基于不确定控制理论的最优策略研究

本文在不确定理论的框架下,研究一类带背景状态变量的最优控制模型.在乐观值准则下,利用不确定动态规划的方法,证明了不确定最优性原则,得到最优性方程.作为应用,求解一个固定缴费(DC)型养老金的最优投资策略问题,在乐观值准则下,以工资变量为背景状态变量,建立养老金模型.通过求解不确定最优性方程得到最优投资策略和最优支付率.     

基本养老保险缴费心理活动维度的实证研究:个人心理账户视角

本文从心理账户理论视角,通过问卷调查,运用非集计模型,对个人基本养老保险缴费心理活动维度进行了实证研究。研究结果表明,受教育程度、非常规的额外收入、经营性收入、安全型保障账户和风险型存储账户是影响缴费的关键性因素,进而提出引导设立特定缴费心理账户、增强缴费制度弹性,改变缴费者的选择框架, 提升缴费遵从度。     

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.     

Optimal investment strategies and risk-sharing arrangements for a hybrid pension plan

A continuous time stochastic model is used to study a hybrid pension plan, where both the contribution and benefit levels are adjusted depending on the performance of the plan, with risk sharing between different generations. The pension fund is invested in a risk-free asset and multiple risky assets. The objective is to seek an optimal investment strategy and optimal risk-sharing arrangements for plan trustees and participants so that this proposed hybrid pension system provides adequate and stable income to retirees while adjusting contributions effectively, as well as keeping its sustainability in the long run. These goals are achieved by minimizing the expected discount disutility of intermediate adjustment for both benefits and contributions and that of terminal wealth in finite time horizon. Using the stochastic optimal control approach, closed-form solutions are derived under quadratic loss function and exponential loss function. Numerical analysis is presented to illustrate the sensitivity of the optimal strategies to parameters of the financial market and how the optimal benefit changes with respect to different risk aversions. Through numerical analysis, we find that the optimal strategies do adjust the contributions and retirement benefits according to fund performance and model objectives so the intergenerational risk sharing seem effectively achieved for this collective hybrid pension plan.     

Multi-period defined contribution pension funds investment management with regime-switching and mortality risk

Using mean–variance criterion, we investigate a multi-period defined contribution pension fund investment problem in a Markovian regime-switching market. Both stochastic wage income and mortality risk are incorporated in our model. In a regime-switching market, the market mode changes among a finite number of regimes, and the market state process is modeled by a Markov chain. The key parameters, such as the bank interest rate, or expected returns and covariance matrix of stocks, will change according to the market state. By virtue of Lagrange duality technique, dynamic programming approach and matrix representation method, we derive expressions of efficient investment strategy and its efficient frontier in closed-form. Also, we study some special cases of our model. Finally, a numerical example based on real data from the American market sheds light on our theoretical results.     

Making demography relevant: The Canadian baby boom

The paper presents a model for teaching demography used at the University of Waterloo which requires student projects. Three projects are described in some detail. They are analyses of unemployment rates, future housing requirements in the Province of Ontario, and the need to modify the normal retirement age of 65 used in the Canada/Quebec Pension Plan.     

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.     

生态位视角下都市区村落养老价值评价体系研究

从生态位相关理论应用出发,基于生态位宽度、重叠度和密度解析村落养老价值的影响源和影响机制。在建立都市区村落养老行业系统的基础上,结合需求度调查,归纳了行业生态链中的生态元功能组成。并以影响源推导评价子系统,以生态元功能衍生出评价模块,从村落养老的时间位、空间位、功能位上的优势目标出发,构建了一个与生态位关联,由评价维度、价值子系统、模块、指标变量4个层级组成的都市区村落养老价值评价体系。此体系的研究立足于生态位对村落养老价值的影响机制和养老产业良性发展的适应性,为村落养老价值评价体系的构建提供了新视角,为村落发展养老产业的可行性判定提供了综合性方法。     

生态位视角下都市区村落养老价值评价体系研究

从生态位相关理论应用出发,基于生态位宽度、重叠度和密度解析村落养老价值的影响源和影响机制。在建立都市区村落养老行业系统的基础上,结合需求度调查,归纳了行业生态链中的生态元功能组成。并以影响源推导评价子系统,以生态元功能衍生出评价模块,从村落养老的时间位、空间位、功能位上的优势目标出发,构建了一个与生态位关联,由评价维度、价值子系统、模块、指标变量4个层级组成的都市区村落养老价值评价体系。此体系的研究立足于生态位对村落养老价值的影响机制和养老产业良性发展的适应性,为村落养老价值评价体系的构建提供了新视角,为村落发展养老产业的可行性判定提供了综合性方法。     

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.