Maximum entropy likelihood (MEEL) methods also known as exponential tilted empirical likelihood methods using constraints from model Laplace transforms (LT) are introduced in this paper. An estimate of overall loss of...Maximum entropy likelihood (MEEL) methods also known as exponential tilted empirical likelihood methods using constraints from model Laplace transforms (LT) are introduced in this paper. An estimate of overall loss of efficiency based on Fourier cosine series expansion of the density function is proposed to quantify the loss of efficiency when using MEEL methods. Penalty function methods are suggested for numerical implementation of the MEEL methods. The methods can easily be adapted to estimate continuous distribution with support on the real line encountered in finance by using constraints based on the model generating function instead of LT.展开更多
对于m个相互独立的随机向量X_1=(X_(1,1),X_(1,2),…,X_(1,n)),X_2=(X_(2,1),X_(2,2),…,X_(2,n)),…,X_m=(X_(m,1),X_(m,2),…,X_(m,n)),记S^((m))=sum from (i=1) to n X_(1,i)X_(2,i)…X_(m,i).讨论了S^((m))在凸序意义下的上下界,...对于m个相互独立的随机向量X_1=(X_(1,1),X_(1,2),…,X_(1,n)),X_2=(X_(2,1),X_(2,2),…,X_(2,n)),…,X_m=(X_(m,1),X_(m,2),…,X_(m,n)),记S^((m))=sum from (i=1) to n X_(1,i)X_(2,i)…X_(m,i).讨论了S^((m))在凸序意义下的上下界,得到了S^((3))上下界的分布函数和停止损失保费;给出了随机年金在凸序意义下的上界,并得到了随机利率下离散随机年金现值的期望.展开更多
文摘Maximum entropy likelihood (MEEL) methods also known as exponential tilted empirical likelihood methods using constraints from model Laplace transforms (LT) are introduced in this paper. An estimate of overall loss of efficiency based on Fourier cosine series expansion of the density function is proposed to quantify the loss of efficiency when using MEEL methods. Penalty function methods are suggested for numerical implementation of the MEEL methods. The methods can easily be adapted to estimate continuous distribution with support on the real line encountered in finance by using constraints based on the model generating function instead of LT.
文摘对于m个相互独立的随机向量X_1=(X_(1,1),X_(1,2),…,X_(1,n)),X_2=(X_(2,1),X_(2,2),…,X_(2,n)),…,X_m=(X_(m,1),X_(m,2),…,X_(m,n)),记S^((m))=sum from (i=1) to n X_(1,i)X_(2,i)…X_(m,i).讨论了S^((m))在凸序意义下的上下界,得到了S^((3))上下界的分布函数和停止损失保费;给出了随机年金在凸序意义下的上界,并得到了随机利率下离散随机年金现值的期望.
