随机环境下具有最低担保约束的DC养老金鲁棒投资策略

针对近年来养老金管理遇到的问题,基于模型不确定性,考虑随机环境和退休保障限制的DC型养老金最优投资策略具有重要意义.以养老金的最终价值相对于退休后年金担保的不变相对风险厌恶期望效用最大化为目标,利用随机动态规划的方法,求出鲁棒最优投资策略及相应的价值函数.最后,通过数值分析,得到各参数对最优投资策略的影响.     

激励机制和VaR约束下的DC养老金计划的最优投资

研究了DC养老金经理在单一管理费以及混合收费(同时收取管理费与绩效费)这两种不同的薪酬机制和损失厌恶下的最优投资组合问题。利用凹化方法得到了存在终端财富约束下的最优财富过程和最优投资策略的解析表达式。数值结果表明损失厌恶,VaR约束和薪酬机制会极大地影响最优终端财富的分布。特别地,在决策参照点较高时,损失厌恶会导致混合薪酬机制下最优终端财富的尾部风险较低。     

Ornstein-Uhlenbeck模型下DC养老金计划的最优投资策略

本文研究了Ornstein-Uhlenbeck模型下确定缴费型养老金计划(简称DC计划)的最优投资策略,其中以最大化DC计划参与者终端财富(退休时其账户金额)的CRRA效用为目标.假定投资者可投资于无风险资产和一种风险资产,风险资产的瞬时收益率由Ornstein-Uhlenbeck过程驱动,该过程能反映市场所处的状态.利用随机控制理论,给出了相应的HJB方程与验证定理;并通过求解相应的HJB方程,得到了最优投资策略和最优值函数的解析式.最后分析了瞬时收益率对最优投资策略的影响,发现当市场向良性状态发展时,投资在风险资产上的财富比例呈上升趋势;当初始财富足够大且市场状态不变时,投资在风险资产上的财富比例几乎不受时间的影响.     

通胀风险与波动风险环境下带有保费返还条款的DC型养老金计划

通胀风险和波动风险是影响养老金计划的最重要的两个因素,保费返还条款可以保障死亡的养老基金持有者的权益.文章研究了通胀风险和波动风险环境下带有保费返还条款的确定缴费型(DC型)养老金计划问题.模型中假设风险资产价格由Heston随机波动率模型驱动,养老金被允许投资于一种无风险资产、一种风险资产和一种通胀相关指数债券.在均值-方差准则下,利用随机控制理论、博弈论和变量分离法得到了时间一致最优投资策略和有效前沿的显性解.最后通过应用数值算例对最优投资策略和有效前沿进行了敏感性分析.     

基于加权效用和VaR-PI约束下DC型养老金计划的最优资产配置

本文从养老金计划参与人和基金经理的双重视角出发,以最大化双方加权的期望效用为目标,研究了在最低保障和VaR约束下,DC养老金计划的最优资产配置问题。假设养老金计划参与人和基金经理均是损失厌恶的,分别用两个S型的效用函数来刻画双方的损失厌恶行为。VaR约束和加权的效用函数使得本文所研究的优化问题成为一个复杂的非凹效用最大化问题。利用拉格朗日对偶理论和凹化方法求得了最优财富和最优投资组合的封闭解。数值结论表明当更为看重养老金计划参与人的利益时,基金经理会采取更为激进的投资策略,VaR约束可以改进对DC养老金计划的风险管理。     

基于Hurwicz准则的不确定养老金最优投资策略问题

本文提出一种新的养老金最优投资策略模型,研究了带有不确定工资过程的DC型养老金最优投资策略问题.以二次损失函数的Hurwicz加权平均值最小化为目标,针对两类相对财富过程,给出了养老金最优投资策略的显式表达式.最后,通过数值分析,研究了模型参数对最优投资策略的影响.     

带有通胀风险的退休后最优投资-年金化时刻决策

研究了带通货膨胀的确定缴费养老计划退休后最优投资-年金化决策。假设通货膨胀过程是一个随机过程,建立了真实财富的波动过程。先相对固定年金化时刻,采取目标定位型模型,预设未来各时期的投资目标,利用贝尔曼优化原理,得到从退休时刻到相对固定年金化时刻之间的最优投资策略。接着建立了最优年金化时刻的评估标准,最优的年金化时刻使得年金化前后的累加消费折现均值得到最大。证明了在随机通货膨胀的假设下,传统的自然投资目标不存在;当随机通胀过程退化到确定过程时,求出了自然投资目标的显式表达式,并且在这两种情况下,分析了通胀情况对最优投资策略的影响。最后利用数值分析手段, 研究了通货膨胀、风险偏好、折现率对最优年金化时刻的影响。     

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.     

随机利率下DC型养老金的随机微分博弈

本文研究了Vasicek随机利率下DC型养老金的随机微分博弈.金融市场是博弈的"虚拟"手,博弈中养老金计划投资者占主导.研究目标是:通过养老金计划投资者和金融市场之间的博弈,寻找最优的策略使得终止时刻财富的期望效用达到最大.在幂效用函数下,运用随机控制理论求得了最优策略和值函数的显式解.最后,解释了所研究的结果在经济上的意义,并通过数值计算分析了一些参数对最优策略的影响.     

不完全信息环境下具有随机工资和保费返还条款的DC养老金均衡策略

在不完全信息环境下,文章研究了具有随机工资和保费返还条款,且面临通胀风险的DC养老金均衡投资策略.假设养老金参与者连续不断地将其随机工资的固定比例作为保费缴纳到自己的养老金账户,基金经理将保费投资于一个无风险资产,一支股票和一支通胀指数债券以使养老金保值增值.其中股票预期收益率是随机的,并遵循均值回复过程,但基金经理无法直接观测.由于考虑了保费返还条款,则在累积期间死亡的参与者可提取按预先设定利率累积的保费.基金经理的决策目标是使每个幸存参与者养老金的终端价值期望最大化,并最小化终端价值的方差.利用滤波技术和纳什均衡框架,文章得到了DC养老金均衡策略和均衡值函数的解析式.最后,数值算例表明保费返还条款和信息损失都会使基金经理对风险投资更谨慎,但是保费返还条款对通胀指数债券均衡策略的影响更显著,而信息损失对股票均衡策略的影响更显著.     

Asset allocation under loss aversion and minimum performance constraint in a DC pension plan with inflation risk

In this paper we investigate an optimal investment strategy for a defined-contribution (DC) pension plan member who is loss averse, pays close attention to inflation and longevity risks and requires a minimum performance at retirement. The member aims to maximize the expected S-shaped utility from the terminal wealth exceeding the minimum performance by investing her wealth in a financial market consisting of an indexed bond, a stock and a risk-free asset. We derive the optimal investment strategy in closed-form using the martingale approach. Our theoretical and numerical results reveal that the wealth proportion invested in each risky asset has a V-shaped pattern in the reference point level, while it always increases in the rising lifespan; with a positive correlation between salary and inflation risks, the presence of salary decreases the member’s investment in risky assets; the minimum performance helps to hedge the longevity risk by increasing her investment in risky assets.     

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.     

基于Stein-Stein波动率和动态VaR约束下DC型养老基金的最优投资策略

研究了确定缴费型养老基金在退休前累积阶段的最优资产配置问题.假设养老基金管理者将养老基金投资于由一个无风险资产和一个价格过程满足Stein-Stein随机波动率模型的风险资产所构成的金融市场.利用随机最优控制方法,以最大化退休时刻养老基金账户相对财富的期望效用为目标,分别获得了无约束情形和受动态VaR (Value at Risk)约束情形下该养老基金的最优投资策略,并获得相应最优值函数的解析表达形式.最后通过数值算例对相关理论结果进行数值验证并考察了最优投资策略关于相关参数的敏感性.     

奈特不确定下带通胀的跨国直接投资问题

本文研究了一家公司在含糊下带通胀的跨国直接投资(FDI)问题.利用Ito公式推导出含糊下考虑通胀因素的消费篮子价格动力学方程.结合公司进行跨国投资决策时需要缴纳的法人税,给定了跨国直接投资的价值,并在通胀折现的跨国直接投资价值最大化标准下,分析了公司进行(不可逆)跨国直接投资的最优时间,通过解HJB方程推导出了公司由出口转向跨国直接投资时的最优GDP水平.通过进行数值模拟,定量分析了通胀因素对公司跨国直接投资策略的影响.     

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.     

随机利率及随机收益保证下的投资策略

考虑随机利率环境及随机收益保证下基金经理的投资组合问题。利用鞅方法,得到了最优投资策略的显性解。结论表明,最优投资策略包括三个部分：投机策略、利率套期保值策略以及随机收益保证的复制策略,且该最优策略等价于将一部分资金投资于确保终端时刻获得最低收益的基准组合,而剩余资金则依照无保证情况下的最优策略进行投资。     

Optimal investment of DC pension plan under short-selling constraints and portfolio insurance

In this paper we investigate an optimal investment problem under short-selling and portfolio insurance constraints faced by a defined contribution pension fund manager who is loss averse. The financial market consists of a cash bond, an indexed bond and a stock. The manager aims to maximize the expected S-shaped utility of the terminal wealth exceeding a minimum guarantee. We apply the dual control method to solve the problem and derive the representations of the optimal wealth process and trading strategies in terms of the dual controlled process and the dual value function. We also perform some numerical tests and show how the S-shaped utility, the short-selling constraints and the portfolio insurance impact the optimal terminal wealth.     

Nash equilibrium strategies for a defined contribution pension management

This paper studies the time-consistent investment strategy for a defined contribution (DC) pension plan under the mean–variance criterion. Since the time horizon of a pension fund management problem is relatively long, two background risks are taken into account: the inflation risk and the salary risk. Meanwhile, there are a risk-free asset, a stock and an inflation-indexed bond available in the financial market. The extended Hamilton–Jacobi–Bellman (HJB for short) equation of the equilibrium value function and the verification theorem corresponding to our problem are presented. The closed-form time-consistent investment strategy and the equilibrium efficient frontier are obtained by stochastic control technique. The effects of the inflation and stochastic income on the equilibrium strategy and the equilibrium efficient frontier are illustrated by mathematical and numerical analysis. Finally, we compare in detail the time-consistent results in our paper with the pre-commitment one and find the distinct properties of these two results.