In recent years, human lifespan is extended obviously, which has an impact on national pension system and insurance company’s life insurance business. Longevity risk is caused by unexpected changes in population mortality, so accurate prediction of population mortality is an important topic of longevity research. This paper proposes a new method by introducing the co-integration theory of econometrics to the prediction of mortality to make up for China’s lack of historical data, by using the extreme value theory to predict unstable time factors in Lee Carter model.

Based on profiled empirical likelihood method, the quasi-likelihood functions of the double generalized linear models were considered as the constraints of the profile empirical likelihood ratio function. The confidence intervals of unknown parameters in double generalized linear models were constructed. Finally, simulation studies show that this method is more useful and effective than normal approximation.

Factor analysis model plays an important role in characterizing dependence of latent factors on the observed variables and interpreting the correlation among the observed indexes (variables). However, in real applications, data set often takes on the temporal variability, multimode, skewness, and so on. In this paper, we extended the classic factor analysis model to the dynamic factor model mixed with homogenous hidden Markov model, and developed a Bayesian semiparametric analysis procedure. Blocked Gibbs sampler is used to implement posterior sampling. The empirical results show that our method is effective.

In this paper, a discrete-time interaction risk model with delayed claims and a constant dividend barrier is considered. the interaction comes from the assumption that each main claim in one class induces a by-claim in the other class with a certain probability. The occurrences of induced claim may be delayed. A system of difference equations with certain boundary conditions for the expected present value of total dividend payments prior to ruin is derived and solved. Explicit expressions for the corresponding results are derived in a special case, numerical examples are also given.

In this text, the nonlinear variational inequality problem which arises from the valuation of American barrier option is studied. Firstly, the weak solution of the variational inequality is defined. Secondly, the existence and uniqueness of the solutions in the weak sense are proved by using the Schaefer fixed point theory and penalty method.

Using the strong invariance principle for the array of the independent and identically distributed random variables, the law of the single logarithm for the R/S statistics of array is obtained. In particular, the sufficient and necessary conditions are obtained for the law of the single logarithm for the adjusted range of partial sums.

In this paper, the pricing of corporate bonds is analyzed with consideration of credit rating migration risks. Assume that the credit rating migration relates to the firm’s asset value which follows a geometric Brownian motion. Under the structure framework, two pricing models are established. The models can be transformed to two partial differential equations which coupled by different given conditions at the transfer boundary. The relationship of the two model has been discussed, and a closed form solution of Model II has been obtained. Furthermore, graphs of the solutions of both models with parameters analysis are presented, and their financial meanings are discussed.

In this paper, a local linear composite quantile regression estimator of regression function is constructed in the regression model with heteroscedastic error under left-truncated data. The asymptotic normality of the proposed estimator is also established. The estimator is much more efficient than the local linear regression estimator for commonly-used non-normal error distributions via simulations.

In this paper, by using the boundary perturbation of the generator, the sufficient conditions for the quasi-compactness and irreducibility of the $C_0$-semigroups on Banach lattice were given. Then apply these sufficient conditions to study the quasi-compactness and irreducibility of a series repairable system.

For a multi-loss function, at a given confidence level, the concepts of the loss value not exceeding a given minimum value at risk (VaR) and the corresponding cumulative expected loss value (i.e., the CVaR loss value) with the corresponding weight value level are introduced first. Then, a multi-level programming model of the multi-loss CVaR model is obtained. The goal of the model is to get an optimal strategy of the minimum CVaR value each level. This model can be solved more easily through another multi-level programming model to obtain the optimal solution. Finally, a multi-product pricing and ordering of a three-stage supply chain model (a tri-level linear programming model) is presented.

Contact-Riemannian manifolds, without necessarily integrable complex structures, are the generalization of pseudohermitian manifolds in CR geometry. The Tanaka-Webster-Tanno connection plays the role of Tanaka-Webster connection in the pseudohermitian case. Pseudo-hermitian immersions of CR geometry can be developed to contact-Rimannian immersions of contact Riemannian manifold, and it can be proved that any contact-Riemannian immersion is minimal.

By using fixed point theory of cone expansion and compression of norm type, a class of boundary value problem of fractional differential system with Riemann-Liouville fractional integral conditions is investigated. Combining with the relevant properties of Green function, some sufficient conditions on the existence of positive solutions are established. Some examples are given to illustrate the application of the result．

In this paper, a singularly perturbed nonlinear mixed boundary value problem for third-order semilinear differential equation is studied. The formal asymptotic solution to this problem is constructed by the method of boundary layer functions. According to the theory of differential inequalities, the existence of solution is proved and the error estimate of asymptotic solution is given. Finally, the exponential decay of boundary layer functions for this problem is concluded.