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The classical autoregressive (AR) model has been widely applied to predict future data using m past observations over five decades. As the classical AR model required m unknown parameters, this paper implements the AR model by reducing m parameters to two parameters to obtain a new model with an optimal delay called as the m-delay AR model. We derive the m-delay AR formula for approximating two unknown parameters based on the least squares method and develop an algorithm to determine optimal delay based on a brute-force technique. The performance of the m-delay AR model was tested by comparing with the classical AR model. The results, obtained from Monte Carlo simulation using the monthly mean minimum temperature in Perth Western Australia from the Bureau of Meteorology, are no significant difference compared to those obtained from the classical AR model. This confirms that the m-delay AR model is an effective model for time series analysis.

© 2020, Journal of Industrial and Management Optimization. This paper investigates the asset liability management problem for an ordinary insurance system incorporating the standard concept of proportional reinsurance coverage in a stochastic interest rate and stochastic volatility framework. The goal of the insurer is to maximize the expectation of the constant relative risk aversion (CRRA) of the terminal value of the wealth, while the goal of the reinsurer is to maximize the expected exponential utility (CARA) of the terminal wealth held by the reinsurer. We assume that the financial market consists of risk-free assets and risky assets, and both the insurer and the reinsurer invest on one risk-free asset and one risky asset. By using the stochastic optimal control method, analytical expressions are derived for the optimal reinsurance control strategy and the optimal investment strategies for both the insurer and the reinsurer in terms of the solutions to the underlying Hamilton-Jacobi-Bellman equations and stochastic differential equations for the wealths. Subsequently, a semi-analytical method has been developed to solve the Hamilton-Jacobi-Bellman equation. Finally, we present numerical examples to illustrate the theoretical results obtained in this paper, followed by sensitivity tests to investigate the impact of reinsurance, risk aversion, and the key parameters on the optimal strategies.

© 2019, The Author(s). A static mixer is a fidelity engineered device for the continuous mixing of fluid/solid materials. To meet the requirements for mixing purpose, a proper design of the static mixer is important. In this study, we proposed various designs of static mixer based on the blade geometry. Six blade patterns including four twisted blades, four elliptical blades and other four combined geometries of two twisted blades and two elliptical blades are chosen to investigate its mixing performance. Mathematical model of the two-phase flow with fluid/solid interaction in the static mixer is presented. Numerical solution of the flow patterns of particulate solids, and the velocity and the pressure fields of the fluid in the static mixer with different blade geometries are carried out. To evaluate the quality of the mixing performance, the results obtained from six blade designs are compared via the relative standard deviation and the amount of pressure drop along the mixing path.

© 2019, The Author(s). This paper studies the transient slip flow and heat transfer of a fluid driven by the oscillatory pressure gradient in a microchannel of elliptic cross section. The boundary value problem for the thermal-slip flow is formulated based on the assumption that the fluid flow is fully developed. The semi-analytical solutions of velocity and temperature fields are then determined by the Ritz method. These solutions include some existing known examples as special cases. The effects of the slip length and the ratio of minor to major axis of the elliptic cross section on the velocity and temperature distribution in the microchannel are investigated.

© 2019, The Author(s). The street under a skytrain station can be seen in many urban cities. Due to the cavity geometry of the street canyon, natural ventilation is decreased. The reduction of the ventilation causes the heat accumulation in the street canyon. To keep the thermal climate at an acceptable level in the street canyon, controlling the air movement with proper temperature is important. In this paper, mathematical models of air flow and heat transfer in the skytrain street canyon are developed. The governing equations are the Reynolds-averaged Navier–Stokes equations and the energy equation. Finite element method is applied for the solution of the problem. The effect of wind speeds on temperature distribution in the street canyon is investigated. Three levels of wind speed including gentle, moderate, and strong wind speeds are chosen in this study. The results indicate that our model can capture the air flow and temperature distribution within a street canyon with a skytrain station.

© 2019, The Author(s). This paper focuses on effects of the wind flow velocity on the air flow and the air pollution dispersion in a street canyon with Skytrain. The governing equations of air pollutants and air flow in this study area are the convection–diffusion equations of species concentration and the Reynolds-averaged Navier–Stokes (RANS) equations of compressible turbulent flow, respectively. Finite element method is utilized for the solution of the problem. To investigate the impact of the air flow on the pattern of air pollution dispersion, three speeds of inlet wind in three different blowing directions are chosen. The results illustrate that our model can depict the airflows and dispersion patterns for different wind conditions.