Time-inconsistent stochastic linear-quadratic control problem with indefinite control weight costs

A time-inconsistent linear-quadratic optimal control problem for stochastic differential equations is studied.We introduce conditions where the control cost weighting matrix is possibly singular.Under such conditions,we obtain a family of closed-loop equilibrium strategies via multi-person differential games.This result extends Yong’s work(2017) in the case of stochastic differential equations,where a unique closed-loop equilibrium strategy can be derived under standard conditions(namely,the control cost weighting matrix is uniformly positive definite,and the other weighting coefficients are positive semidefinite).

Discount Rate of China’s New Energy Power Industry

Under the dual pressures of energy crisis and environmental pollution,China’s new energy power industry has become a focal point for environmental management and requires greater investment.In this context,as a significant input of investment projects,discount rate requires a well-calibrated evaluation because new energy power investment projects are highly capital intensive.The main objective of this paper is to evaluate the discount rate of China’s new energy power industry.First,we use Moving Average to correct the parameters of capital asset pricing model(CAPM)and weighted average cost of capital,which extends the literature on the avoidance of CAPM noise information problem.Second,we study the industry-level annual discount rates of mainly China’s new energy power industries,including hydropower,nuclear power,wind power,and photovoltaic power industries for the period of 2014-2019.The results show that discount rates in China’s new energy power industries evolved differently between the years of 2014-2019 with average annual discount rates being 7.56%,5.83%,5.60%,and 8.64%,for the hydropower,nuclear power,wind power,and photovoltaic power industries,respectively.In 2019,the four annual discount rates were highest for the photovoltaic power industry(8.66%),followed by hydropower(7.17%),wind power(5.72%),and nuclear power industry(5.26%).Forecasting to 2020 from the 2019 evaluation base period,the discount rates are 6.37%,5.00%,6.57%,and 9.05%for the photovoltaic power,hydropower,wind power,and nuclear power industries,respectively.Under the different capital structures,their forecasts for the photovoltaic power,hydropower,wind power,and nuclear power industries in 2020 are,respectively,within[4.35%,9.24%],[3.92%,7.10%],[4.58%,10.40%],[5.46%,14.81%].We also discussed more details on capital structure and forecast period of discount rates for China’s new energy power industries.Our analysis shows that it is necessary to establish a new energy power industry database and steadily promote the implementation of policies.

The study on county accessibility in China： Characteristics and effects on population agglomeration

This paper calculated spatial accessibility of all counties （city,urban district） in China with cost weighted distance method. Region divisions of county accessibility were conducted,and relation of traffic accessibility and population aggregation was discussed in this paper. The results indicated that county accessibility in China had mainly low values and a distribution structure of circle layer and reverse-to-natural gradient. There was an obvious correlation between county accessibility and population density in China. With these analyses,inner mechanisms of population migration in different traffic conditions and region types were revealed,and can provide useful proposals to regional planning,traffic planning and smart distribution of people in China.

Mathematical approaches for optimization of dengue fever dynamics

Background and Objective:For dengue outbreak prevention and vectors reduction,fundamental role of control parameters like vaccination against dengue virus in human population and insecticide in mosquito population have been addressed theoretically and numerically.For this purpose,an existing model was modified to optimize dengue fever.Methodology:Using Pontryagin’s maximum principle,the dynamics of infection for the optimal control problem was addressed,further,defined cost functional,established existence of optimal control,stated Hamiltonian for characterization of optimization.Results:Numerical simulations for optimal state variables and control variables were performed.Conclusion:Our findings demonstrate that with low cost of control variables,state variable such as recovered population increases gradually and decrease other state variables for host and vector population.