scholarly journals A note on Gollier's model for a collective pension scheme

2020 ◽  
pp. 1-25
Author(s):  
Johannes M. Schumacher
Keyword(s):  
Risk Sharing ◽  
Infinite Horizon ◽  
Effective Rate ◽  
Pension Scheme ◽  
Black Scholes ◽  
Investment Returns ◽  
Relative Attractiveness ◽  
Participation Constraint ◽  
Ownership Rights ◽  
The Impact

Abstract Gollier proposed in 2008 a model for the analysis of pension schemes that is helpful to focus attention on the impact of intergenerational risk sharing and on the role of the participation constraint. He uses the model to analyze the relative attractiveness of a collective scheme with respect to schemes that may be implemented by individuals for themselves. The analysis makes use of an assumption concerning the ownership rights of investment returns realized by generations that are between career start and retirement at the time of the transition from an individual to a collective system. The present paper investigates the consequences of adopting an alternative assumption. In a calibration exercise, the increase of the effective rate of return obtained by switching from an existing ‘autarky’ scheme to an infinite-horizon ‘collective’ scheme is found to be 8 basis points, as opposed to 72 basis points as reported by Gollier. Additionally, the effects are considered of changes in the specification of agents' preferences, aiming to express the specific nature of retirement income provision in the second pillar. The Black–Scholes assumptions are used to model the economic environment, so that many results can be obtained in closed form.

Causes of defined benefit pension scheme funding ratio volatility and average contribution rates

2011 ◽  
Vol 6 (1) ◽  
pp. 76-102 ◽  
Author(s):  
Adam Butt
Keyword(s):  
Asset Allocation ◽  
Demographic Factors ◽  
Pension Scheme ◽  
Defined Benefit ◽  
Equity Investment ◽  
Investment Returns ◽  
Typical Scheme ◽  
Mortality Improvement ◽  
The Impact ◽  
Average Contribution

AbstractSimulations of a model pension scheme are run with stochastic economic and demographic factors, with an aim to investigate the impact of these factors on movements in funding ratio and average contribution rates. These impacts are analysed by running regressions of movements in funding ratio and average contribution rates against the economic and demographic factors. It is found that, for a typical scheme closed to new entrants and a balanced asset allocation including equity investment, the mismatch between discount rate movements and investment returns is by far the biggest predictor of funding ratio movements, with average contribution rates affected more by events in a few individual years rather than averaged over an entire simulation. Where the scheme invests to cash-flow match liabilities, mortality improvement becomes the most significant predictor of funding ratio movements, although mortality improvement still has little impact on average contribution rates.

Pension Reform in Russia: Assessing the Susceptibility of GDP Production to a Shift in the Number of the Working-Age Population

2019 ◽  
pp. 80-86
Author(s):  
T. P. Skufina ◽  
S. V. Baranov
Keyword(s):  
Pension Reform ◽  
Fixed Capital ◽  
Economic Effects ◽  
Pension Scheme ◽  
Retirement Age ◽  
Working Age ◽  
Working Age Population ◽  
Long Term Forecasting ◽  
The Impact

The presented study considers the susceptibility of gross domestic product (GDP) production to a shift in the number of the working-age population due to an increase in retirement age starting with 2019.Aim. The study aims to examine the quantitative assessments of GDP production in Russia with allowance for the changes in the number of the working-age population due to an increase in the actual retirement age.Tasks. The authors forecast the number of the working-age population with allowance for an increase in the retirement age; develop a model to establish a correlation between the number of the workingage population, investment in fixed capital, and GDP production; quantify the impact of the shift in the number of the working-age population on GDP production in Russia. Methods. This study is based on the results of modeling and long-term forecasting.Results. An economic-mathematical model to establish a correlation between the number of the working-age population, investment in fixed capital, and GDP production is presented. To specify the economic effects of a shift in the number of the working-age population due to an increase in the retirement age, Russia’s GDP production is forecasted for the “old” and “new” (increased retirement age) pension scheme. The forecast is provided for three variants of the number of the working-age population.Conclusions. It is found that with the “old” pension scheme with a lower retirement age GDP production across all three variants will decrease by 2036 compared to 2017. With regard to the “new” scheme that increases the retirement age, it is concluded that an increase in the retirement age is a factor that facilitates GDP production. However, its effect on economic growth will be insignificant.

scholarly journals How Risky Is That Risk Sharing Agreement? Mean-Variance Tradeoffs and Unintended Consequences of Six Common Risk Sharing Agreements

2021 ◽  
Vol 6 (1) ◽  
pp. 238146832199040
Author(s):  
Gregory S. Zaric
Keyword(s):  
Risk Sharing ◽  
Financial Risk ◽  
Unintended Consequences ◽  
Drug Costs ◽  
New Drugs ◽  
Total Drug ◽  
Number Of Patients ◽  
Clinical Benefits ◽  
The Impact ◽  
Mean Variance

Background. Pharmaceutical risk sharing agreements (RSAs) are commonly used to manage uncertainties in costs and/or clinical benefits when new drugs are added to a formulary. However, existing mathematical models of RSAs ignore the impact of RSAs on clinical and financial risk. Methods. We develop a model in which the number of patients, total drug consumption per patient, and incremental health benefits per patient are uncertain at the time of the introduction of a new drug. We use the model to evaluate the impact of six common RSAs on total drug costs and total net monetary benefit (NMB). Results. We show that, relative to not having an RSA in place, each RSA reduces expected total drug costs and increases expected total NMB. Each RSA also improves two measures of risk by reducing the probability that total drug costs exceed any threshold and reducing the probability of obtaining negative NMB. However, the effects on variance in both NMB and total drug costs are mixed. In some cases, relative to not having an RSA in place, implementing an RSA can increase variability in total drug costs or total NMB. We also show that, for some RSAs, when their parameters are adjusted so that they have the same impact on expected total drug cost, they can be rank-ordered in terms of their impact on variance in drug costs. Conclusions. Although all RSAs reduce expected total drug costs and increase expected total NMB, some RSAs may actually have the undesirable effect of increasing risk. Payers and formulary managers should be aware of these mean-variance tradeoffs and the potentially unintended results of RSAs when designing and negotiating RSAs.

scholarly journals The cult of the equity for pension funds: should it get the boot?

2005 ◽  
Vol 4 (1) ◽  
pp. 57-85 ◽  
Author(s):  
CHARLES SUTCLIFFE
Keyword(s):  
Asset Allocation ◽  
Risk Sharing ◽  
Pension Scheme ◽  
Defined Benefit ◽  
Turn Of The Millennium ◽  
Equity Prices ◽  
Risk Return ◽  
History Of ◽  
Complete Rejection ◽  
The Uk

Over the last half century UK defined benefit pension schemes have followed the cult of the equity by investing a large proportion of their assets in equities. However, since the turn of the millennium this cult has faced two serious challenges – the halving of equity prices, and the complete rejection of equity investment by the Boots pension scheme in 2001. This paper summarises the history of the cult in the UK and the arguments advanced at the time to support its adoption. It then presents the case for the cult (excluding taxation, risk sharing and default insurance). This is followed by a detailed consideration of the validity of this case, including an examination of the relevant empirical evidence. It is concluded that, in the absence of taxation, risk sharing and default insurance, the asset allocation is indeterminate; and depends on the risk-return preferences adopted by the trustees.

scholarly journals DC Pension Plan with Refund of Contributions under Affine Interest Rate Model

2020 ◽  
pp. 1-16
Author(s):  
Udeme O. Ini ◽  
Obinichi C. Mandah ◽  
Edikan E. Akpanibah
Keyword(s):  
Interest Rate ◽  
Optimal Investment ◽  
Hjb Equation ◽  
Pension Scheme ◽  
Theoretic Approach ◽  
Rate Model ◽  
Risky Assets ◽  
Investment Plan ◽  
Interest Rate Model ◽  
The Impact

This paper studies the optimal investment plan for a pension scheme with refund of contributions, stochastic salary and affine interest rate model. A modified model which allows for refund of contributions to death members’ families is considered. In this model, the fund managers invest in a risk free (treasury) and two risky assets (stock and zero coupon bond) such that the price of the risky assets are modelled by geometric Brownian motions and the risk free interest rate is of affine structure. Using the game theoretic approach, an extended Hamilton Jacobi Bellman (HJB) equation which is a system of non linear PDE is established. Furthermore, the extended HJB equation is then solved by change of variable and variable separation technique to obtain explicit solutions of the optimal investment plan for the three assets using mean variance utility function. Finally, theoretical analyses of the impact of some sensitive parameters on the optimal investment plan are presented.

14. Investment

2019 ◽  
pp. 320-343
Author(s):  
Gary Watt
Keyword(s):  
Portfolio Theory ◽  
Capital Gains ◽  
Investment Policy ◽  
Legal Knowledge ◽  
Modern Portfolio Theory ◽  
General Law ◽  
Appropriate Care ◽  
Key Points ◽  
Investment Returns ◽  
The Impact

Without assuming prior legal knowledge, books in the Directions series introduce and guide readers through key points of law and legal debate. Questions, diagrams and exercises help readers to engage fully with each subject and check their understanding as they progress. Part II of the Trustee Act 2000 gives every trustee the power to make any kind of investment as long as he is absolutely entitled to the assets of the trust, a power that permits trustees to hold investments jointly or in common with other persons. There are no unauthorised types of investment, but it is important to know whether the type of investment chosen was appropriate to the trust on the basis of the ‘standard investment criteria’. This chapter examines the types of investment permitted by the general law, a breach of the duty to invest with appropriate care, the significance of modern portfolio theory to trustee investments and the impact of the Trustee Act 2000 upon trustee investments. It also looks at the historical need for income production and discusses capital gains as investment returns, the standard investment criteria, the need for trustees to obtain and consider proper advice about investments, particular types of investment and investment policy.

The Impact of National Insurance Act, 1959, on Private Pension Schemes

1961 ◽  
Vol 16 (04) ◽  
pp. 233-260
Author(s):  
T. Hugh Beech
Keyword(s):  
Subject Matter ◽  
Present Situation ◽  
Pension Scheme ◽  
Private Pensions ◽  
Contracting Out ◽  
Pension Schemes ◽  
National Insurance ◽  
History Of ◽  
The Subject ◽  
The Impact

Can the National Pension Scheme as a whole now be expected to maintain solvency? On what lines may the Scheme be expected to develop in the future? Should contracting out not have been permitted?The temptation to go into these and other fascinating questions will be resisted as far as possible; it is proposed instead to confine the subject matter of this paper reasonably closely within the area implied in the title. In order to establish the context in which the present situation has arisen, it is appropriate, however, to begin with a very brief survey of the more recent history of national and private pensions in Britain before the passing of the National Insurance Act 1959, which will be referred to henceforward simply as ‘the Act’; the situation before the Act comes into operation will similarly be referred to as ‘pre-Act’. When the Act comes into operation two new situations will arise; ‘Contracted-in’ and ‘Contracted-out’. There are thus three conditions to consider, and as far as possible when using expressions in connexion with contracting out such as saving, extra cost, etc., it will be stated whether these are by comparison with the contracted-in or pre-Act position, lack of clarity on this point having been a source of confusion in some of the literature on the subject.

scholarly journals The impact of the Chebyshev collocation method on solutions of the time-fractional Black–Scholes

2020 ◽  
Author(s):  
H. Mesgarani ◽  
A. Beiranvand ◽  
Y. Esmaeelzade Aghdam
Keyword(s):  
Collocation Method ◽  
Linear Interpolation ◽  
Stability And Convergence ◽  
Finite Domain ◽  
European Options ◽  
Chebyshev Collocation Method ◽  
Chebyshev Collocation ◽  
Black Scholes ◽  
Temporal Derivative ◽  
The Impact

AbstractThis paper presents a numerical solution of the temporal-fractional Black–Scholes equation governing European options (TFBSE-EO) in the finite domain so that the temporal derivative is the Caputo fractional derivative. For this goal, we firstly use linear interpolation with the $$(2-\alpha)$$ ( 2 - α ) -order in time. Then, the Chebyshev collocation method based on the second kind is used for approximating the spatial derivative terms. Applying the energy method, we prove unconditional stability and convergence order. The precision and efficiency of the presented scheme are illustrated in two examples.

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