering real data. The results showns that were not difference in assets selection and in return rate, however, There was a change in the risk rate, which was higher in the Laplace distribution than in the normal distribution.

scholarly journals Multiple Linear Regressions by Maximizing the Likelihood under Assumption of Generalized Gauss-Laplace Distribution of the Error

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Lorentz Jäntschi ◽  
Donatella Bálint ◽  
Sorana D. Bolboacă
Keyword(s):  
Normal Distribution ◽  
Linear Models ◽  
Linear Regression Analysis ◽  
Likelihood Estimation ◽  
Real Data ◽  
Multiple Linear Regression Analysis ◽  
Laplace Distribution ◽  
New Approach ◽  
Feature Information ◽  
Linear Regressions

Multiple linear regression analysis is widely used to link an outcome with predictors for better understanding of the behaviour of the outcome of interest. Usually, under the assumption that the errors follow a normal distribution, the coefficients of the model are estimated by minimizing the sum of squared deviations. A new approach based on maximum likelihood estimation is proposed for finding the coefficients on linear models with two predictors without any constrictive assumptions on the distribution of the errors. The algorithm was developed, implemented, and tested as proof-of-concept using fourteen sets of compounds by investigating the link between activity/property (as outcome) and structural feature information incorporated by molecular descriptors (as predictors). The results on real data demonstrated that in all investigated cases the power of the error is significantly different by the convenient value of two when the Gauss-Laplace distribution was used to relax the constrictive assumption of the normal distribution of the error. Therefore, the Gauss-Laplace distribution of the error could not be rejected while the hypothesis that the power of the error from Gauss-Laplace distribution is normal distributed also failed to be rejected.

The Solution of an Integer Problem Based on Geometric Method

2014 ◽  
Vol 496-500 ◽  
pp. 2852-2856
Author(s):  
Jia Min Zhou ◽  
Jin Rui Guo ◽  
Ren Er Yang ◽  
Wei Hua Li
Keyword(s):  
Approximate Method ◽  
Calculation Method ◽  
Algebraic Approach ◽  
Optimal Solution ◽  
Real Data ◽  
Quadratic Equation ◽  
Geometric Method ◽  
Variance Model ◽  
Integer Problem ◽  
Mean Variance

This paper studies the integer solution of the Markowitz mean-variance model. To avoid solving the quadratic equation with constraints directly, it uses geometric linear approximate method, and gives a practical and effective calculation method. Then it conducts the corresponding calculations regarding the real data, and reaches an optimal solution while the time of calculations is largely reduced, compared to the direct way and the algebraic approach.

scholarly journals Mean-Variance Model for Portfolio Selection

2012 ◽  
Author(s):  
Frank J. Fabozzi ◽  
Harry M. Markowitz ◽  
Petter N. Kolm ◽  
Francis Gupta
Keyword(s):  
Portfolio Selection ◽  
Variance Model ◽  
Mean Variance
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