Empirical investigation of nonlinear asset pricing kernel with human capital and housing wealth

In a traditional framework, asset returns are captured by simple linear asset pricing models. They include Capital Asset Pricing Model (CAPM) and Fama-French threefactor model. However, the empirical study shows that the asset returns are fat tailed, that cannot be accurately predicted by normal distribution. Kurtosis and skewness should be considered when pricing those non-normal assets. Various literatures can be found focused on this topic. Bansal and Viswanathan (1993) and Chapman (1997) developed nonparametric model. They find that the nonparametric models perform better in explaining expected returns. Most recently, nonlinear asset pricing models developed by Dittmar (2002) shows more significantly improvements in return estimation, compared to the linear single and linear multi-factor models. In this study, I focus on an asset-pricing model of higher order risk factors and use polynomial pricing kernel to generate the empirical performance of a nonlinear model. This is an extension to both Bansal and Dittmar’s work, by extending the definition of the total wealth including human capital and housing wealth. This research work is novel and especially important to understand asset price behavior after year 2007, the credit crisis. Housing price growth rate is a very critical indicator for long-term investment, reflecting consumer confidence on the long-term global economy. It can be used to estimate the turning point for the recent economic down turn. In addition, since the credit crisis 2008 is triggered by liquidity shortage in banking systems, the level of housing price has direct impact on the balance sheet of those banking sectors. The higher the house price, the more willingness banks have to release the credit to the market. The housing wealth factor can be used to estimate when the credit crunch will disappear and global economy gets fully recovered. In this study, the risk factors that represent the aggregate wealth in the economic are tested. The best possible proxy of return on the total wealth is discussed. The thesis can be divided into 2 parts. In the first part of my thesis, a higher order moment model to explain the asset price behaviour is developed. Similar to the work presented by Dittmar (2002), pricing kernel is approximated using Taylor Series expansion and Hansen-Jagannathan (1997) weighting matrix. The time-varying coefficients with respected sign of coefficients are estimated. Housing factor is added to extend the model, as we believe that housing plays an important role in the return on aggregate wealth. In the second part of my thesis, I test models in three time periods. They include Dittmar’s period from 1963 to 1995, the full sample period from 1963 to 2009 and recent period from 1996 to 2009. Our results confirm that nonlinear models outperform than linear models in explaining the cross section of returns. The higher order risk factors give the magnitude improvement in model fitting. This is consistent with the result given by Dittmar (2002). Moreover, my results conclude that the models with the housing wealth included performs significantly better than the models with human capital only

Fermionic phase transition induced by the effective impurity in holography

We investigate the holographic fermionic phase transition induced by the effective impurity in holography, which is introduced by massless scalar fields in Einstein-Maxwell-massless scalar gravity. We obtain a phase diagram in $(\alpha, T)$ plane separating the Fermi liquid phase and the non-Fermi liquid phase.Comment: 17 pages, 9 figure

Infinitely many solutions for elliptic problems in RN\mathbb{R}^N involving the p(x)p(x)-Laplacian

We consider the $p(x)$-Laplacian equations in $\mathbb{R}^N$. The potential function does not satisfy the coercive condition. We obtain the existence of infinitely many solutions of the equations, improving a recent result of Duan--Huang [L. Duan, L. H. Huang, Electron. J. Qual. Theory Differ. Equ. 2014, No. 28, 1--13]

Multiplicity of solutions for p-Laplacian equation in R^N with indefinite weight

In this article, we study the existence of infinitely many nontrivial solutions for a class of superlinear $p$-Laplacian equations $$-Delta_p u+V(x)|u|^{p-2}u=f(x,u),$$ where the primitive of the nonlinearity $f$ is of subcritical growth near $infty$ in $u$ and the weight function $V$ is allowed to be sign-changing. Our results extend the recent results of Zhang and Xu [Q. Y. Zhang, B. Xu, {em Multiplicity of solutions for a class of semilinear Schr"{o}dinger equations with sign-changing potential}, J. Math. Anal. Appl {bf 377}(2011), 834--840]

Regression Analysis of Recurrent Gap Times with Time-Dependent Covariates

Individual subjects may experience recurrent events of same type over a relatively long period of time in a longitudinal study. Researchers are often interested in the distributional pattern of gaps between the successive recurrent events and their association with certain concomitant covariates as well. In this article, their probability structure is investigated in presence of censoring. According to the identified structure, we introduce the proportional reverse-time hazards models that allow arbitrary baseline function for every individual in the study, when the time-dependent covariates effect is of main interest. Appropriate inference procedures are proposed and studied to estimate the parameters of interest in the models. The proposed methodology is demonstrated with the Monte-Carlo simulations and applied to a well-known Denmark schizophrenia cohort study data set

Semiparametric Regression Analysis on Longitudinal Pattern of Recurrent Gap Times

In longitudinal studies, individual subjects may experience recurrent events of the same type over a relatively long period of time. The longitudinal pattern of the gaps between the successive recurrent events is often of great research interest. In this article, the probability structure of the recurrent gap times is first explored in the presence of censoring. According to the discovered structure, we introduce the proportional reverse-time hazards models with unspecified baseline functions to accommodate heterogeneous individual underlying distributions, when the ongitudinal pattern parameter is of main interest. Inference procedures are proposed and studied by way of proper riskset construction. The proposed methodology is demonstrated by Monte-Carlo simulations and an application to the well-known Denmark schizophrenia cohort study data se

Investigation on dynamic characteristics of mechanical assembly

Mechanical assembly is important process affecting product dynamic quality. To completely inspect assembly quality, dynamic characteristic analysis is necessary. Based on substructuring dynamic analysis, this paper theoretically analyzes the changes of dynamic characteristics due to assembling process. Assembly coupling dynamic stiffness computed by inverse substructuring analysis is considered as a critical measure on the changes. The results obtained have been well validated by a lumped-parameter model for two-level of substructures