Population Dynamics And Stochastic Economic Growth

In recent years, domestic and foreign scholars regard economic theories and models as analytical tools on the issues of fertility, immigration and population aging, and gradually form some schools of thought. Therefore, establishing the stochastic models between the population dynamics and economic growth has some theoretical significance.Population dynamics mainly includes fertility, mortality and migration, and changes in the size of population is the ultimate form of population dynamics. Obviously, the economic impact of demographic change can't be overlooked. Therefore, creating the stochastic models between the population dynamics and economic growth also has some practical significance.On the basis of previous work, this paper uses the stochastic dynamic optimization to make some models and obtain some useful results. The first chapter briefly reviews the theory of economic growth and gives some necessary prior knowledge. Chapter two presents the needed mathematic tools──the optimization method and stochastic analysis. In the third chapter, a model is established to discuss the relationship between fertility and stochastic economic growth. The model analyses macro-equilibrium, equilibrium economic growth rate and the impact of fertility and longevity on social welfare. In the fourth chapter, the uncertain fertility and endogenous mortality are introduced into a stochastic model in the continuous time, overlapping generations'economy. By using stochastic optimal methods, this paper obtains the macro-equilibrium. This paper also discusses the impact of birth of risk, child-raising cost and fertility on mortality and economic growth. The fifth chapter mainly considers two economic growth models which include the factor of immigrants.