Time-Consistent Investment Strategy for DC Pension Plan with Stochastic Salary Under CEV Model

This paper aims to derive the time-consistent investment strategy for the defined contribution(DC) pension plan under the mean-variance criterion.The financial market consists of a risk-free asset and a risky asset of which price process satisfies the constant elasticity of variance(CEV) model.Compared with the geometric Brownian motion model,the CEV model has the ability of capturing the implied volatility skew and explaining the volatility smile.The authors assume that the contribution to the pension fund is a constant proportion of the pension member's salary.Meanwhile,the salary is stochastic and its volatility arises from the price process of the risky asset,which makes the proposed model different from most of existing researches and more realistic.In the proposed model,the optimization problem can be decomposed into two sub-problems:Before and after retirement cases.By applying a game theoretic framework and solving extended Hamilton-Jacobi-Bellman(HJB) systems,the authors derive the time-consistent strategies and the corresponding value functions explicitly.Finally,numerical simulations are presented to illustrate the effects of model parameters on the time-consistent strategies.

Defined Contribution Pension Planning with the Return of Premiums Clauses and HARA Preference in Stochastic Environments

This paper studies a defined contribution(DC)pension fund investment problem with return of premiums clauses in a stochastic interest rate and stochastic volatility environment.In practice,most of pension plans were subject to the return of premiums clauses to protect the rights of pension members who died before retirement.In the mathematical modeling,we assume that a part of pension members could withdraw their premiums if they died before retirement and surviving members could equally share the difference between accumulated contributions and returned premiums.We suppose that the financial market consists of a risk-free asset,a stock,and a zero-coupon bond.The interest rate is driven by a stochastic affine interest rate model and the stock price follows the Heston’s stochastic volatility model with stochastic interest rates.Different fund managers have different risk preferences,and the hyperbolic absolute risk aversion(HARA)utility function is a general one including a power utility,an exponential utility,and a logarithm utility as special cases.We are concerned with an optimal portfolio to maximize the expected utility of terminal wealth by choosing the HARA utility function in the analysis.By using the principle of dynamic programming and Legendre transform-dual theory,we obtain explicit solutions of optimal strategies.Some special cases are also derived in detail.Finally,a numerical simulation is provided to illustrate our results.

Multi-Period Telser's Safety-First Portfolio Selection Problem in a Defined Contribution Pension Plan

This paper investigates a multi-period portfolio optimization problem for a defined contribution pension plan with Telser's safety-first criterion.The plan members aim to maximize the expected terminal wealth subject to a constraint that the probability of the terminal wealth falling below a disaster level is less than a pre-determined number called risk control level.By Tchebycheff inequality,Lagrange multiplier technique,the embedding method and Bellman's principle of optimality,the authors obtain the conditions under which the optimal strategy exists and derive the closed-form optimal strategy and value function.Special cases show that the obtained results in this paper can be reduced to those in the classical mean-variance model.Finally,numerical analysis is provided to analyze the effects of the risk control level,the disaster level and the contribution proportion on the disaster probability and the value function.The numerical analysis indicates that the disaster probability in this paper is less than that in the classical mean-variance model on the premise that the value functions are the same in two models.

Optimal Investment Strategy of Target Benefit Pension Plan Based on Random Inflation and Intergenerational Risk

In this paper,based on the stochastic optimal control method,the intergenerational risk and inflation risk,the optimal investment strategy of the target benefit pension plan is investigated on the basis of measuring the random wage rate under the random mortality and inflation risk of the personnel in the plan and the correlation between the wage change and the fluctuation of the financial market.The research shows that the financial market parameters and wage rate have a great influence on the optimal investment strategy,and gives the optimal investment strategy and the optimal income adjustment strategy of the target benefit pension.The research of this paper provides a reference for the policy formulation and implementation of the Target Benefit Pension Plan in our country.

Optimal portfolio for a defined-contribution pension plan under a constant elasticity of variance model with exponential utility

Based on the Lie symmetry method,we derive the explicit optimal invest strategy for an investor who seeks to maximize the expected exponential(CARA)utility of the terminal wealth in a defined-contribution pension plan under a constant elasticity of variance model.We examine the point symmetries of the Hamilton-Jacobi-Bellman(HJB)equation associated with the portfolio optimization problem.The symmetries compatible with the terminal condition enable us to transform the(2+1)-dimensional HJB equation into a(1+1)-dimensional nonlinear equation which is linearized by its infinite-parameter Lie group of point transformations.Finally,the ansatz technique based on variables separation is applied to solve the linear equation and the optimal strategy is obtained.The algorithmic procedure of the Lie symmetry analysis method adopted here is quite general compared with conjectures used in the literature.

Optimal investment for the defined-contribution pension with stochastic salary under a CEV model

In this paper, we study the optimal investment strategy of defined-contribution pension with the stochastic salary. The investor is allowed to invest in a risk-free asset and a risky asset whose price process follows a constant elasticity of variance model. The stochastic salary follows a stochastic differential equation, whose instantaneous volatility changes with the risky asset price all the time. The HJB equation associated with the optimal investment problem is established, and the explicit solution of the corresponding optimization problem for the CARA utility function is obtained by applying power transform and variable change technique. Finally, we present a numerical analysis.

账户养老金运营方式的国际比较与借鉴

与传统的现收现付制度相比,个人账户基金需获取高于人口与工资增长率的收益率才具有优势。因此,账户养老金计划下基金运营是账户养老金计划可持续发展的关键所在。从美国、澳大利亚等8个国家的情况看,账户养老金的运营大致可以被划分为两类:一类是政府不直接介入运营,另一类是政府强力介入运营。但不论是哪一类,各个国家都根据本国具体情况做出了不同选择。我国养老金体系的三个支柱中都存在账户养老金,其运营都面临着亟须解决的基本问题。借鉴国外经验,结合本国具体国情,可以为解决我国账户养老金运营面临的基本问题提出一些政策建议。

中国城乡空巢老年人的养老经济规划——来自中国老年社会追踪调查的发现

文章利用中国老年社会追踪调查2018年数据,分析了城乡空巢老年人的养老经济规划的现状及其影响因素。研究发现,约41.46%的空巢老年人有养老经济规划,有养老经济规划的独居空巢老年人比例低于夫妇空巢老年人,现金储蓄是空巢老年人做经济规划的主要方式。经济收入对空巢老年人的养老经济规划既具有显著的直接影响,也存在通过养老责任观念的中介作用对空巢老年人的养老经济规划的隐含效应。经济收入越多空巢老年人越可能做养老经济规划,有劳动收入、有企事业单位养老保险、子女给予经济支持的空巢老年人更可能做养老经济规划。认同由政府、社会和家庭共同承担养老责任的观念会促使经济收入多、有企事业单位养老保险和子女给予经济支持的空巢老年人做养老经济规划的可能性显著提高。

混合随机波动模型下带随机工资的DC型养老金最优投资策略

针对养老金的保值增值问题,分析具有利率风险和波动风险的DC(defined contribution)型养老金最优投资策略。假设金融市场包含一种无风险资产和一种股票,其中股票价格服从混合随机波动(Heston-Hull-White)模型。设定养老金计划成员的工资是随机的。基于终端财富预期效用最大化标准,在CARA效用函数下,通过建立相应的HJB(Hamilton-Jacob-Bellman)方程,求解出最优投资策略,并利用数值算例分析主要模型参数对最优投资策略的影响。结果表明:风险规避系数的增大会导致投资者对股票的投资比例下降,利率风险和波动风险对DC型养老金的最优投资策略有显著影响。所得结果对基金管理者具有一定的指导作用。

金融素养过度自信对城镇老人金融受骗的影响机制研究

随着人口老龄化的加剧,以及数字金融普惠的发展,老年群体金融受骗问题越来越成为社会关注的重点。文章利用2021年中国养老金融调查(CAFS)数据,基于行为金融理论,考察了金融素养过度自信对我国城镇老年群体金融受骗的影响机制。结果发现,金融素养过度自信的城镇老年人更容易遭受金融诈骗,遭受损失也更大;在金融素养过度自信和老年人金融受骗之间,风险态度这一变量发挥着部分中介作用;且养老规划起到了负向调节作用。基于此,文章对防止老年人遭受金融诈骗提出了针对性的建议。

完备市场和不确定性风险下的养老金投资组合

为了更好地契合实际金融市场,同时为模糊厌恶的养老投资者提供最优的投资策略,将价格扩散不确定性、波动扩散不确定性及跳跃过程的不确定性整合到具有罕见事件的传统股票市场中,推导出半封闭形式的稳健动态衍生品投资策略。通过数值分析,得出以下结论:在波动率跳跃幅度较大的情况下,投资者倾向于在负价格跳跃时增加对价格和波动率的风险敞口,并减少对市场跳跃的敞口。股票和波动率风险的最优敞口主要受到投资者对股票价格和波动率风险因素的模糊厌恶的影响,而市场跳跃风险的最优敞口则受到投资者对波动率和罕见事件风险因素的模糊厌恶的显著影响。

英国养老保险体系自主投资个人养老金的制度设计与运行实践

个人养老金制度是多支柱养老保险制度的重要组成部分,发挥着补充保障的重要功能。文章以英国自主投资个人养老金计划为主要研究对象,重点介绍计划的开户方式、计划类型、账户管理、税收优惠政策、投资管理和待遇领取等关键制度要素,总结该计划具有的便捷、投资自主性和灵活性强、差异化税优激励性、投资管理兼具收益性和安全性等实践特征。英国自主投资个人养老金制度发展的经验给处于发展初期的中国个人养老金制度带来启示:一是明晰个人养老金制度的功能定位,二是增强账户管理的灵活性,三是多举措并举降低投资风险和优化投资收益,四是注重专业投资教育和咨询服务的重要作用。

基于TPB/TAM的养老服务金融参与意向影响因素实证研究——以济南市城市居民为例

基于计划行为理论和技术接受模型,对城市居民养老服务金融参与意向进行研究,构建养老服务金融参与意向的结构方程模型,揭示影响城市居民养老服务金融参与意向的关键因素及其机理;采用问卷调查法,搜集986份有效样本数据进行实证分析。结果表明,感知行为控制、主观规范、感知易用性和感知有用性正向影响城市居民参与养老服务金融的意向,感知风险负向影响济南市城市居民参与养老服务金融的意向,初始信任在用户感知易用性、感知有用性正向影响养老服务金融行为意向的关系中具有显著的中介效应。

养老社区的空间组织与建筑规划思路分析

文章简要介绍城市社区综合养老服务设施的基本概念,以大兴区旧宫镇德茂地区社区综合管理与养老服务中心设计项目为例,分析养老社区服务中心区域的设计原则,分析其室内、室外的环境空间、建筑规划设计要点,突出养老服务设施与社区环境融合重要性。社区环境与养老功能设施的融合,能够实现社区空间环境、服务资源的最大化利用,能够缓解家庭养老压力。

医养结合型养老社区前期策划方法研究

我国老龄化进程加速,养老问题受到重视,养老社区成为浪潮下的产物并推动土地开发建设形成独特的产品类型。根据市场整体呈现,养老社区类产品存在设施匹配度与医养功能融合度较低等问题。在医养结合需求下,分析养老社区前期策划方法,探索其规划设计的实施路径,为其他类似项目前期策划提供参考。

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.

养老金会计的国际比较研究及借鉴

我国养老金会计与国外相比存在一些差异,主要表现在对养老金性质的认识不同,养老金会计核算的主体、原则及会计处理方法不同,养老金会计信息披露不同,会计环境不同。随着我国养老金制度改革的深化,我们应借鉴国外养老金会计的先进经验,逐步完善我国的养老金会计,以发挥其服务功能,主要侧重三个方面,即引进新的养老金会计核算原则、重新设置养老金会计的账户体系、政府对企业进行养老金会计核算给以必要的帮助和支持。

挤入抑或替代:家庭养老、社会养老对个人养老影响研究

回答家庭养老、社会养老对个人养老存在挤入还是替代效应是建立和完善第三支柱个人养老金制度,构建多层次养老保障体系的基础。文章基于新三支柱橄榄型可持续发展养老制度调查数据,运用Logit和Probit模型分析家庭结构、养老保险参与对居民个人养老储蓄意愿影响以尝试对上述问题进行回答。研究结果表明:(1)仅有一个子女和需要赡养老人数量较多的居民个人养老储蓄意愿更强;(2)希望提高养老保险缴费个人比例并不能显著提高个人养老储蓄意愿,但父母参加社会养老保险能显著提高个人养老储蓄意愿;(3)家庭结构、养老保险参与对个人养老储蓄意愿影响存在性别、年龄、收入、户口等异质性。整体来说,家庭结构小型化、核心化带来的家庭养老功能的弱化会激发个人养老储蓄意愿而社会养老由于替代了家庭养老部分功能同样对个人养老存在挤入效应。因此应在提高居民个人养老储蓄意愿,推动第三支柱养老金制度完善的同时,注重家庭养老、社会养老与个人养老等养老模式之间的协调。

美国401K计划的创新与发展——罗斯401K计划运行机制研究

401K计划是美国职业养老金计划的重要组成部分。从2006年1月1日起,发起401K计划的雇主可以为其雇员提供一种新的缴费方式——指定罗斯缴费,这种缴费方式形成的计划即为罗斯401K计划。我们介绍罗斯401K计划的基本特征及其运行机制,对比分析原有401K计划和罗斯401K计划在税收政策方面的差异性,并就如何完善我国企业年金税收政策提出建议。

先发地区养老服务设施规划编制方法探讨——以昆山市为例

基于昆山的规划实践,分析外来人口对先发地区老龄化的影响,总结出隐性化、空巢化、高龄化,以及老年人口总量分布和密度分布相悖是先发地区老龄化的主要特征;指出养老服务设施建设存在着内涵模糊、总量不足、布局错位、市场化运营滞后等问题。构建以养老模式为基础,实现多重属性相统一的养老服务设施体系;从等级体系、配置标准、城乡差异、资源整合和空间分析等方面探讨了养老服务设施规划编制方法;提出图则指引、弹性规划、管理创新等强化规划实施的方法以及多部门联合编制、规划与政府决策相结合、"开门规划"等规划编制工作方法的创新。