The bi-directional long short-term memory neural network model is widely used in natural language processing, but hyperparameter tuning of the model is difficult in practice. In this paper, we take the semantic role recognition task as an example, consider four candidate features (word, part of speech, target word and position) and two hyperparameters (the number of layers of the network and whether CRF classifier is used) as factors in robust design, and select the optimal combination of features and hyperparameters by setting levels of each factor and performing experiments. In particular, we perform 32 cross validation on a small datasets to select the optimal configuration combination of the model based on the SNR of robust design. Then, we analyze the influence of each factor on the performance of the model by quantitatively analyze so that the model has a certain degree of interpretability. Moreover, in order to verify the superiority of our tuning method, we use the standard segmentation of natural language processing on a big dataset, adopt the traditional greedy strategy to select the optimal configuration combination, and compare with our method on the test set. The results show that our method is better than the traditional tuning method.

As the continuation and deepening of \ncite{1},this paper focuses on the center of economic equilibrium and uses mathematics as a tool to explore two themes in the economy: firstly, the ``pillar'' industry and ``bottle strength'' industry, ``top'' products and ``weak'' products in the economic system, that is, the ranking and
stability analysis of products; secondly, forecast and adjust, optimize the design and debugging of economic structure.

Index tracking mainly focuses on replicating or tracking the performance of a financial index which is also a popular passive portfolio management strategy. The classical methods often considerthe full replication consisted of all asserts of an index. However, the full replication often suffers from small and illiquid positions and high cost as the number of asserts increasing. Thus, the investors intend to purchase sparse portfolios. In stock markets, besides, there are still apparently existing group effects among stocks. This paper proposes the nonnegative sparse group lasso method for model selection and estimation to grouped variables without overlapping. We provide almost necessary and sufficient conditions for the variable selection and estimation consistency of the method in finite dimensional group cases. To get the solutions of the model, we derive a computational method based on coordinate decent algorithm. To track the index, the nonnegative sparse group lasso outperforms other current methods with group effects such as nonnegativeelastic net, according to tracking error.

This paper studies an iterative method of estimating parameters in Gamma distribution based on maximum likelihood estimation and EM algorithm improved by non gradient information spectrum residual method in the case of classified data, Type-I interval censered data, Type-II interval censered data, and it proves the strong consistency of the algorithm. The simulation results show that the iterative method proposed in this paper can greatly shorten the running time while ensuring the accuracy, the estimated mean square error tends to zero with the increase of sample size.

This paper analyzes the risk spillover effects of the stock market on commercial banks from a new perspective. First, we use the Granger causality test to verify the relationship between the stock market and the commercial banks. Then, we use the CoVaR model based on quantile regressions to calculate the risk spillover effects of the stock market to commercial banks. Although the risk level of the state-owned banks is relatively minimal, the banks experience the largest risk spillover effects in the stock market. The risk spillover effects of the stock market to the city commercial banks are in the middle, while the overall systematic
risk impacts of the stock market on the joint-stock banks are small. In addition, the sensitivity of the state-owned banks, joint-stock banks, and city commercial banks to the stock market increased gradually. The results of this paper have important policy implications for weakening the impacts of the stock market on commercial banks, and reducing external risks on commercial banks.

Interval-censored failure time data are a general type of failure time or time-to-event data where the failure time of interest is known or observed only to lie in an interval or window instead of being observed exactly. They often occur in many fields, including demographical studies, epidemiological studies, medical or public health research and social science, and in different forms. A common and general set-up that naturally yields interval-censored data is the study with
longitudinal or periodical follow-ups such as many clinical trials or observation studies. In this paper, after some brief discussion about the background and some commonly used models, we will review some recent advances, mainly during about last five years, on several important topics related to regression analysis as well as some issues that need more research in the analysis of interval-censored data.

In this paper, we consider the ultrahigh dimensional partially linear model, in which the dimension of the parametric vector is exponential order of the sample size. Based on profile least squares and regularization after retention method, we propose a new method to perform variable selection for the ultrahigh dimensional partially linear model. Under certain regularity conditions, it is proved that the estimator achieves sign consistency. Compared with Lasso, SIS-Lasso and adaptive Lasso, it is found that the proposed method is better in terms of recovering the coefficient sign of linear part through the numerical simulation and real data analysis.

This paper constructs the assets portfolio of lever corporation by the structural approach. Because irreversibility and uncertainty of corporate bankruptcy, the corporate bankruptcy is equivalent to a default of the bonds. By using the parabolic stochastic partial differential equations (SPDE) which the lookback option satisfied,the assets portfolio pricing model of lever corporation is derived under the mixed jump-diffusion fractional Brownian motion (MJD-fBm) environment.
When the lever corporation in the financial crisis, Shareholders use capital injection to make up for operating losses and debt servicing, then the probability of no default before the bonds maturity and the conditional distribution of the lever corporation assets is obtained, and the pricing formula for lookback option is derived. In the end, a numerical example is given to illustrate the influence of different Hurst parameters and risk coefficient and stock asset weight to the default
probability of the lever corporation.

With the deep development of the economic society,and the remarkable rise in people's living standards, customer requirements are becoming more and more intense. Meanwhile, the rapid development of the Internet technology and smart manufacturing has provided a solid industrial foundation for meeting such needs. Customized production has gradually become an important production mode. Different from traditional massive production, in a customized production mode, a product often consists of multiple customized modules, generating thousands of customized combinations, and usually a small number of products will be produced for each combination. Taking certification cost into account, the customized production makes the traditional product certification procedure unrealistic because we can not authenticate several prototypes for each customized combination. Therefore, there is an urgent requirement for developing theories and methods of customized product certification, which can accurately assess the quality of customized products at an acceptable certification cost. In this article, we propose a general framework for customized product certification based on certification big data and statistical models and illustrate it on
refrigerator safety certification. This framework transforms the safety certification of customized products into the assessment of product safety risks, establishes a quantitative statistical model to characterize the risks, and uses the principles and methods of experimental design to develop economical certification schemes. Our certification big data based simulation results indicate that this framework has the potential to achieve reliable, efficient, and intelligent customized product certification, which has important theoretical and practical significance for certification mode innovation.

Modeling analysis and reasonable prediction of medical costs are the basis and foundation for the determination of medical insurance costs. High-dimensional additional information in medical costs plays an important role in long-term prediction. This paper proposes a partial linear multi-indicator additive model to fit
and predict longitudinal medical cost data with high-dimensional features and uses two different dimensionality reduction estimation methods to estimate the model and applies the model to a set of high-dimensional dimensions. The longitudinal medical cost data of the variable is used for case analysis.

In this paper we investigate a continuous-time optimal portfolio selection problem for a risk-averse investor based on a relative log-return. Investor can invest her wealth in a risk-free asset and a risky stock. The objective of the investor is to exceed the performance of a stochastic benchmark that is not perfectly correlated
with the risky stock. Investor chooses a dynamic portfolio strategy in order to maximize her expected terminal utility of the weight sum of absolute log-return and relative log-return. By using the dynamic programming principle, the corresponding Hamilton-Jacobi-Bellman equation of the optimal portfolio strategy and the value function is established. Furthermore, closed-form expressions of the optimal portfolio strategy and the value function under the investor with a exponential utility function are derived. The effect of the relative return on the optimal portfolio strategy is also analyzed. The result shows that the relative return works against a investor's intrinsic risk-taking tendency. Finally, numerical examples are provided to illustrate how the optimal portfolio strategy and the value function change when some model parameters vary.

Variable selection is of significant importance for classification and regression tasks in machine learning and statistical applications where both predictability and explainability are needed. In this paper, a Copula Entropy (CE) based method for variable selection which use CE based ranks to select variables is proposed. The method is both model-free and tuning-free. Comparison experiments between the proposed method and traditional variable selection methods, such as distance correlation, Hilbert-Schmidt independence criterion, stepwise selection, regularized generalized linear models and adaptive LASSO, were conducted on
the UCI heart disease data. Experimental results show that CE based method can select the `right' variables out more effectively and derive better interpretable results than traditional methods do without sacrificing accuracy performance. It is believed that CE based variable selection can help to build more explainable models.

In actual data, especially medical data, the covariates are contaminated or interfered by certain factors, while the real covariates cannot be observed. This paper discusses how to adjust the disturbed covariates in the proportional risk model. Covariate existed in the adjustment methods cannot be directly used for survival
data, in order to solve this problem, we use kernel functions to construct the interference factors of the distribution function, the interference of covariate smoothly get the estimate of the real covariate, again to get the parameters in the model of regression estimate, and completed the estimate satisfying consistency and asymptotic normality. We also proposed the use of Minorization-Maximization (MM) algorithm to obtain parameter estimates. The first M is to construct a surrogate function by the convexity of the exponential function and the negative logarithm function, which the Hessian matrix is a diagonal matrix; The second M is to obtain the estimators by maximizing the surrogate function. Finally, we demonstrate the feasibility of our proposed method through numerical simulation and real data research.

Assuming the observations are imprecise and modeling the observations by uncertain variables, this paper proposes statistical inferences for uncertain semiparametric regression model when nonparametric function is subject to monotonicity constraint. Monotonic Bernstein polynomials are used to approximate the nonparametric function and quadratic programming algorithm is used to compute the estimate. A numerical example is given to illustrate the proposed methods.

Lasso is a variable selection method commonly used in machine learning, which is suitable for regression problems with sparsity. Distributed computing is an important way to reduce computing time and improve efficiency when large sample sizes or massive amounts of data are stored on different agents. Based on the equivalent optimization model of Lasso model and the idea of alternating stepwise iteration, this paper constructs a distributed algorithm suitable for
Lasso variable selection. And the convergence of the algorithm is also proved. Finally, the distributed algorithm constructed in this paper is compared with cyclic-coordinate descent and ADMM algorithm through numerical experiments. For the sparse regression problem with large sample set, the algorithm proposed in this paper has better advantages in computing time and precision.

The paper consists of three parts. The first one is from the ergodic theorem of Markov chain to L.K. Hua's fundamental theorem on the optimization of economics. The second one is the Hua's revised version and the author's modification of Hua's theorem. The third one is the computational algorithms on the maximal eigenpair of the structure matrix in the economic system. Some examples are illustrated.

This article considers the optimal dividend policy with delayed capital injections, and assumes that the capital injection delay follows the exponential distribution. We aim to find the optimal dividend and capital injection strategies to maximize the utility of dividend and capital. Since surplus process of the insurance company involves a mixed Poisson process, we use a stochastic differential equation to characterize the surplus process by adopting diffusion approximation
techniques, and then we obtain the value function under the utility criterion. When the value function is smooth, the quasi variational inequality is obtained by using the dynamic programming principle. In this paper, we consider the value function from three different regions (the dividend area, the continuous area and the capital injection area). Through the boundary conditions, we derive the expression of the value function in different regions and present the verification theorem. A numerical example is presented to illustrate the effects of the capital injection delay under different parameters.

This paper considers a discrete-time risk model with compound dependence. The risk-free and risky investments of an insurer lead to arbitrarily dependent stochastic discount factors. The claim-sizes are assumed to follow a one-sided linear process with pairwise asymptotically independent innovations. The innovations and the stochastic discount factors are mutually independent. We assume that innovations are not necessarily identically distributed nonnegative random variables with distributions F_1,F_2,\cdots,F_n. When the average distribution n^{-1}\tsm_{i=1}^nF_iis heavy-tailed, we establish some asymptotic estimates for the finite-time ruin probabilities of this discrete time risk model. We demonstrate our obtained results through a crude Monte Carlo simulation.

In the context of the aging population, longevity risk will increase great economic pressure to the national endowment security system. How to measure and manage longevity risk has become the focus of research in recent years. Based on the Chinese population mortality data, and Lee-Carter model, we introduce DEJD model (double exponential jump diffusion model) to describe the jump asymmetry of time series factors, and prove that DEJD model is more effective than Lee-Carter model in fitting time series factors. In addition, we use the population mortality data predicted by DEJD model to price the SM bonds in Chinese market, providing an important reference for the promotion of SM bond in China.

The price fluctuations in the stock market and the changes in the rate of return brought by it have attracted the attention of experts. In this context, this paper focuses on the changes in the volatility of long-term asset return series, and being used in analysis of the Shanghai Composite Index. Since the most commonly used GARCH model is available when the observation period is short, and the volatility for long-term asset return series tends to have long memory, this paper
proposes an improved time varying GARCH model. In order to fit the change of volatility well, we decompose the variance of volatility into a conditional part and an unconditional part. Through reasonable model transformation, the conditional variance follows the GARCH process, while the unconditional variance, which is changing smoothly over time, is estimated by the nonparametric method (B-spline estimation). The simulation research shows that the model proposed in this paper can better capture the change of volatility in a long run. In order to verify the proposed estimation method, the daily return series of the Shanghai Composite Index are taken for the empirical analysis. In the end, we found that: (i) The nonparametric estimation method proposed in this paper performs well. (ii) The variation of the unconditional variance has a strong correlation with the economic recession; (iii) An apparent variation in the time-varying GARCH model can be explained by the variation of the non-stationary component.

In fields of sociology, psychology, ecology, insurance, medicine and epidemiology, count data are often collected for specific studies. While count data without zero-category or with excess zeros arise quite frequently, a series of zero-truncated and zero-inflated models were soon developed to analyze these kinds of data, such as zero-truncated/inflated Poisson distribution and zero-truncated/inflated negative binomial distribution. It is necessary to make statistical inferences on unknown parameters when fitting data by these models. Existing studies merely focus on one of these models. In this paper, based on the stochastic representations of zero-truncated and zero-inflated distributions proposed in recent years, we construct a general method to obtain the maximum likelihood estimates of parameters under a unified framework, and make a review on familiar discrete distributions. Moreover, zero-adjusted models are further proposed to extend the applications, aiming to provide researchers appropriate and convenient methods in count data analyses. All methods are demonstrated by simulation studies and two real data analyses.

In reliability engineering, components of the coherent system may be dependent since they operate in a common random environment. This paper uses multivariate distortion function to describe the dependence among lifetimes of components and the structure function of the coherent system. Some sufficient conditions are given to compare two coherent systems under different random environments in the sense of usual stochastic order, failure rate order, reversed failure rate order and likelihood ratio order.

General minimum lower-order confounding and minimum aberration are two important criteria to select s\,(s\geq 2)-level optimal regular fractional factorial designs. Their classification are based on the aliased component-number and word-length patterns, respectively. The paper mainly studies some properties of the aliased component-number pattern for s-level regular designs. We obtain that the elements of word-length pattern are expressed as some functions of aliased component-numbers under s-level case. It reveals the relationship between the aliased component-number and word-length patterns. On the other hand, we can calculate some aliased component-numbers by word-length pattern. Further, the formulas of some aliased component-numbers are provided for two-level designs.

{Many tests have been developed to check the normality assumption. These tests are mainly defined in two types: one is empirical distribution function test, the other is correlation and regression test. In this paper, we propose a new two-step test method based on the L_2 Wasserstein distance and the approximate distribution of i th sample order statistic. We discuss the properties of the new test method under the null hypothesis, and compare the power with other most commonly tests for four alternative groups. Finally, the new method is applied to analyse the real problem. The simulation results show that the new test
method improves the efficiency in identifying asymmetric long-tailed alternatives.

This paper investigates a bidimensional risk model with interference, in which the vectors of claim process and premium process are both compound Poisson-Geometric processes. Through martingale method and stopping time technique, we get the upper bound of the ruin probability. When the marginal of claim vector and premium vector follow bivariate FGM (Farlic-Gumbel-Morgenstern) class, we have discussed some properties of the upper bound.

The classical Heston model does not consider no long-term dependence of asset, and the financial empirical analysis proves that it can not describe the real situation of assets well. In this article, the mixed Gaussian Heston model is established and stocks data are analyzed. Firstly, the existence and uniqueness of the solution and the properties of the p-order moment of the solution are discussed, respectively. Secondly, the unknown parameters in the model are estimated and the sensitivity analysis are carried out. The actual data of three stocks are used to compare the price path satisfied by Heston model and mixed Gaussian Heston model with the real path. It shows that the mixed Gaussian Heston model can describe the asset price better than the Heston model.vvv

In this paper, the compound binomial risk model is extended by involving the random premium income with Markov property and random dividend strategy. By the method of generating function, the recursive formula and initial values for the expected penalty functions with different initial states are obtained. Finally, some values of the ruin probability that change with the initial value and dividend barrier are shown in a numerical example.

In this paper, we introduce three new classes of multivariate risk statistics, named multivariate comonotonic quasiconvex risk statistics, multivariate quasiconvex risk statistics and multivariate empirical-law-invariant quasiconvex risk statistics, respectively. Representation results for them are provided by dual method. The results of this paper is not only the generalization of one-dimensional quasiconvex risk statistics, but also the extension of multivariate convex risk statistics.

This paper consideres an M/M/1 queue model with preemptive and non-preemptive priorities. Customers are divided into three priority levels. The first category of customers enjoy the priority of preemptive, the second category of customers enjoy the priority of non-preemptive, and the third category of customers have no priority. When the first kind of customers arrive, they will interrupt the second or third kind of customers who are receiving the service immediately; When
the second type of customers arrive, if there are only the third type of customers in the system, the customer must wait for the current service to be completed before accepting the service. Customers of the same type follow the queuing rule of FCFS. A multi-dimensional vector Markov process is constructed here using the supplementary variable method, and the probability generating functions of three types of joint distribution of queue length are obtained. Then, each category of customer's average queue length and the probabilities in service are obtained. The influence of the change of service rate on the average queue length of all kinds of customers in the system is studied using MATLAB software. Finally, different cost functions are constructed for optimization analysis.

This paper studies the statistical inference and algorithm design problems in the mixture model with change point. For multi-classified mixture data with change point, this paper designs an improved EM algorithm based on the maximum likelihood estimation of parameters, and proves the large sample nature of the change point estimator and the mixture parameter estimator. In order to verify the effectiveness of the method, we conducted some simulation experiments.
The results show that the EM algorithm that does not consider the change point has a poor estimate on the classification result, and even loses some categories; Our improved EM algorithm can accurately locate the location of the change point, and at the same time obtain accurate estimates for the corresponding parameters of each category.

Due to the correlation between the trigger events of traditional multi-event catastrophe bonds, investors are more likely to suffer losses and their returns are more volatile. In order to reduce the impact of this disadvantage, taking earthquake catastrophe bond as an example, this paper reconstructs the payment function of multi-events catastrophe bond considering risk feedback. Under the objective of maximizing the hedging efficiency of insurance companies, we obtain the optimal discount coefficient of the cash flow payment after triggering all risk events by Monte Carlo simulation. The results show that under the
new payment function, the expected return of investors increases and the volatility of return decreases, which makes the bond more attractive to the market. Finally, we focuses on the analysis of the impact of catastrophe triggering parameters on the optimal discount coefficient.

By the empirical analysis of the open data on COVID-19 in the America, this paper proposes a stochastic dynamic infection model for the regions in America during the pandemic period of COVID-19. To solve when to ``open'' or ``restrict'' the economic and social activities, we construct a multi-regional optimal prevention and control switching Nash equilibrium strategy based on maximizing the expected utility with mean-field interactions. Then, we consider the infection population model for the representative region and solve the corresponding optimal prevention and control switching strategy under the infinite number of regions. Meanwhile, we prove that this strategy is an $\epsilon$-Nash equilibrium for finite regions when the number of regions tends to infinity. By comparing and analyzing the optimal switching boundaries under different process states, we will give specific suggestions on when and how to adjust the prevention
efforts.

Prospective phase II trials usually result in failures in phase III trials. For randomized controlled phase II and phase III trials which are conducted with patients randomized to one of two treatments where the variances of the normally distributed responses are assumed to be known, we analytically obtain the estimated
and theoretical assurances for the three cases (no, additive, and multiplicative bias adjustments). Under some minor assumptions, we show that the estimated assurances for the three cases are increasing functions of the per group number of patients and the observed treatment effect of the phase II trial, respectively; and for Case 3, the estimated assurance is an increasing function of the retention factor. When the true treatment effect of phase III is assumed to be a known constant, we show that the theoretical assurances for the three cases are constants which are equal to the designed power or one minus the type II error. Moreover, we show that the estimated assurances are always less than the theoretical assurance. We also obtain the analytical formulas of the probabilities of launching a phase III study for the three cases. Moreover, for Case 3, we show that the probability of launching a phase III study is an increasing function of the retention factor. According to our theoretical investigations, we find that the true treatment effect of phase III has no effect in the simulations. Finally, the simulations are conducted to illustrate the theoretical investigations.

In the Collective risk model, the claim amount is divided into large claims and small claims. Under the variance-related premium principle, the Bayesian estimation of the risk premium in the binary Bayesian collective risk model is derived. The conclusion shows that both the conditional expectation and conditional variance parts of risk premium can be expressed as a weighted form of sample function and aggregate premium, where the weight satisfies the property of ``credibility factor''. Furthermore, the strong consistency and asymptotic normality of Bayesian estimation is proved. Finally, the method of numerical simulation
is used to verify the large sample properties of Bayesian estimation.

For the comprehensive ranking of urban economic level and environmental level in China, there have been some index system ranking methods, but most of them involve multivariate data. With the rapid change of data acquisition technology, data become more and more complex. The observational data produced in some fields is no longer a single type of data, but a combination of various types of data. This paper studies how to rank them when the index system involves functional data. In this paper, four ranking methods are proposed and compared. The results are as follows: when the functional data is contaminated, the
entropy weight method results are relatively stable; when the scalar data is contaminated, the multivariate modified banding depth is more stable. The research shows that the selection of ranking methods for multi-type data depends on the characteristics of the data. This research enriches the comprehensive ranking of multi-type data and has good practical significance.

Regression models are traditionally estimated using the least square estimation (LSE) method which may result in non-robust parameter estimates when data includes non-normal feature or outliers. Compared to LSE approach, composite quantile regression (CQR) can provide more robust estimation results even suffering non-normal errors or outliers. Based on a composite asymmetric Laplace distribution (CALD), the weighted composite quantile regression (WCQR) can be treated in the Bayesian framework. Regularization methods have been verified to be very effective for high-dimensional sparse regression models in that
it can simultaneously conduct variable selection and parameters estimation. In this paper, we combine Bayesian LASSO regularization methods with WCQR to fit linear regression models. Bayesian LASSO-regularized hierarchical models of WCQR are constructed and the conditional posterior distributions of all unknown parameters are derived to conduct statistical inference. Finally, the developed methods are illustrated by Monte Carlo simulations and a real data analysis.

This paper summarizes the growth of mathematical stochastics. It includes two periods of early history, the syllabus of ``College Mathematics'' for non-mathematics majors facing the new century, the teaching materials and research institutions of ``mathematical stochastics'', the mark of grow up of mathematical stochastics, etc.

When the response variables are missing randomly, in the process of statistical inference of the parameters of interest, two common working models are the regression function model and the selection probability model. In order to avoid the inference bias caused by the model setting error, the regression function model and selection probability models are necessary and meaningful for model testing. For this reason, for the first time in this paper, the feature functions are applied to the model testing problem of random missing response variables and discrete variable response variables, and a Euclidean distance between sample points is constructed based on test statistic. The proposed test avoids the selection of smoothing parameters such as bandwidth, and at the same time can detect the local alternative hypothesis at the fastest parameter speed. Further, this paper aims at the composite null hypothesis: at least one of the two working models is designed. It is correct, and a test method of the merged model is proposed. An important application scenario of this test is to determine whether the bistable estimation of the parameter is a coincident estimate. This article deeply studies the test of the merged model in the original hypothesis, the global alternative hypothesis, and the local alternative hypothesis. The asymptotic property of the following, and using the boostrap method to determine the rejection domain of the test, study the performance of the merge model test under a limited sample. Finally, this article applies the proposed merge model test method to
analyze the clinical research of AIDS research Test Data. It is worth mentioning that the combined model test mentioned in this article not only has good performance, but also the method is simple and easy to implement, and the corresponding p-value is easy to calculate.

In this paper, we use the complex fourier series expansion method (CFS) to price guaranteed minimum death benefits (GMDB). The main idea is to expand the Fourier series of the auxiliary function. The density function of remaining lifetime has two forms in this paper, namely combination-of-exponentials density and piecewise constant forces of mortality assumption, and the coefficients of series are estimated by using the known characteristic function of the general L\'{e}vy model. We mainly consider the value of GMDB products under call options and put options. In the numerical experiment section, we also demonstrate the
advantages of CFS in calculation accuracy and running time by comparing with cosine series expansion method (COS) and Monte Carlo method (MC).