An equivalent condition is derived for g-concave function defined by (static) g-expectation. Several extensions including quadratic generators and (g,h)-concavity are also considered.
In this study, the exact solutions for the propagation of pulses in optical fibers are obtained.Special values are given in the model used, and two nonlinear differential equations are obtained.Nonlinear equations are...In this study, the exact solutions for the propagation of pulses in optical fibers are obtained.Special values are given in the model used, and two nonlinear differential equations are obtained.Nonlinear equations are reduced to ordinary differential equations with the help of wave transformations. Then, the obtained differential equations are solved by two different methods,namely the modified simplest equation and the modified Kudryashov procedures. The solutions are given by hyperbolic, trigonometric and rational functions and the results are useful for optics,engineering and other related areas. Finally three-dimensional, contour and two-dimensional shapes are given for some solutions. These figures are important for understanding the motion of the wave. The given methods are applied to the equations for the first time. To the best of the authors' knowledge, these results are new and have not been obtained in the literature. The results are useful for applied mathematics, physics and other related areas.展开更多
G-VaR,which is a type of worst-case value-at-risk(VaR),is defined as measuring risk incorporating model uncertainty.Compared with most extant notions of worst-case VaR,G-VaR can be computed using an explicit formula,a...G-VaR,which is a type of worst-case value-at-risk(VaR),is defined as measuring risk incorporating model uncertainty.Compared with most extant notions of worst-case VaR,G-VaR can be computed using an explicit formula,and can be applied to large portfolios of several hundred dimensions with low computational cost.We also apply G-VaR to robust portfolio optimization,thereby providing a tractable means to facilitate optimal allocations under the condition of market ambiguity.展开更多
基金supported by the NSFC(11871050 and11401414)SF of Jiangsu Province(BK20160300+3 种基金BK2014029914KJB110022)supported by NSFC(11171186)the"111"project(B12023)
文摘An equivalent condition is derived for g-concave function defined by (static) g-expectation. Several extensions including quadratic generators and (g,h)-concavity are also considered.
文摘In this study, the exact solutions for the propagation of pulses in optical fibers are obtained.Special values are given in the model used, and two nonlinear differential equations are obtained.Nonlinear equations are reduced to ordinary differential equations with the help of wave transformations. Then, the obtained differential equations are solved by two different methods,namely the modified simplest equation and the modified Kudryashov procedures. The solutions are given by hyperbolic, trigonometric and rational functions and the results are useful for optics,engineering and other related areas. Finally three-dimensional, contour and two-dimensional shapes are given for some solutions. These figures are important for understanding the motion of the wave. The given methods are applied to the equations for the first time. To the best of the authors' knowledge, these results are new and have not been obtained in the literature. The results are useful for applied mathematics, physics and other related areas.
基金supported by Natural Science Foundation of China and Jiangsu Province(No.11871050,No.11971342,No.11401414,No.BK20140299,No.14KJB110022)。
文摘G-VaR,which is a type of worst-case value-at-risk(VaR),is defined as measuring risk incorporating model uncertainty.Compared with most extant notions of worst-case VaR,G-VaR can be computed using an explicit formula,and can be applied to large portfolios of several hundred dimensions with low computational cost.We also apply G-VaR to robust portfolio optimization,thereby providing a tractable means to facilitate optimal allocations under the condition of market ambiguity.
