Growth and distribution in a model with endogenous time preferences and borrowing constraints

This paper proposes an AK-model with endogenous time preferences and borrowing constraints. It is assumed that the subjective discount factor of a household is an increasing function of its relative income. First, we describe the structure of balanced-growth equilibrium paths, on which the population splits into two groups: the rich and the poor. Secondly, we study sliding equilibrium paths, show that they become balanced from some time onwards and that eventually all the capital is owned by those households that were the richest at the initial state. It follows that the long-run rate of growth depends on the initial distribution of wealth and income.     

Convergence to an exponential wealth distribution in a random market model

We study the discrete-time model of López-Ruiz, López and Calbet, describing the evolution of a wealth distribution under random pairwise exchanges of wealth among agents. This requires the analysis of the behaviour of iterations of a non-linear operator defined on a space of probability distributions. We prove that, as conjectured by López-Ruiz, López and Calbet, starting from a general wealth distribution, the wealth distribution converges to the exponential equilibrium distribution. The proof employs a special metric defined on spaces of probability distributions through their Laplace transforms.     

假期中顾客以概率θ进人的Geo/G/1(E,SV)排队系统的队长分布

考虑单重休假的Geo/G/1离散时间排队系统,其中在服务员休假期间到达的顾客以概率θ(0<θ≤1)进入系统.通过引入"服务员忙期"和使用全概率分解技术,从任意初始状态出发,研究了队长的瞬态和稳态性质,导出了在任意时刻n瞬态队长分布的z-变换的递推表达式和稳态队长分布的递推表达式,以及稳态队长的随机分解.最后,通过数值实例,讨论了稳态队长分布对系统参数的敏感性,并阐述了获得便于计算的稳态队长分布的表达式在系统容量设计中有重要的价值.     

Heterogeneous time preferences and the distribution of wealth

This paper shows that when households are heterogeneous with respect to time preference, the capital market functions as a powerful mechanism generating and maintaining a highly skewed distribution of wealth. A simple model of household savings is embedded into (1) a consumption loans economy and (2) a productive capital economy. The robustness of the conclusions is tested by relaxing some of the simplifying assumptions. Various counteracting instruments of social policy are discussed.     

Optimal Consumption Under Deterministic Income

We consider an individual or household endowed with an initial wealth, having an income and consuming goods and services. The wealth development rate is assumed to be a deterministic continuous function of time. The objective is to maximize the discounted consumption over a finite time horizon. Via the Hamilton–Jacobi–Bellman approach, we prove the existence and the uniqueness of the solution to the considered problem in the viscosity sense. Furthermore, we derive an algorithm for explicit calculation of the value function and optimal strategy. It turns out that the value function is in general not continuous. The method is illustrated by two examples.     

完备市场下的均衡和财富优化

针对跳扩散模型中的优化与均衡问题,利用鞅方法和随机点过程理论,建立了跳扩散模型下的均衡市场,分析了市场中的财富优化问题,给出了均衡大宗商品现货价格、最优财富过程、最优投资组合及最优消费过程.     

On the stability of open networks: A unified approach by stochastic dominance

Using stochastic dominance, in this paper we provide a new characterization of point processes. This characterization leads to a unified proof for various stability results of open Jackson networks where service times are i.i.d. with a general distribution, external interarrivai times are i.i.d. with a general distribution and the routing is Bernoulli. We show that if the traffic condition is satisfied, i.e., the input rate is smaller than the service rate at each queue, then the queue length process (the number of customers at each queue) is tight. Under the traffic condition, the pth moment of the queue length process is bounded for allt if the p+lth moment of the service times at all queues are finite. If, furthermore, the moment generating functions of the service times at all queues exist, then all the moments of the queue length process are bounded for allt. When the interarrivai times are unbounded and non-lattice (resp. spreadout), the queue lengths and the remaining service times converge in distribution (resp. in total variation) to a steady state. Also, the moments converge if the corresponding moment conditions are satisfied.     

Extinction and blow-up phenomena in a non-linear gender structured population model

In this article we consider a gender structured model in population dynamics. We assume that the fertility rate depends upon the weighted population of males instead of total population of males. The proportion of males in the population is determined by fixed environmental or social conditions. Here we prove an existence and uniqueness result for a non-trivial steady state. If the initial age distribution is uniformly below the non-trivial steady state then we show that the total population goes extinct in infinite time. On the other hand, if we take the initial age distribution to be uniformly above the steady state then the total population blows up exponentially with time.     

Steady State and Long Time Convergence of Spirals Moving by Forced Mean Curvature Motion

In this paper, we prove the existence and uniqueness of a “steady” spiral moving with forced mean curvature motion. This spiral has a stationary shape and rotates with constant angular velocity. Under appropriate conditions on the initial data, we also show the long time convergence (up to some subsequence in time) of the solution of the Cauchy problem to the steady state. This result is based on a new Liouville result which is of independent interest.     

Discrete time queueing networks with product form steady state. Availability and performance analysis in an integrated model

For a discrete time network of generalized Bernoulli servers with unreliable nodes we derive the steady state probabilities for the joint queue length vector for all nodes and the availability status of the network. This allows us to assess the performance behavior and the reliability, resp. availability, of the network in an integrated model. Because our result exhibits a product form for the steady state distribution it opens the path to fast algorithmic evaluation of the desired performance and reliability indices.     

推广的多重休假$M^X/G/1$排队系统

在平稳状态下,Baba利用补充变量方法研究了多重休假的MX/G/1排队,但作者假定了休假时间和服务时间都有概率密度函数.本文考虑推广的多重休假MX/G/1排队,在假定休假时间和服务时间都是一般概率分布函数下,我们研究了队长的瞬态和稳态性质.通过引进"服务员忙期"和使用不同于Baba文中使用的分析技术,我们导出了在任意时刻t瞬态队长分布的L变换的递推表达式和稳态队长分布的递推表达式,以及平稳队长的随机分解.特别地,通过本文可直接获得多重休假的M/G/1与标准的MX/G/1排队系统相应的结果.     

KINETIC FLUX VECTOR SPLITTING FOR THE EULER EQUATIONS WITH GENERAL PRESSURE LAWS

This paper attempts to develop kinetic flux vector splitting(KFVS)for the Euler equa-tions with general pressure laws.It is well known that the gas distribution function forthe local equilibrium state plays an important role in the construction of the gas-kineticschemes.To recover the Euler equations with a general equation of state(EOS),a newlocal equilibrium distribution is introduced with two parameters of temperature approx-imation decided uniquely by macroscopic variables.Utilizing the well-known connectionthat the Euler equations of motion are the moments of the Boltzmann equation wheneverthe velocity distribution function is a local equilibrium state,a class of high resolutionMUSCL-type KFVS schemes are presented to approximate the Euler equations of gas dy-namics with a general EOS.The schemes are finally applied to several test problems for ageneral EOS.In comparison with the exact solutions,our schemes give correct location andmore accurate resolution of discontinuities.The extension of our idea to multidimensionalcase is natural.     

Exponential wealth distribution in a random market. A rigorous explanation

In simulations of some economic gas-like models, the asymptotic regime shows an exponential wealth distribution, independently of the initial wealth distribution given to the system. The appearance of this statistical equilibrium for this type of gas-like models is explained in a rigorous analytical way.     

Bifurcations of fuzzy nonlinear dynamical systems

We present some recent developments of the fuzzy generalized cell mapping method (FGCM) in this paper. The topological property of the FGCM and its finite convergence of membership distribution vector are discussed. Powerful algorithms of digraphs are adopted for the analysis of topological properties of the FGCM systems. Bifurcations of fuzzy nonlinear dynamical systems are studied by using the FGCM method. A backward algorithm is introduced to study the unstable equilibrium solutions and their bifurcation. We have found that near the deterministic bifurcation point, the fuzzy system undergoes a complex transition as the control parameter varies. In this transition region, the steady state membership distribution is dependent on the initial condition. If we use the measure and topology of the α-cut (α = 1) of the steady state membership function of the persistent group representing the stable fuzzy equilibrium solution to characterize the fuzzy bifurcation, assuming the uniform initial condition within the persistent group, the bifurcation of the fuzzy dynamical system is then completed within an interval of the control parameter, rather than at a point as is the case of deterministic systems.     

延迟Min(N,D)-策略的M/G/1排队系统的队长分布与数值计算

考虑延迟Min(N, D)-策略的M/G/1排队系统. 运用更新过程理论、全概率分解技术和Laplace变换工具, 从任意初始状态出发, 研究了队长的瞬态和稳态性质, 获得了瞬态队长分布的Laplace变换的递推表达式和稳态队长分布的递推表达式, 同时求出了附加队长分布的显示表达式. 进一步讨论了当N \to \infty, 或D \to \infty, 或N=1且P{Y=0}=1, 或P{Y=0}=1时的特殊情形. 最后通过数值实例, 讨论了稳态队长分布对系统参数的敏感性, 并阐述了稳态队长分布的表达式在系统容量优化设计中的重要价值.     

基于生命周期模型的农户储蓄变动机制研究

运用1997-2006年省际动态面板数据研究了我国农村居民储蓄率变动的决定因素,并检验了永久收入假说(生命周期理论)对中国农村居民的适应性。实证研究发现,我国农村家庭储蓄率持续攀升以及时空差异的主要原因在于农村居民储蓄习惯(滞后储蓄率)、收入增长率、实际利率和宏观经济波动;但与人口年龄结构相关的因素对农村居民储蓄率变动影响较小,实证结果部分地支持生命周期理论假说。因此,从中短期来看,我国农村居民家庭储蓄率依然较高,应设计出刺激农民消费、减少储蓄的中短期政策组合,同时从制度层面来理顺农村储蓄资金转化为投资的渠道。     

Complex dynamics in an OLG model of neoclassical growth with endogenous retirement age and public pensions

This study analyses the dynamics of a general equilibrium, overlapping-generations (closed) economy with pay-as-you-go public pensions and tax-financed health investments that affect the retirement time when old. Life of the typical agent is divided between youth (firth period) and old age (second period). The latter period of life is, in turn, divided between work time and retirement time in a proportion contingent on an individual’s state of health. We show that: (i) a unique non-trivial steady state exists, and (ii) when the labour income tax rates used to finance health expenditure or public pensions are included in an intermediate range of values, complex dynamics occur when individuals have perfect foresight. This holds because the increase either in the fraction of time spent working when old or disability pensions reduces savings and capital accumulation. In addition, dynamic phenomena such as multiple bubbling structures related to the bifurcation diagram can be observed. Under some general assumptions, we show that the rise in health care expenditure and/or public pensions initially destabilises the steady-state equilibrium and causes complex dynamics but eventually acts as a stabilising device.     

带启动时间的N-策略Geo/G/1排队系统的队长分布及容量的优化设计

考虑带启动时间的N-策略离散时间Geo/G/1排队系统,使用全概率分解技术,从任意初始状态出发,研究了队长的瞬态和稳态性质,推导出了在任意时刻n瞬态队长分布的z -变换的递推表达式、稳态队长分布的递推表达式和附加队长分布的表达式,并获得稳态队长的随机分解结果.最后,通过数值实例,讨论了稳态队长分布对系统参数的敏感性,并阐述了获得便于计算的稳态队长分布的表达式在系统容量的优化设计中的重要应用价值.     

Multiple Equilibria and Thresholds Due to Relative Investment Costs

A dynamic model of the firm is studied in which investment costs depend on the magnitude of the investment relative to the stock of capital goods. It is shown that in general nonunique steady states can exist which can be stable or unstable. It is possible that unstable steady states occur in the concave domain of the Hamiltonian. For a particular specification, a scenario occurs with two stable steady states and one unstable steady state. The two stable steady states are long run equilibria; which one of them is reached in the long run depends on the initial state. In case the Hamiltonian is locally concave around the unstable steady state, this steady state is the threshold that separates the domain of initial conditions that each of the stable steady states attracts. The unstable steady state is a node and investment is a continuous function of the capital stock. If the unstable steady state lies in the nonconcave domain of the Hamiltonian, this steady state can either be a node or a focus. Furthermore, continuity can (but need not) be retained similarly to the concave case, a fact which has been entirely overlooked in the literature.     

Fluctuations in a SIS epidemic model with variable size population

In an epidemiological model, time spent in one compartment is often modeled by a delay in the model. In general the presence of delay in differential equations can change the stability of an equilibrium to instability and causes the appearance of oscillatory solutions.In this paper we consider a SIS epidemiological model with demographic effects: birth, mortality and mortality caused by infection. The delay is the period of infection. We define the concept of oscillation in the sense that solutions of the model studied fluctuate around a steady state. Our goal is to show that in this model, there are oscillating solutions for certain parameters values. We determine a large set of initial data for which solutions of this model are slowly oscillating.