Generalized moment estimation for uncertain differential equations

Abstract Parameter estimation is a critical problem for the uncertain differential equation to achieve its full potential. Based on the Liu process’s properties and the difference form of the uncertain differential equation, the existing method of moments is intuitive but sometimes has no solution. As a result, this method is invalid and alternative ways are needed to estimate unknown parameters in the uncertain differential equation. Motivated by this, this paper proposes the generalized moment estimation which is the optimal solution of a minimization problem. Generalized moment estimation is equivalent to moment estimation when moment estimation exists, and still works well when moment estimation is invalid. Numerical examples and an empirical analysis on the interest rate illustrate the rationality and superiority of the generalized moment estimation.

[1]  Liqun Liu,et al.  Decreasing absolute risk aversion, prudence and increased downside risk aversion , 2012 .

[2]  Luiz Koodi Hotta,et al.  Generalized moment estimation of stochastic differential equations , 2016, Comput. Stat..

[3]  L. Hansen.  Large Sample Properties of Generalized Method of Moments Estimators , 1982 .

[4]  Campbell R. Harvey,et al.  An Empirical Comparison of Alternative Models of the Short-Term Interest Rate , 1992 .

[5]  Baoding Liu,et al.  Parameter estimation in uncertain differential equations , 2019, Fuzzy Optimization and Decision Making.

[6]  Kai Yao,et al.  Uncertain Differential Equations , 2016 .

[7]  Baoding Liu.  Some Research Problems in Uncertainty Theory , 2009 .

[8]  Rong Gao,et al.  Milne method for solving uncertain differential equations , 2016, Appl. Math. Comput..

[9]  Kai Yao,et al.  Uncertain partial differential equation with application to heat conduction , 2016, Fuzzy Optimization and Decision Making.

[10]  Xiangfeng Yang,et al.  Runge-Kutta Method for Solving Uncertain Differential Equations , 2015 .

[11]  K. Pearson.  Contributions to the Mathematical Theory of Evolution , 1894 .

[12]  Yi Zhang,et al.  Hamming method for solving uncertain differential equations , 2017, Appl. Math. Comput..

[13]  X. Chen,et al.  Existence and uniqueness theorem for uncertain differential equations , 2010, Fuzzy Optim. Decis. Mak..

[14]  Baoding Liu.  Toward uncertain finance theory , 2013 .

[15]  Jinwu Gao,et al.  Uncertain differential games with application to capitalism , 2013 .

[16]  Baoding Liu,et al.  Uncertainty Theory - A Branch of Mathematics for Modeling Human Uncertainty , 2011, Studies in Computational Intelligence.

[17]  Baoding Liu.  Fuzzy Process, Hybrid Process and Uncertain Process , 2008 .

[18]  Iuliana Carmen,et al.  UNCERTAINTY FUNCTIONAL DIFFERENTIAL EQUATIONS FOR FINANCE , 2010 .

[19]  Dan A. Ralescu,et al.  Adams method for solving uncertain differential equations , 2015, Appl. Math. Comput..

[20]  Jinwu Gao,et al.  Uncertain term structure model of interest rate , 2013, Soft Comput..

[21]  Xiaowei Chen,et al.  A numerical method for solving uncertain differential equations , 2013, J. Intell. Fuzzy Syst..

[22]  Yuanguo Zhu,et al.  Please Scroll down for Article Cybernetics and Systems Uncertain Optimal Control with Application to a Portfolio Selection Model Uncertain Optimal Control with Application to a Portfolio Selection Model , 2022 .

[23]  Kai Yao,et al.  A type of uncertain differential equations with analytic solution , 2013 .