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If general relativity is correct, then the origin of the universe is a simple mathematical problem. The Friedmann equation in cosmology is a well-structured ordinary differential equation, and the global properties of its solutions can be qualitatively analyzed by the phase-trajectory method. In this paper we show that the total energy density of matter in the universe is positive, and the total pressure near the Big Bang is negative. By analyzing the global properties of the solutions to the Friedmann equation according to these two conditions of state functions, we find that the Big Bang is impossible, and the space must be a closed 3-dimensional sphere, the cosmological constant is likely to be zero, and the evolution of the universe should be cyclic. The analysis and the proof are simple and straight forward, therefore these conclusions should be reliable.
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A portfolio optimization model under uncertain random environment
Article ID: 2859
Vol 2, Issue 1, 2024
DOI: https://doi.org/10.54517/mss.v2i1.2859
Vol 2, Issue 1, 2024
Received: 29 May 2024; Accepted: 22 June 2024; Available online: 30 June 2024; Issue release: 30 June 2024
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Abstract
Uncertain events frequently occur in today’s financial markets. Consequently, the issue of portfolio selection is becoming increasingly significant. This paper thoroughly considers the complexities of stock returns in real-world scenarios and employs uncertain differential equations (UDE), uncertain time series analysis (UTSA), stochastic differential equations (SDE), and random time series analysis (RTSA) to predict stock returns, thereby enhancing the accuracy of these predictions. Furthermore, this paper addresses investors’ preferences and the limitations of using variance as a measure of investment risk. It introduces a risk preference factor and proposes an uncertain random mean-lower variance model. Finally, a genetic algorithm is utilized to solve the model, and numerical simulations are conducted to demonstrate the model’s practicality.
Keywords
uncertain random portfolio; uncertain differential equation; uncertain time series analysis; stochastic differential equation; random time series analysis; genetic algorithm
References
Markowitz H. Portfolio selection*. The Journal of Finance. 1952; 7(1): 77-91. doi: 10.1111/j.1540-6261.1952.tb01525.x
Jin Y, Zhang W. Robust portfolio optimization with higher moments. Mathematical Finance, 2021, 31(4): 1132-1165.
Yang J, Li Y. Stochastic dominance and portfolio optimization. Review of Financial Studies, 2024, 37(1): 50-78.
Konno H, Suzuki K ichi. A mean-variance-skewness portfolio optimization model. Journal of the Operations Research Society of Japan. 1995; 38(2): 173-187. doi: 10.15807/jorsj.38.173
Huang X. Portfolio selection with a new definition of risk. European Journal of Operational Research. 2008; 186(1): 351-357. doi: 10.1016/j.ejor.2007.01.045
Krejić N, Kumaresan M, Rožnjik A. VaR optimal portfolio with transaction costs. Applied Mathematics and Computation. 2011; 218(8): 4626-4637. doi: 10.1016/j.amc.2011.10.047
Li B, Shu Y. The skewness for uncertain random variable and application to portfolio selection problem. Journal of Industrial & Management Optimization. 2022; 18(1): 457. doi: 10.3934/jimo.2020163
Li J, Liu X. GARCH model with fractional Brownian motion correction. Statistics and Decision, 2021, 1(5): 29-33.
Konno H, Shirakawa H, Yamazaki H. A mean-absolute deviation-skewness portfolio optimization model. Annals of Operations Research. 1993; 45(1): 205-220. doi: 10.1007/bf02282050
Farrar D. The Investment decision under Uncertainty. Prentice Hall, Englewood Cliffs, New Jersey, 1962.
Li X, He L. Higher-order moments and risk management in portfolio optimization. Quantitative Finance, 2023, 23(1): 57-76.
Wang Z, Liu Q. Incorporating higher-order moments into portfolio construction under uncertainty. Review of Financial Studies, 2024, 37(3): 987-1020.
Zadeh L. Fuzzy sets. Information and Control, 1965, 8(3): 338-353.
Deng X, Li R. A portfolio selection model with borrowing constraint based on possibility theory. Applied Soft Computing. 2012; 12(2): 754-758. doi: 10.1016/j.asoc.2011.10.017
Pahade JK, Jha M. Credibilistic variance and skewness of trapezoidal fuzzy variable and mean–variance–skewness model for portfolio selection. Results in Applied Mathematics. 2021; 11: 100159. doi: 10.1016/j.rinam.2021.100159
Liu B. Uncertainty Theory, 2nd ed Springer-Verlag, Berlin, 2007.
Liu B. Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty. Springer-Verlag, Berlin, 2010.
Yu L, Wang L. Uncertainty Modeling in Portfolio Optimization: A Review. European Journal of Operational Research, 2021, 293(2): 645-659.
Cai X, Zhu H. Robust Portfolio Optimization under Uncertainty with Conditional Value-at-Risk. Operations Research Letters, 2022; 50(1): 82-90.
Liu S, Zhou X. Dynamic Portfolio Optimization with Uncertainty: A Stochastic Programming Approach. Mathematical Finance, 2023; 33(3): 678-705.
Liu Y. Uncertain random variables: a mixture of uncertainty and randomness. Soft Computing. 2012; 17(4): 625-634. doi: 10.1007/s00500-012-0935-0
Qin Z. Mean-variance model for portfolio optimization problem in the simultaneous presence of random and uncertain returns. European Journal of Operational Research. 2015; 245(2): 480-488. doi: 10.1016/j.ejor.2015.03.017
Mehlawat MK, Gupta P, Khan AZ. Portfolio optimization using higher moments in an uncertain random environment. Information Sciences. 2021; 567: 348-374. doi: 10.1016/j.ins.2021.03.019
Treanja, S. LU-Optimality Conditions in Optimization Problems with Mechanical Work Objective Functionals. IEEE Transactions on Neural Networks and Learning Systems, 2021.
Holland J. Adaptation in natural and artificial systems. University of Michigan Press, New York, 1975.
Kaya O, Schildbach J, Schneider S, Darius R. Robo-advice-a true innovation in asset management, Deutsche Bank Research, 2017.
DeMiguel V, Garlappi L, Uppal R. Optimal Versus Naive Diversification: How Inefficient is the 1/NPortfolio Strategy? Review of Financial Studies. 2007; 22(5): 1915-1953. doi: 10.1093/rfs/hhm075
Kearney C, Liu S. Textual sentiment in finance: A survey of methods and models. International Review of Financial Analysis. 2014; 33: 171-185. doi: 10.1016/j.irfa.2014.02.006
Yao K, Chen X. A numerical method for solving uncertain differential equations. Journal of Intelligent & Fuzzy Systems. 2013; 25(3): 825-832. doi: 10.3233/ifs-120688
Liu B. Uncertainty Theory, 4th ed Springer Berlin Heidelberg; 2015. doi: 10.1007/978-3-662-44354-5
Ye T, Liu B. Uncertain hypothesis test with application to uncertain regression analysis. Fuzzy Optimization and Decision Making. 2021; 21(2): 157-174. doi: 10.1007/s10700-021-09365-w
Phillips PCB, Perron P. Testing for a unit root in time series regression. Biometrika. 1988; 75(2): 335-346. doi: 10.1093/biomet/75.2.335
Akhter MF, Hassan D, Abbas S. Predictive ARIMA Model for coronal index solar cyclic data. Astronomy and Computing. 2020; 32: 100403. doi: 10.1016/j.ascom.2020.100403
Evans L. An Introduction to Stochastic Differential Equations. 2013. doi: 10.1090/mbk/082
Harlow WV, Rao RKS. Asset Pricing in a Generalized Mean-Lower Partial Moment Framework: Theory and Evidence. The Journal of Financial and Quantitative Analysis. 1989; 24(3): 285. doi: 10.2307/2330813
Yang X, Liu B. Uncertain time series analysis with imprecise observations. Fuzzy Optimization and Decision Making. 2018; 18(3): 263-278. doi: 10.1007/s10700-018-9298-z
Yao K, Liu B. Parameter estimation in uncertain differential equations. Fuzzy Optimization and Decision Making. 2019; 19(1): 1-12. doi: 10.1007/s10700-019-09310-y
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