Pension expectations as disincentives to job mobility

I address the measurement problem of the extent to which workers in an industry face disincentives to changing employment because of an interest in private pension benefits. I take an individual worker as the unit of analysis and represent job mobility over the work life by a time-varying point process. I treat the various plan types (pension systems) in a unified way through a general reward function (accumulated benefit function). By merging the employment termination process with this function, I derive two other benefit functions to measure the pension expectations of a worker from current and future employments. I then use these functions to construct a loss function that trades off the benefit gains and losses faced by a worker in a pension system at the time of a potential job change. I apply the methodology developed in the paper to the United States pension system, using data from the 1989 Survey of Consumer Finances. © 1997 by John Wiley & Sons, Ltd.     

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。     

Valuation of intergenerational transfers in funded collective pension schemes

This paper applies contingent claim analysis to value pension contracts for real-life collective pension plans with intergenerational risk sharing and offering DB-like benefits. We rewrite the balance sheet of such a pension fund as an aggregate of embedded generational options. This implies that a pension fund is a zero-sum game in value terms, so any policy change inevitably leads to value transfers between generations. We explore intergenerational value transfers that may arise from a plan redesign or from changes in funding policy and risk sharing rules. We develop a stochastic framework which accounts for time-varying investment opportunities and computes the embedded generational options. Changes in the values of the generational options enable us to evaluate the impact of policy modifications in the pension contract with respect to intergenerational transfers and redistribution. We find that a switch to a less risky asset mix is beneficial to elderly members at the expense of younger members who lose value. A reallocation of risk bearing from a plan with flexible contributions and fixed benefits to a plan with fixed contributions and flexible benefits leads to value redistribution from older plan members to younger ones.     

Stochastic pension funding when the benefit and the risky asset follow jump diffusion processes

We study the asset allocation of defined benefit pension plans of the type designed and sponsored by firms with the aim of providing a lifetime pension to the employees at the age of retirement. Benefits are stochastic, combining Poisson jumps with Brownian uncertainty. The sponsor dynamically forms portfolios where the risky asset is also subjected to Poisson jumps and Brownian uncertainty, possibly correlated with the evolution of benefits. The objective is to assure future benefits, while controlling the contribution made to the fund reserves. The problem is solved analytically using dynamic programming techniques.     

Optimal mix between pay-as-you-go and funding for DC pension schemes in an overlapping generations model

Public pension systems are usually pay-as-you-go financed, that is, current contributions cover the pension expenditures. However, some countries combine funding and pay-as-you-go within the first pillar. This article studies a mixed system where a part of the individual’s contribution accrues funded rights whereas the other part accrues pay-as-you-go rights. Diversification conditions between these two financing techniques are derived in a mean–variance framework for two distinct contexts: for a cohort entering the system (named ex-ante case) and for multiple cohorts coexisting at the same period of time (named ex-post case). The diversification benefits in presence of a liquidity constraint which ensures that the income from contributions is sufficient to cover the pension expenditures are also studied. We show that, on the one hand, diversification benefits individuals when the economy is dynamically efficient for the ex-ante case. On the other hand, diversification is unattractive when pay-as-ou-go and funding are positively correlated for the ex-post case.     

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.     

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.     

Optimal Dynamic Control for the Defined Benefit Pension Plans with Stochastic Benefit Outgo

Abstract

This work is devoted to a continuous time dynamic pension funding model in a defined benefit plan of an employment system. We extend the analysis of some standard models by incorporating a source of uncertainty in the benefit outgo. The key assumption is that the random benefits increase on average at an exponential rate. We model the preference of the manager with the main objective of minimizing both the contribution rate risk and the solvency risk. Two different situations are studied regarding the investment decisions. In the first case, the fund is invested at a constant, risk-free rate of interests; in the second case, the promoter invests in a portfolio with a risky asset and a risk-free bond. We provide, in both cases, explicit expressions for the actuarial liability, normal costs, value function, and the supplementary contribution rate.     

Managing contribution and capital market risk in a funded public defined benefit plan: Impact of CVaR cost constraints

Using a Monte Carlo framework, we analyze the risks and rewards of moving from an unfunded defined benefit pension system to a funded plan for German civil servants, allowing for alternative strategic contribution and investment patterns. In the process we integrate a Conditional Value at Risk (CVaR) restriction on overall plan costs into the pension manager’s objective of controlling contribution rate volatility. After estimating the contribution rate that would fully fund future benefit promises for current and prospective employees, we identify the optimal contribution and investment strategy that minimizes contribution rate volatility while restricting worst-case plan costs. Finally, we analyze the time path of expected and worst-case contribution rates to assess the chances of reduced contribution rates for current and future generations. Our results show that moving toward a funded public pension system can be beneficial for both civil servants and taxpayers.     

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.     

Pension scheme redesign and wealth redistribution between the members and sponsor: The USS rule change in October 2011

The redesign of defined benefit pension schemes usually results in a substantial redistribution of wealth between age cohorts of members, pensioners, and the sponsor. This is the first study to quantify the redistributive effects of a rule change by a real world scheme (the Universities Superannuation Scheme, USS) where the sponsor underwrites the pension promise. In October 2011 USS closed its final salary scheme to new members, opened a career average revalued earnings (CARE) section, and moved to ‘cap and share’ contribution rates. We find that the pre-October 2011 scheme was not viable in the long run, while the post-October 2011 scheme is probably viable in the long run, but faces medium term problems. In October 2011 future members of USS lost 65% of their pension wealth (or roughly £100,000 per head), equivalent to a reduction of roughly 11% in their total compensation, while those aged over 57 years lost almost nothing. The riskiness of the pension wealth of future members increased by a third, while the riskiness of the present value of the sponsor’s future contributions reduced by 10%. Finally, the sponsor’s wealth increased by about £32.5 billion, equivalent to a reduction of 26% in their pension costs.     

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．     

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.     

Dynamic project selection and funding under risk: A decision tree based MILP approach

This paper presents a mixed integer linear programming (MILP) model for a new class of dynamic project selection and funding problems under risk given multiple scarce resources of different qualifications. The underlying stochastic decision tree concept extends classical approaches mainly in that it adds a novel node type that allows for the continuous control of discrete branching probability distributions. The control functions are piecewise linear and are convex for the costs and concave for the benefits. The MILP-model has been embedded in a prototype Decision Support System (DSS). With respect to the proposed solution the DSS provides complete probability distributions for both costs and benefits.     

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.     

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.     

Sustainability of pension systems with voluntary participation

Motivated by declining support for mandatory participation in pension arrangements, we explore whether the intergenerational risk-sharing benefits that these arrangements offer suffice to ensure their survival when participation becomes voluntary. Funded systems with asset buffers are particularly interesting since these buffers make contributions more sensitive to financial returns. Equilibria are characterised by thresholds on the young’s willingness to contribute. Standard values for our parameters yield two such equilibria; only the one with the higher threshold is consistent with the initial young being prepared to start the system. An advancement relative to the related literature is that the equilibria feature a non-zero probability of collapse. Finally, we explore the social welfare maximising values for the pension parameters for various levels of uncertainty and risk aversion.     

Longevity risk in pension annuities with exchange options: The effect of product design

We consider defined benefit pension plans that, at retirement age, allow the participant to choose between a single life annuity and a joint and survivor annuity. We compare two plans that differ in terms of how pension rights are accrued. In one plan, the participant accrues the right to receive a single life annuity, and can exchange that annuity for an actuarially equivalent joint and survivor annuity at retirement date. The opposite holds in the other plan. We show that both plans are affected by longevity risk in two ways. First, the participants’ choices at retirement age affect the ratio of survivor benefits over single life benefits, and, therefore, affect the natural hedge potential that arises from combining single life and survivor annuities. Second, uncertainty in the rate at which the participant will be allowed to exchange one type of annuity for the other at retirement date induces uncertainty in the level of the nominal rights for single life and survivor annuities, respectively. We compare the two plans, and show that longevity risk is substantially lower in case rights are accrued in the form of a joint and survivor annuity.     

Equilibrium investment strategy for DC pension plan with default risk and return of premiums clauses under CEV model

This paper considers an optimal investment problem for a defined contribution (DC) pension plan with default risk in a mean–variance framework. In the DC plan, contributions are supposed to be a predetermined amount of money as premiums and the pension funds are allowed to be invested in a financial market which consists of a risk-free asset, a defaultable bond and a risky asset satisfied a constant elasticity of variance (CEV) model. Notice that a part of pension members could die during the accumulation phase, and their premiums should be withdrawn. Thus, we consider the return of premiums clauses by an actuarial method and assume that the surviving members will share the difference between the return and the accumulation equally. Taking account of the pension fund size and the volatility of the accumulation, a mean–variance criterion as the investment objective for the DC plan can be formulated, and the original optimization problem can be decomposed into two sub-problems: a post-default case and a pre-default case. By applying a game theoretic framework, the equilibrium investment strategies and the corresponding equilibrium value functions can be obtained explicitly. Economic interpretations are given in the numerical simulation, which is presented to illustrate our results.     

Cooperation in assembly systems: The role of knowledge sharing networks

Process improvement plays a significant role in reducing production costs over the life cycle of a product. We consider the role of process improvement in a decentralized assembly system in which a buyer purchases components from several first-tier suppliers. These components are assembled into a finished product, which is sold to the downstream market. The assembler faces a deterministic demand/production rate and the suppliers incur variable inventory costs and fixed setup production costs. In the first stage of the game, which is modeled as a non-cooperative game among suppliers, suppliers make investments in process improvement activities to reduce the fixed production costs. Upon establishing a relationship with the suppliers, the assembler establishes a knowledge sharing network – this network is implemented as a series of meetings among suppliers and also mutual visits to their factories. These meetings facilitate the exchange of best practices among suppliers with the expectation that suppliers will achieve reductions in their production costs from the experiences learned through knowledge sharing. We model this knowledge exchange as a cooperative game among suppliers in which, as a result of cooperation, all suppliers achieve reductions in their fixed costs. In the non-cooperative game, the suppliers anticipate the cost allocation that results from the cooperative game in the second stage by incorporating the effect of knowledge sharing in their cost functions. Based on this model, we investigate the benefits and challenges associated with establishing a knowledge sharing network. We identify and compare various cost allocation mechanisms that are feasible in the cooperative game and show that the system optimal investment levels can be achieved only when the most efficient supplier receives the incremental benefits of the cost reduction achieved by other suppliers due to the knowledge transfer.