可持续的中国城乡居民养老保险体系数学模型

本文从我国现行养老金政策出发,利用灰关联分析得到养老金收支的影响因素的排序,建立中国城乡居民养老金收支模型.然后利用Logistic人口预测模型估计出不同替代率下2013-2035未来23年我国养老金缺口,并利用仿真方法算出保证我国养老保险体系的可持续性的替代率的合理区间为50%-70%.进一步分析影响替代率各因素的灵敏性,并考虑延迟退休、做实个人账户以及市场化投资等因素对模型进行改进.最后以养老金替代率为切入点,对退休年龄等模型参数的调整和有关措施进行了分析与评价.     

可持续的中国城乡居民养老保险体系的数学模型研究

考虑了替代率、缴费率、人口结构、分年龄段死亡率、经济增速、财政补贴、工资水平、投资效益,引入收缴率、通货膨胀率等当今影响养老保险的活跃因素,建立了"城乡结合"的中国城乡基本养老保险收支跨期叠代模型,并在此基础上进行优化.通过仿真,探讨了替代率和缴费率的合理区间.     

中国城乡居民养老制度可持续性的精算研究

围绕我国城乡居民养老保险体系可持续化问题,从中国实际出发,分层次、多角度的分析了当前我国的养老保险制度.首先,针对中国养老保险基金问题,基于当前养老保险体制,分别从三个层次入手,建立中国城乡居民养老保险基金收支模型;其次,基于养老制度的可持续性,建立了养老金缺口模型,并对养老金缺口的未来趋势进行了合理预测;最后,对所建立的模型进行了评价及推广.     

Urban public pension, replacement rates and population growth rate in China

This paper uses an overlapping generations model to investigate the urban public pension in China. It examines the effects of the replacement rates and population growth rate on the capital–labor ratio, pension benefits, consumption and utility, and finds the optimal replacement rate. It is shown that raising the individual account benefit replacement rate only induces the increase in the individual account benefits. Raising the social pool benefit replacement rate induces the increase in the social pool benefits and retirement-period consumption, while the decrease in the capital–labor ratio, individual account benefits, working-period consumption and utility. The fall in the population growth rate leads to the increase in the capital–labor ratio, social pool benefits, individual account benefits, working-period consumption and utility, and leads to a decrease in the retirement-period consumption. The optimal social pool benefit replacement rate depends on the individual discount factor, social discount factor, capital share of income and population growth rate, and it decreases in the case of falling population growth rates. It will do more good than harm to raise the individual account benefit replacement rate, reduce the social pool benefit replacement rate and strictly implement China’s population policy.     

中国基本养老保险替代率精算模型及其应用

利用年金理论并结合1997年国务院《关于建立统一的企业职工基本养老保险制度的决定》文件,得到我国职工在不同缴费年限下基本养老保险替代率精算模型,并利用该模型对基本养老保险替代率进行模拟分析.这对于明确我国当前基本养老保险替代率及完善基本养老保险政策具有重要的理论指导意义和实际应用价值.     

Optimal DB-PAYGO pension management towards a habitual contribution rate

In this paper, we propose a new objective function, which reflects the costs of unstable contribution risk and discontinuity risk in DB-PAYGO pension system. The problem is to minimize the quadratic deviation between the actual contribution rate and a habitual target and the quadratic proportional deviation of the pension accumulation. A modified non-negative constraint of the contribution rate is added, which together with a stochastic habitual target process, causes difficulty in solving the minimization problem by Lagrange dual method. The results are split into two cases which depend on the habit-adjusted adequacy of the pension budget. In the inadequate case, the optimal contribution rate reveals a hump shape curve with respect to time, which is different from the exponential growth curve of the model with a fixed target. By moderately raising the contribution rate in the initial phase, it helps to increase the accumulation and reduce the contribution burden of the follow-up policyholders. Notably, the hump shape curve is a more practical policy, because of that the exponential growth curve raises anxiety about the unlimited growth of the contribution rate and harms the confidence in the sustainability of the pension fund. We also study the impacts of the certain trend in demography, and the uncertain fluctuations in salary and investment on the optimal control policies.     

Existence and Asymptotic Behavior of Solutions for the Unstirred Chemostat Model with Ratio-Dependent Function

A system of reaction-diffusion equations arising from the unstirred chemostat model with ratio-dependent function is considered. The asymptotic behavior of solutions is given and all positive steady-state solutions to this model lie on a single smooth solution curve. It turns out that the ratio-dependence effect will not affect the dynamics, compared with (Hsu and Waltman in SIAM J. Appl. Math. 53(4):1026–1044, 1993) and (Nie and Wu in Sci. China Math. 56(10):2035–2050, 2013).

     

Optimal management of DC pension plan under loss aversion and Value-at-Risk constraints

This paper studies the risk management in a defined contribution (DC)pension plan. The financial market consists of cash, bond and stock. The interest rate in our model is assumed to follow an Ornstein–Uhlenbeck process while the contribution rate follows a geometric Brownian Motion. Thus, the pension manager has to hedge the risks of interest rate, stock and contribution rate. Different from most works in DC pension plan, the pension manger has to obtain the optimal allocations under loss aversion and Value-at-Risk(VaR) constraints. The loss aversion pension manager is sensitive to losses while the VaR pension manager has to ensure the quality of wealth at retirement. Since these problems are not standard concave optimization problems, martingale method is applied to derive the optimal investment strategies. Explicit solutions are obtained under these two optimization criterions. Moreover, sensitivity analysis is presented in the end to show the economic behaviors under these two criterions.     

Optimal management of DC pension plan in a stochastic interest rate and stochastic volatility framework

This paper investigates an optimal investment strategy of DC pension plan in a stochastic interest rate and stochastic volatility framework. We apply an affine model including the Cox–Ingersoll–Ross (CIR) model and the Vasicek mode to characterize the interest rate while the stock price is given by the Heston’s stochastic volatility (SV) model. The pension manager can invest in cash, bond and stock in the financial market. Thus, the wealth of the pension fund is influenced by the financial risks in the market and the stochastic contribution from the fund participant. The goal of the fund manager is, coping with the contribution rate, to maximize the expectation of the constant relative risk aversion (CRRA) utility of the terminal value of the pension fund over a guarantee which serves as an annuity after retirement. We first transform the problem into a single investment problem, then derive an explicit solution via the stochastic programming method. Finally, the numerical analysis is given to show the impact of financial parameters on the optimal strategies.     

Mean–variance efficiency of DC pension plan under stochastic interest rate and mean-reverting returns

This paper studies the optimization problem of DC pension plan under mean–variance criterion. The financial market consists of cash, bond and stock. Similar to Guan and Liang (2014), we assume that the instantaneous interest rate is an affine process including the Cox–Ingersoll–Ross (CIR) model and Vasicek model. However, we assume that the expected return of the stock follows a completely different mean-reverting process, which can well display the bear and bull features of the market, and the market price of the stock index is the Ornstein–Uhlenbeck process. The pension manager thus has to undertake the risks of interest rate and market price of stock index. Besides, a special stochastic contribution rate is formulated. The goal of the pension manager is to maximize the expected terminal value and minimize the variance of terminal value. We will use the technique developed by Guan and Liang (2014) to tackle this problem and derive the closed-forms of efficient frontier and strategies. Numerical analysis is given in the end of this paper to show the economic behavior of the efficient frontier and strategies.     

我国人口发展总量的中长期预测模型

通过对1994―2005年男、女出生人口性别比的变化和2001―2005年城镇化趋势的分析,建立了我国人口发展总量的中长期预测模型,并针对在总和生育率四种不同情况下2006-2100年的人口发展状况进行了长期预测和详细分析.在目前人口结构状况下,将总和生育率控制在更替水平左右,既可保证总人口不超过15亿,又能降低人口老龄化程度,可为人口控制、决策提供较为科学的依据.     

A GLOBAL MODEL OF POPULATION‐RESOURCE INTERACTION

ABSTRACT. A global model of population‐resource interaction is proposed consisting of two first order ordinary differential equations. In it the population growth rate increases due to increasing technology, then declines due to declining resources. When the model is fit to twentieth century data it predicts that global population will peak and then decline while already declining global resources bottom out; both will eventually stabilize slightly above their lows. Because of the uncertainty of model parameters and resource data, the values and times of these peaks and lows are uncertain, but the qualitative behavior of the model transcends this uncertainty. Actual best‐fit values of population include a peak of nearly nine billion about year 2050 and a peak rate of decline of 0.3% about year 2100. Global resources bottom out at 70% of optimum around year 2100. Variability and sensitivity analyses are also provided.     

Optimal assets allocation and benefit outgo policies of DC pension plan with compulsory conversion claims

In this paper, we study optimal asset allocation and benefit outgo policies of DC (defined contribution) pension plan. We extend He and Liang model (2013a,b) to describe dynamics of individual fund scale during distribution period. The fund scale is affected by investment return, benefit outgo and mortality credit. The management of the pension plan controls the asset allocation and benefit outgo policies to achieve the objective of pension members. The goal of the management is to minimize accumulated deviations between the actual benefit outgo and a pre-set target during the whole distribution period. The performance function (criterion) is the weighted average of the square and linear deviations to express more penalty on negative deviation than positive deviation. Using HJB (Hamilton–Jacobi–Bellman) equations and variational inequality methods, the closed-forms of the optimal policies are derived. The counterintuitive effect of the optimal proportion allocated in the risky asset with respect to the fund scale is also derived, and the optimal benefit outgo has the form of the spread method. Moreover, we use Monte Carlo Methods (MCM) to analyze economic behaviors of the optimal asset allocation and benefit outgo policies.     

中国FDI的混沌吸引子检测及非线性动力学预测——基于logistic模型

应用logistic模型对我国1980~2005年FDI序列进行检测,并没有发现FDI混沌吸引子存在.预测结果显示,我国FDI已趋于平稳增长,"十一五"期间FDI年均增长为3.41%,年均FDI流入量为654亿美元,预计累计吸引FDI在2978.291~3562.052亿美元之间.这为我国"十一五"利用外资规划中的目标提供了有力的支持.同时,我国FDI具有拥塞现象,且所产生的阻力日益加剧,FDI需外部激励才能持续增长.为实现"十一五"利用FDI目标,一方面我国要努力调节FDI的地区分布结构和产业分布,扩大FDI环境容量,更重要的是要保持经济持续增长,改善投资环境,提高服务质,增加外商对华直接投资的信心.     

A comparison of two legislative approaches to the pay-as-you-go pension system in terms of adequacy. The Italian case

The aim of our work is to evaluate a new legislative proposal of the Italian pension system due to Giuliano Cazzola e Tiziano Treu and to compare it with the system in force due to former Minister Elsa Fornero. The evaluation is made in terms of adequacy. We make use of a mathematical model which, under the hypothesis of demographic equilibrium, formalizes the legislative changes of the pay-as-you-go pension system. The model is tested using Italian demographic and socio-economic data.The pay-as-you-go pension system in force is notional defined contribution and has the huge drawback that the replacement rate (the ratio between the monthly pension and the last wage perceived by the worker) is very low. We compare the two pension systems evaluating the dynamics of the replacement rate.     

基于Lee-Carter模型的互助养老年金研究

基于经典的双线性随机Lee-Carter模型,采用经济学的协整理论,对中国大陆男性人口死亡率进行预测,克服了ARIMA模型预测的局限性.在随机利率和Lee-Carter模型的基础上度量退休年金和生命年金的长寿风险,并为此提出应对策略,引入由消费者承担系统长寿风险、年金池承担个体长寿风险的群体自助养老年金(GSA),然后对其进行实证分析发现,与普通年金相比,GSA模型分担模式拥有较高的给付额.     

Altruistic motives,uncertain lifetime and urban public pension replacement rates

This article employs an overlapping generations model with altruistic motives and uncertain lifetime to investigate China's urban public pension system. We examine the effects of the individual account benefit replacement rate, social pool benefit replacement rate, life expectancy and population growth rate on the capital-labour ratio, pension benefits, consumption and utility. We also find the optimal social pool benefit replacement rate. Raising the individual account benefit replacement rate only increases the individual account benefits. Raising the social pool benefit replacement rate increases the social pool benefits and retirement-period consumption, whereas decreases the capital-labour ratio, individual account benefits, working-period consumption and utility. The fall in the population growth rate increases the capital-labour ratio, social pool benefits, individual account benefits, working-period consumption and utility, whereas decreases the retirement-period consumption. The rise in the life expectancy decreases the six variables. The optimal social pool benefit replacement rate falls in case of either risen life expectancy or fallen population growth rate. It further falls under the joint case of risen life expectancy and fallen population growth rate. It will do more good than harm to raise the individual account benefit replacement rate, reduce the social pool benefit replacement rate and strictly implement the population policy.     

中国人口死亡率建模比较及长寿风险度量

以我国颁布的3套保险行业经验生命表为基础，结合1995-2017年国家统计局发布的《中国统计年鉴》中的死亡率数据，首先分析了中国全年龄人口数据死亡率动静态变动特点，其次比较了LC，CBD和APC 3种模型对中国死亡率数据的拟合优劣，最后采用最优APC模型度量了不同生命表下的长寿风险.死亡率的动态变化会导致以经验生命表为依据的年金产品定价出现偏差，增加养老金管理机构的承保风险.     

Dynamic activity analysis model-based win-win development forecasting under environment regulations in China

Porter hypothesis states that environmental regulation may lead to win-win opportunities, that is, improve the productivity and reduce the undesirable output simultaneously. Based on directional distance function, this paper proposes a novel dynamic activity analysis model to forecast the possibilities of win-win development in Chinese industry between 2011 and 2050. The consistent bootstrap estimation procedures are also developed for statistical inference of the point forecasts. The evidence reveals that the appropriate energy-saving and emission-abating regulation will significantly result in both the net growth of potential output and the increasing growth of total factor productivity for most industrial sectors in a statistical sense. This favors Porter hypothesis.     

Evaluating the UK and Dutch defined-benefit pension policies using the holistic balance sheet framework

This paper compares the UK and Dutch occupational defined-benefit pension policies using the holistic balance sheet (HBS) framework. The UK DB pension system differs from the Dutch one in terms of the steering tools and adjustment mechanisms. In addition to the sponsor guarantee, the UK system has the protection from the Pension Protection Fund (PPF) that guarantees DB pension schemes’ funding shortfalls if the sponsors of the schemes are insolvent. The paper first introduces a multi-period model called value-based ALM to value the embedded options implied by both UK and Dutch pension policies and build the HBS. The HBS framework allows us to have a holistic view on the real and contingent assets and liabilities of a pension scheme and evaluate the impact of introducing a new policy for the stakeholders of the pension scheme. Then, we compare the results of a typical UK policy with a typical Dutch one. The comparison suggests the UK policy is better for participants but worse for the sponsor compared to the Dutch policy. The UK policy is more generous in indexation and participants do not have the burden to contribute to the funding recovery of the pension scheme. The PPF provides protection of the benefits up to a certain level if the sponsor is insolvent, thus, participants in a scheme with a UK pension policy are exposed to limited downside risk. On the other hand, the sponsor of the pension scheme with the UK policy shoulders a heavier burden to contribute to the recovery of the pension funding shortfalls than that of the pension scheme with the Dutch policy.