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This article studies an optimal control problem for the financial investment strategy with random incomes. The investment portfolio is simplified to be composed of a risk-free asset and a risky asset. The price of a risky asset is followed by a constant variance elasticity (CEV) model. We consider any correlation coefficient ρ ∈ [ − 1 , 1 ] between the income risk and the risk of risky asset. By applying the Legendre transformation, dual theory, and asymptotic expansion approach, we obtain an asymptotic strategy for the exponential utility function. Numerical examples are presented to illustrate the effects of parameters on the optimal strategy. [ABSTRACT FROM AUTHOR]

This paper studies the autoregressive integrated moving average (ARIMA) state space model combined with Kalman smoothing to impute missing values in a univariate time series before detecting change points. We estimate a scale-dependent time-average variance constant that depends on the length of the data section and is robust to mean shifts under serial dependence. The consistency of the proposed estimator is shown under the assumption allowing heavy tailedness. Integrating the proposed estimator with the moving sum and wild binary segmentation procedures to determine the number and locations of change points is discussed. Furthermore, the performance of the proposed methods is evaluated through extensive simulation studies and applied to the Beijing multi-site air quality dataset to impute missing values and detect mean changes in the data. [ABSTRACT FROM AUTHOR]

In periods of dramatic stock price volatility, the identification of change points in stock price time series is important for analyzing the structural changes in financial market data, as well as for risk prevention and control in the financial market. As their residuals follow a generalized error distribution, the problem of estimating the change point parameters of the β -ARCH model is solved by combining the Kalman filtering method and the Bayes method innovatively, and we give a method for parameter estimation of the Bayes factors for the occurrences of change points, the expected values of the change point positions, and the variance of the change points. By detecting the change points of the price of eight stocks with a high number of limit up and limit down changes occurring in the observation period, the following conclusions are obtained: (1) Change point detection using the β -ARCH model based on the Bayes method is effective. (2) For different values of β , this research study finds that based on the classical ARCH model (i.e., β = 1 ) of the change point parameter, the results are relatively optimal. (3) The accuracy of change point detection can be improved by correcting stock short-term effects by using the Kalman filtering method. [ABSTRACT FROM AUTHOR]

This paper studies the stochastic pantograph model, which is considered a subcategory of stochastic delay differential equations. A more general jump process, which is called the Lévy process, is added to the model for better performance and modeling situations, having sudden changes and extreme events such as market crashes in finance. By utilizing the truncation technique, we propose the diffused split-step truncated Euler–Maruyama method, which is considered as an explicit scheme, and apply it to the addressed model. By applying the Khasminskii-type condition, the convergence rate of the proposed scheme is attained in L p (p ≥ 2) sense where the non-jump coefficients grow super-linearly while the jump coefficient acts linearly. Also, the rate of convergence of the proposed scheme in L p (0 < p < 2) sense is addressed where all the three coefficients grow beyond linearly. Finally, theoretical findings are manifested via some numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, the spatial dynamic panel data (SDPD) model with fixed effects is extended to a non-parametric form by relaxing the linear or nonlinear parameter structure of explanatory variables. The non-parametric spatial dynamic panel data (NSDPD) model with fixed effects not only retains the advantages of the SDPD model which can deal with spatial and/or temporal individual characteristics and spatio-temporal dependencies but also solves the limitation that may lead to specification errors. It also enhances the flexibility and practicability of the spatial econometric model. Since the model to be estimated contains unknown functions, we propose this profile maximum likelihood (PML) method to solve the problem of the incidental parameters in the estimation. Under the assumption that the spatial coefficients are known, we first eliminate the influence of the time effect by substitution and then use the local polynomial estimation to preliminarily estimate the unknown function so as to transform the model into the parametric form for solving. We derive the asymptotic properties of PMLEs and find that under certain regularity conditions, both parametric and non-parametric estimators are consistent. The Monte Carlo results show that the estimators have good finite sample performance. We illustrate the empirical relevance of the model by applying it to examine the impact of tourism dynamics on economic development in the Yangtze River Delta region of China. [ABSTRACT FROM AUTHOR]

In this paper, we propose a user-friendly integral inequality to study the coupled parabolic chemotaxis system with singular sensitivity under the Neumann boundary condition. Under a low diffusion rate, the classical solution of this system is uniformly bounded. Our proof replies on the construction of the energy functional containing ∫ Ω | v | 4 v 2 with v > 0 . It is noteworthy that the inequality used in the paper may be applied to study other chemotaxis systems. [ABSTRACT FROM AUTHOR]

We are interested in modeling the influence of random fluctuations on population systems. In this paper, we consider the population dynamics of jellyfish stochastic differential equation by introducing the random perturbation. Firstly, we provide the sufficient criteria to study the existence and uniqueness of non-negative solution. We prove that population will be permanence and persistence in mean when the noise is relatively small as well as it is discussed that the population may become extinct with probability one when the noise is too large. Then we show that the system has a stationary distribution under sufficient conditions using Hasminskii's methods and Lyapunov function. Finally, numerical simulations are performed to verify the results attained in this paper. [ABSTRACT FROM AUTHOR]

The optimal subsampling is an statistical methodology for generalized linear models (GLMs) to make inference quickly about parameter estimation in massive data regression. Existing literature only considers bounded covariates. In this paper, the asymptotic normality of the subsampling M-estimator based on the Fisher information matrix is obtained. Then, we study the asymptotic properties of subsampling estimators of unbounded GLMs with nonnatural links, including conditional asymptotic properties and unconditional asymptotic properties. [ABSTRACT FROM AUTHOR]

The density function of the limiting spectral distribution(LSD) of sample covariance matrices is widely used in large scale statistical inference when the sample size and dimension both tend to infinity. However, there are no explicit expressions for the density function generated by vector autoregressive moving average(VARMA) models. For such models whose sample covariance matrices do not have independence structure in columns, we propose to use modified kernel estimators which are proved to be consistent. A simulation study is also conducted to show the performance of the estimators. [ABSTRACT FROM AUTHOR]

In this paper, we derive the Tracy–Widom law for the largest eigenvalue of sample covariance matrix generated by the vector autoregressive moving average model when the dimension is comparable to the sample size. This result is applied to make inference on the vector autoregressive moving average model. Simulations are conducted to demonstrate the finite sample performance of our inference. [ABSTRACT FROM AUTHOR]

This paper investigates the first-order random coefficient integer valued autoregressive process with the occasional level shift random noise based on dual empirical likelihood. The limiting distribution of log empirical likelihood ratio statistic is constructed. Asymptotic convergence and confidence region results of empirical likelihood ratio are given. Hypothesis testing is considering, and maximum empirical likelihood estimation for parameter is acquired. Simulations are given to show that the maximum empirical likelihood estimation is more efficient than the conditional least squares estimation. [ABSTRACT FROM AUTHOR]