���ڹ���FGM Copula���������Ŷ�����ģ���µ�Gerber-Shiu��������

??In this paper, we consider a perturbed compound Poisson risk model with dependence, where the dependence structure for the claim size and the inter-claim time is modeled by a generalized Farlie-Gumbel-Morgenstern copula. The integro equations, the Laplace transforms and the defective renewal equations for the Gerber-Shiu functions are obtained. For exponential claims, some explicit expressions are obtained, and some numerical examples for the ruin probabilities are also provided.     

�ɲ����˶�����ά��������������һ�������ڵ����Զ������������������

??We study the linear quadratic optimal stochastic control problem which is jointly driven by Brownian motion and L\'{e}vy processes. We prove that the new affine stochastic differential adjoint equation exists an inverse process by applying the profound section theorem. Applying for the Bellman's principle of quasilinearization and a monotone iterative convergence method, we prove the existence and uniqueness of the solution of the backward Riccati differential equation. Finally, we prove that the optimal feedback control exists, and the value function is composed of the initial value of the solution of the related backward Riccati differential equation and the related adjoint equation.     

��I�ͻ�Ͻ�β��ָ��——�������ֲ�����ʧЧģ�͵�ͳ�Ʒ���

In this paper, we investigate a competing risks model based on exponentiated Weibull distribution under Type-I progressively hybrid censoring scheme. To estimate the unknown parameters and reliability function, the maximum likelihood estimators and asymptotic confidence intervals are derived. Since Bayesian posterior density functions cannot be given in closed forms, we adopt Markov chain Monte Carlo method to calculate approximate Bayes estimators and highest posterior density credible intervals. To illustrate the estimation methods, a simulation study is carried out with numerical results. It is concluded that the maximum likelihood estimation and Bayesian estimation can be used for statistical inference in competing risks model under Type-I progressively hybrid censoring scheme.     

�г�����������������ϵ�о�

The relationship between futures and spot is still an important issue in academic communities and supervisory departments. In this paper, the Granger Causality Test is extended into quantile regression and then the relationship between futures and spot is investigated at different quantile positions. Note that under the model with differential data, different quantile positions are related to the corresponding financial environments. Consequently, a market-dependent casuality between futures and spot is established, by which we can study the relationship more deeply and comprehensively. The main points of view obtained in this paper are what follows: 1. The relationship between futures and spot is strongly related to the financial environments, besides the features of futures and spot; 2. Under the normal and stable financial markets, there is casuality one another, but the relationship will be abnormal under extremal financial conditions, the common relationship between futures and spot is masked by other financial factors; 3. If the casuality was seen as a normal fact logically, then the abnormal relationship should indicate a bad or extremal financial environment, which provides supervisory departments with a warning signal.     

��Ҷ˹���Ϸ�λ�ع��Gibbs�����㷨

Most regression modeling is based on traditional mean regression which results in non-robust estimation results for non-normal errors. Compared to conventional mean regression, composite quantile regression (CQR) may produce more robust parameters estimation. Based on a composite asymmetric Laplace distribution (CALD), we build a Bayesian hierarchical model for the weighted CQR (WCQR). The Gibbs sampler algorithm of Bayesian WCQR is developed to implement posterior inference. Finally, the proposed method are illustrated by some simulation studies and a real data analysis.     

���������ĸ��Ϸ�λ���ع��SIMEX����

??Composite quantile regression model with measurement error is considered. The SIMEX estimators of the unknown regression coefficients are proposed based on the composite quantile regression. The proposed estimators not only eliminate the bias caused by measurement error, but also retain the advantages of the composite quantile regression estimation. The asymptotic properties of the SIMEX estimation are proved under some regular conditions. The finite sample properties of the proposed method are studied by a simulation study, and a real example is analyzed.     

�����о��ĸ���

??This paper is based on ``Pao-Lu Hsu's lecture' (2019/3/22) at Peking University and the subsequent expansion of his reports. It begins with some recollections benefited of the author from Professor Hsu, and ends with thanking to a group of professors at Peking University for their support and help over the past decades. The middle part is the theme of the talk. It gives first an overview of personal cross research. Then, from a challenge of computing, the author reports on the study looking for a larger class of complex matrices which have real spectrum. This was done mainly in the last year. It involves the fields of computation, probability, statistical mechanics and quantum mechanics Next, the paper introduces the latest development of algorithms, which is another illustration of the intersection between probability theory and computational mathematics. As the end, it also outlines the understanding of the cross study.     

�����������ĺ���������ģ�͵ĸ��Ϸ�λ������

??n this paper, we propose composite quantile regression for functional linear model with dependent data, in which the errors are from a short-range dependent and strictly stationary linear process. The functional principal component analysis is employed to approximate the slope function and the functional predictive variable respectively to construct an estimator of the slope function, and the convergence rate of the estimator is obtained under some regularity conditions. Simulation studies and a real data analysis are presented for illustration of the performance of the proposed estimator.     

�������췽�������EVģ�͵�С�����Ƶ�Berry-Esseen��

Using wavelet smoothing and least-squares methods,we investigate a heteroscedastic partly linear errors-in-variables (EV)model with $\alpha$-mixing random errors. The wavelet estimators of the parametric parts and nonparametric parts are given, and Berry-Esseen bounds of wavelet estimators are obtained under general conditions.