On a spatial Solow model with technological diffusion and nonconcave production function

In this paper the classical Solow model is extended, by considering spatial dependence of the physical capital and technological progress, and by introducing a nonconcave production function. The physical capital and technological progress accumulation equations are governed by semilinear parabolic differential equations which describe their evolution over time and space. The convergence to a steady state according to different hypotheses on the production function is discussed. The analysis is focused on an S-shaped production function, which allows the existence of saddle points and poverty traps. The evolution of this system over time, and its convergence to the steady state is described mainly through numerical simulations.     

Extended Gerber–Shiu functions in a risk model with interest

We consider a compound Poisson risk model with interest. The Gerber–Shiu discounted penalty function is modified with an additional penalty for reaching a level above the initial capital. We show that the problem can be split into two independent problems; an original Gerber–Shiu function and a first passage problem. We also consider the case of negative interest. Finally, we apply the results to a model considered by Embrechts and Schmidli (1994).     

中国经济随机前沿模型效率的贝叶斯统计推断

基于扩展的随机生产前沿模型,研究了区域生产效率的差异和其影响因素的作用效果,应用贝叶斯统计方法对中国各省份2010-2017的年度数据(不包含港澳台地区,下同)进行了实证研究.研究发现:生产效率总体呈逐渐下降的趋势,地区间生产效率有一定的差异,高等教育规模对生产效率具有显著的直接影响.人力资本能有效促进东部和中部地区的经济增长,西部地区主要依靠资本促进经济增长.环境污染对中部地区的经济增长具有一定的负向作用.     

考虑污染控制、技术进步和人力资本积累下的经济可持续增长

构建一个带有环境污染、污染控制、内生人力资本积累和内生技术进步的动态经济增长模型,并运用最优控制方法探讨经济最优增长路径.研究表明:人力资本积累效率、消费跨期替代弹性和时间贴现率决定着经济最优增长路径.消费跨期替代弹性、时间贴现率、人力资本积累效率、物质产品和技术研发部门的投入产出弹性、污染排放的产出和控制弹性会对稳态中的人均经济增长率、人均污染排放增长率产生影响.     

Social status and long-run effects of monetary policy in a two-sector monetary economy of endogenous growth

We develop a two-sector monetary economy with human capital accumulation and a cash constraint applied to both consumption and investment to examine the ways in which social status affects the impact of monetary policy on the long-run economic growth rate. Our findings suggest that the formation of human capital is an important determinant to the super-neutrality of money in the growth-rate sense. Within an economy with Lucas-type human capital formation, money is super-neutral; however, within an economy where human capital accumulation formation is more generalized, and in which both physical and human capital are used as inputs, the growth rate in money will have a negative effect on the long-run growth rate of the economy. The existence, uniqueness and saddle-path stability of balanced-growth equilibrium are also examined.     

Nonlinear oscillations in business cycle model with time lags

In this paper we analyse the dynamics of the Kaldor–Kalecki business cycle model. This model is based on the classical Kaldor model in which capital stock changes are caused by past investment decisions. This lag is connected with time delay needed for new capital to be installed. The dynamics of the model is reduced to the form of damped oscillator with negative feedback connected with lag parameter and next it is analysed in terms of bifurcation theory. We find conditions for existence and persistence of oscillatory behaviour which is represented by limit cycle on some central manifold in phase space, i.e., single Hopf bifurcation. We demonstrate that the Hopf cycles may be exhibited for nonzero measure set of the parameter space. The conditions for bifurcation of co-dimension two connected with interaction of bifurcations as well as bifurcation diagrams are also given. Finally, we obtain numerical values describing an amplitude and a period of oscillation for different parameter of the system. It is also proved that while the investment function is not nonlinear a quasi-periodic solution (a 1:2 resonant double Hopf point) can appear. The source of such a behaviour is rather a consequence of time lag than nonlinearity of the investment function. Our results confirm the existence of asymmetric (two periodic) cycles in the Kaldor–Kalecki model with time-to-build.     

On the Dalgaard-Strulik Model with Logistic Population Growth Rate and Delayed-Carrying Capacity

Recently Dalgaard and Strulik have proposed (in Resour. Energy Econ. 33:782–797, 2011) an energy model of capital accumulation based on the mathematical framework developed by Solow-Swan and coupled with Cobb-Douglas production function (Solow in Q. J. Economics 70:65–94, 1956; Swan in Econ. Rec. 32(63):334–361, 1956). The model is based on a constant rate of population growth assumption. The present paper, according to the analysis performed by Yukalov et al. (Physica D 238:1752–1767, 2009), improves the Dalgaard-Strulik model by introducing a logistic-type equation with delayed carrying capacity which alters the asymptotic stability of the relative steady state. Specifically, by choosing the time delay as a bifurcation parameter, it turns out that the steady state loses stability and a Hopf bifurcation occurs when time delay passes through critical values. The results are of great interest in the applied and theoretical economics.     

Effects of pollution restrictions on dynamic investment policy of a firm

The purpose of this paper is to determine the effects of different pollution standards on the firm's resource allocation decisions. To do so, a dynamic model of the firm is developed in which it is assumed that production causes pollution as an inevitable byproduct. Concerning its investment policy, we suppose that the firm can choose between investing in productive capital goods and investing in abatement efforts.It is shown that, in some cases, future abatement expenses have a negative impact on the present level of productive investment, even if the pollution standard is not binding at the moment. This implies a really dynamic optimal investment policy for the firm, which cannot be obtained within a comparative static analysis.This research has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences. Comments by Frank van der Duyn Schouten and Piet Verheyen (Tilburg University) and by Raymond Gradus (Dutch Ministry of Finance, The Hague) are gratefully acknowledged.     

Change of economic structure-Capital, knowledge, population and pollution

This paper proposes a nonlinear dynamic economic model with endogenous technological change, population, capital accumulation and pollutant accumulation. The system consists of two, industrial and environmental, sectors. The industrial sector produces goods with knowledge, labor, and capital as inputs under perfect competitive conditions, subject to the government's tax policy. The tax income is used by the environmental sector to employ labor and capital. We examine the effects of the environmental policy, knowledge accumulation efficiency and preference change on the environment. We show that the simple system has multiple equilibria and may exhibit permanent oscillations.     

Some Facts about the Ramsey Model

In modeling the dynamics of capital, the Ramsey equation coupled with the Cobb–Douglas production function is reduced to a linear differential equation by means of the Bernoulli substitution. This equation is used in the optimal growth problem with logarithmic preferences. The study deals with solving the corresponding infinite horizon optimal control problem. We consider a vector field of the Hamiltonian system in the Pontryagin maximum principle, taking into account control constraints. We prove the existence of two alternative steady states, depending on the constraints. This result enriches our understanding of the model analysis in the optimal control framework.     

含公共开支的两部门内生经济增长模型

本文研究了一个含公共开支的两部门的内生经济增长模型 ,其生产函数具有最一般的形式 .用于两部分的三要素—物质资本 ,人力资本 ,有效劳动的份额正相关 ,产出用于公共开支的份额与用于生产部门的三要素的份额负相关 ,经济增长极大地依赖于生产弹性 .并给出均衡值为正的条件和经济系统沿二维稳定流形收敛于稳定点的条件     

Omega diffusion risk model with surplus-dependent tax and capital injections

In this paper, we propose and study an Omega risk model with a constant bankruptcy function, surplus-dependent tax payments and capital injections in a time-homogeneous diffusion setting. The surplus value process is both refracted (paying tax) at its running maximum and reflected (injecting capital) at a lower constant boundary. The new model incorporates practical features from the Omega risk model (Albrecher et al., 2011), the risk model with tax (Albrecher and Hipp, 2007), and the risk model with capital injections (Albrecher and Ivanovs, 2014). The study of this new risk model is closely related to the Azéma–Yor process, which is a process refracted by its running maximum. We explicitly characterize the Laplace transform of the occupation time of an Azéma–Yor process below a constant level until the first passage time of another Azéma–Yor process or until an independent exponential time. We also consider the case when the process has a lower reflecting boundary. This result unifies and extends recent results of Li and Zhou (2013) and Zhang (2015). We explicitly characterize the Laplace transform of the time of bankruptcy in the Omega risk model with tax and capital injections up to eigen-functions, and determine the expected present value of tax payments until default. We also discuss a further extension to occupation functionals through stochastic time-change, which handles the case of a non-constant bankruptcy function. Finally we present examples using a Brownian motion with drift, and discuss the pricing of quantile options written on the Azéma–Yor process.     

Optimal dividend strategies in discrete risk model with capital injections

In this paper we consider a doubly discrete model used in Dickson and Waters (biASTIN Bulletin 1991; 21 :199–221) to approximate the Cramér–Lundberg model. The company controls the amount of dividends paid out to the shareholders as well as the capital injections which make the company never ruin in order to maximize the cumulative expected discounted dividends minus the penalized discounted capital injections. We show that the optimal value function is the unique solution of a discrete Hamilton–Jacobi–Bellman equation by contraction mapping principle. Moreover, with capital injection, we reduce the optimal dividend strategy from band strategy in the discrete classical risk model without external capital injection into barrier strategy , which is consistent with the result in continuous time. We also give the equivalent condition when the optimal dividend barrier is equal to 0. Although there is no explicit solution to the value function and the optimal dividend barrier, we obtain the optimal dividend barrier and the approximating solution of the value function by Bellman's recursive algorithm. From the numerical calculations, we obtain some relevant economical insights. Copyright © 2010 John Wiley & Sons, Ltd.     

Growth in Illyria: The role of meritocracy in the accumulation of human capital

In this paper we present a dynamic model of cooperative production with human capital accumulation. We assume CES preferences on consumption and leisure in each period. When agents do not care about future generations, sustained growth occurs iff the elasticity of substitution between consumption and leisure is larger or equal than one. Meritocracy always has a positive effect on output, but when the elasticity of substitution is less than one, is only a level effect. When agents care about future generations, under Cobb–Douglas preferences in each period and some extra conditions, there is constant growth at a rate that is larger than the one when future generations do not count. For any discount rate between generations, there is a unique level of meritocracy for which efficiency is achieved.     

Construction of a regulator for the hamiltonian system in a two-sector economic growth model

We consider an optimal control problem of investment in the capital stock of a country and in the labor efficiency. We start from a model constructed within the classical approaches of economic growth theory and based on three production factors: capital stock, human capital, and useful work. It is assumed that the levels of investment in the capital stock and human capital are endogenous control parameters of the model, while the useful work is an exogenous parameter subject to logistic-type dynamics. The gross domestic product (GDP) of a country is described by a Cobb-Douglas production function. As a utility function, we take the integral consumption index discounted on an infinite time interval. To solve the resulting optimal control problem, we apply dynamic programming methods. We study optimal control regimes and examine the existence of an equilibrium state in each regime. On the boundaries between domains of different control regimes, we check the smoothness and strict concavity of the maximized Hamiltonian. Special focus is placed on a regime of variable control actions. The novelty of the solution proposed consists in constructing a nonlinear stabilizer based on the feedback principle. The properties of the stabilizer allow one to find an approximate solution to the original problem in the neighborhood of an equilibrium state. Solving numerically the stabilized Hamiltonian system, we find the trajectories of the capital of a country and labor efficiency. The solutions obtained allow one to assess the growth rates of the GDP of the country and the level of consumption in the neighborhood of an equilibrium position.     

Optimal dividend payments in the stochastic Ramsey model

We consider the dividend payments of a self-financing firm in the stochastic Ramsey model. The firm invests in capital stock and its production technology is given by the Cobb–Douglas function. Our objective is to maximize the expected present value of future real dividends subject to a positive constraint on the capital stock. We use the penalization method to obtain a solution for the variational inequality associated with the optimal growth problem and give a synthesis of the optimal dividend policy.     

基于跳扩散模型的DC型 养老金时间一致最优投资策略的研究

将养老金投资过程分成财富积累阶段和财富给付阶段,建立了DC型养老金在退休前和退休后个人账户积累额变动的连续时间随机模型.该模型考虑了工资的随机风险因素,并用跳-扩散模型刻画风险资产.以均值-方差准则作为优化目标,运用推广的HJB方程分别得到了退休前和退休后的时间一致最优风险资产投资最优解.最后通过算例及敏感性分析研究了各个因素对风险资产投资的影响.在这些因素中缴费比例、死亡力对风险资产投资比例均有负向影响.     

Welfare measurement and the health environment

An important issue in environmental economics is to augment the conventional net national product measure so as to cover changes in stocks of natural resources. In this paper, we show how to treat health (capital) effects in welfare measures caused by, for example, pollution. We also show the effects the risk of doomsday caused by pollution has on these measures. A Ramsey growth model enlarged with health capital and death risks is used to derive an augmented welfare measure. A way of solving the particular technical problem one faces when the death risk depends on a state variable (health capital) is also presented. This measure is contrasted with the conventional net national product measure. We also briefly discuss the welfare properties of a market economy when individuals invest in health capital but face a strictly positive death risk.     

Pollution,unequal lifetimes and fairness

This paper characterizes the optimal level of pollution in a two-period OLG economy where pollution deteriorates survival conditions. We compare two long-run social optima: on the one hand, the average utilitarian optimum, where the long-run average well-being is maximized, and, on the other hand, the ex post egalitarian optimum, where the realized well-being of the worst-off at the stationary equilibrium is maximized. It is shown that the ex post egalitarian optimum involves, under weak conditions, a higher level of pollution in comparison with the utilitarian optimum. This result is robust to introducing health expenditures in the survival function. Finally, we examine the decentralization of those two social optima, and we compare the associated optimal taxes on capital income aimed at internalizing the pollution externality.     

A STEADY-STATE SATISFACTORY SOLUTION TO AN ENVIRONMENTAL GAME WITH PIECE-WISE DEFINED PAYOFFS

We model a pollution accumulation process through a nonlinear, nondifferentiable state equation and also as dependent on an environmental levy. Then the payoff function to an economic agent is defined piece-wise. However, for a simple demand and cost structure, the combined payoff function of all agents is diagonally strictly concave. This implies that a steady-state Nash equilibrium is unique and can be controlled by the levy. We analytically compute a steady-state Nash equilibrium solution for the agents, and use a Decision Support Tool to determine a satisfactory solution for the interactions between the agents and a legislator responsible for the levy.