企业退休职工养老金模型

本文讨论了目前我国养老保险体制改革的相关问题。首先,通过分析年工资增长趋势,对其数据进行回归分析,构造出工资的Logistic模型,并预测出职工未来年份的年平均年工资;其次构造养老金替代率模型,并得到多种情况下的替代率;再次,建立养老金缺口模型,用来分析养老金缺口情况以及达到平衡时领取养老金的年数;最后分析得出影响养老金替代率和收支平衡的4个因素,即社会统筹基金的缴费比例、基金收益率、退休年龄和开始缴纳养老保险的年龄,对其进行敏感性分析,并提出一些相应的改进建议。     

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.     

中国隐性养老金债务精算模型及其应用研究

根据当前中国养老金发放的实际情况 ,利用生存年金理论 ,改进了国外传统生存年金系数模型 ,得到测算‘老人’养老金债务和‘中人’过渡性养老金债务的精算模型 .利用该模型 ,测算出 2 0 0 0年中国隐性养老金债务规模 ,并对影响养老金债务的因素进行敏感性分析 ,提出缩减隐性养老金债务规模的思路 .     

人口年龄结构变化模型与郑州市基础养老金发展趋势分析

以2010年全国第六次人口普查数据为基础,采用韦伯(weibull)分布拟合人口死亡分布密度函数,推导出未来郑州市人口年龄结构变化模型,运用逻辑斯蒂(Logistic)阻滞模型预测职工的平均工资水平,依据最新的国务院2015年1月14日发布《关于机关事业单位工作人员养老保险制度的决定》(国发[2015]2号)方案,在此基础上构建了养老金的收支平衡及替代率模型.研究结果表明:随着时间的推移郑州市养老金收支将面临严重压力,在2050年养老金缺口将达到高峰,最后给出了政策建议.     

基于人口因素的黑龙江省农村养老金需求总量预测

随着老年人口数量和比例的不断增长,农村养老难问题日益突出.资金是养老问题的核心.通过对养老资金的预测,可以为政策的制定提供数据参考与决策依据.以黑龙江省为例,在对现行农村养老金制度进行分析的基础上,从人口因素角度对农村养老金需求总量进行预测.建立人口增量模型,依据人口统计数据,引入年龄、性别影响参数,得出人口预测结果.进行养老金需求总量预测,分析并确定了人均养老金标准,进而通过人口预测数据求得养老金需求总量数据.     

新型城镇化对养老金收支的影响分析

随着人口老龄化的不断加重,养老金短缺状况日益严重.通过构建城镇化建设对养老金的影响机制,并采用31个省市自治区2009-2018年的统计数据,采用系统广义矩估计方法,分析新型城镇化建设对养老金收支水平的影响作用,发现城镇化对养老金收入的促进作用大于对养老金支出的影响,说明新型城镇化的建设可以有效缓解养老金缺口,实现养老金的累积效应.     

城镇职工养老保险随机模型研究

构建了包含个人、企业、政府等市场参与者相互制衡的城镇职工养老保险随机模型,该模型涉及了储蓄、工作期消费、个人养老金账户、工资、退休后消费共5个随机变量;利用ITo引理证明了随机微分方程解的存在性,唯一性,利用2010-2014年中国有关宏观数据,对5个变量进行了动态模拟,并对部分参数变动对模型的影响进行分析,得出了储蓄替代率和人口出生率与两期消费正相关,两者的小范围变动不会影响两期消费的趋势等结论.     

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.     

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.     

Three retirement decision models for defined contribution pension plan members: A simulation study

This paper examines the hypothetical retirement behavior of defined contribution (DC) pension plan participants. Using a Monte Carlo simulation approach, we compare and discuss three retirement decision models: the two-thirds replacement ratio benchmark model, the option-value of continued work model and a newly-developed “one-year” retirement decision model. Unlike defined benefit (DB) pension plans where economic incentives create spikes in retirement at particular ages, all three retirement decision models suggest that the retirement ages of DC participants are much more smoothly distributed over a wide range of ages. We find that the one-year model possesses several advantages over the other two models when representing the theoretical retirement choice of a DC pension plan participant. First, its underlying theory for retirement decision-making is more feasible given the distinct features and pension drivers of a DC plan. Second, its specifications produce a more logical relationship between an individual’s decision to retire and his/her age and accumulated retirement wealth. Lastly, although the one-year model is less complex than the option-value model as the DC participants’ scope is only one year, the retirement decision is optimal over all future projected years if projections are made using reasonable financial assumptions.     

Valuation of risk-based premium of DB pension plan with terminations

This paper concentrates on the premium valuation of pension insurance provided by the Pension Benefit Guaranty Corporation (PBGC). The PBGC provides a defined benefit pension sponsor with coverage in case that the pension fund fails to make pension payments as promised or that the plan sponsor does not stay in business any more. In practice, both the pension fund and the sponsor assets play a critical role in fulfilling the commitment of pension payments, and thereby it is not reasonable to isolate the risk of distress termination of the sponsor assets from that of the premature termination of the pension fund. Different from previous works in which the premature termination of the pension fund and the distress termination of the sponsor assets are analyzed separately, our model examines the situation in which retirees suffer the risk of two types of terminations at the same time. We evaluate the risk-based fair premium under the framework that the pension fund and the sponsor assets are correlated and subject to the risk of the involuntary termination (i.e., premature termination) and the distress termination, respectively. In this framework, we manage to obtain closed-form pricing formulas. Our model is more practical because of the realistic design of termination schemes. Numerical simulations are also carried out to demonstrate our findings. Our numerical experiments validate that a variable rate premium is more appropriate for the PBGC to implement.     

养老基金投资组合的常方差弹性(CEV)模型和解析决策

针对以年金形式发放待遇的缴费预定制养老基金,在退休前和退休后的两个阶段,分别构建了常方差弹性(CEV)模型,并应用Legendre变换将原问题转化为对偶问题,在追求指数效用最大化的条件下,求得了精确解析解,从而确定了这两个阶段的最优投资决策．     

Exploration of pension funding in case of exact vesting

A pension plan is said to be exactly vested if it provides in addition to the benefit available upon retirement, a benefit, upon termination for any cause prior to retirement, which is exactly equivalent to the actuarial accured liability for the terminating participant.The concept of exact vesting has simple application in defined contribution plans such as those of the Teachers Insurance and Annuity Association. It is also feasible to develop the exact vesting concept for a defined benefit plan which uses an individual type of actuarial cost method. An exactly vested plan would have more individual equity than is available under customary vesting and early retirement provisions of defined benefit plans.In this paper, theory is developed for an exactly vested model plan in parallel to the theory for a pure pension model plan discussed in previous papers on pension funding dynamics.     

固定支付下养老基金资产组合CEV模型及最优投资策略

在固定支付水平的条件之下,就养老基金资产组合问题建立常方差弹性(CEV)模型,应用随机控制原理求出了相应的非线性Hamilton-Jacobi-Bellman偏微方程,再用Legendre变换将其转化为线性偏微方程,建立对偶问题.通过对偶问题的求解,从而求得原问题的精确解析解,确定风险资产和无风险资产的最优投资比例,实现了满足养老基金既定支出水平下总资产的对数效用最大化,从实际市场的角度改进发展了经典的Merton模型结果.     

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.     

Pension funds as institutions for intertemporal risk transfer

A continuous time overlapping generation model is used to analyse defined-contribution pension plans. Without intergenerational risk transfer between employees the optimal investment strategy results from the Merton model. Introducing intergenerational risk transfer leads to an increase in the risk tolerance of future employees and allows us to improve their anticipated expected utility resulting from accrued retirement benefits. Of course, this leads to a risk of temporary underfunding. But even for an underfunded pension plan one can guarantee that in the long run, the median of the funding ratio exceeds one.     

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.