Existing pay-as-you-go (PAYG) schemes based on notional accounts (NAs) have chosen the defined-contribution (DC) setting that forces the rate of interest credited to all individual accounts to change over time to ensure solvency. On the other hand, volatility of the rate of interest is the source of non-negligible disparities of individual internal rates of return (IRRs) both within and across generations. It is argued that these disparities represent a threat to the political appeal of PAYG DC systems, in particular in the present situation characterized by low growth rates of the contribution base. The paper uses a four-overlapping-generations model to prove that the DC setting is not a necessary ingredient of NAs and that their political appeal could be enhanced by extending their use to non-DC pension systems. In fact, redistributions can be avoided by crediting all individual accounts with a constant rate of interest while ensuring financial solvency by fine-tuning of the contribution rate to make the system's revenues grow at the same (constant) rate credited to all accounts. The proof requires constancy of the employment growth rate but not of average earnings. Changes in the employment growth rate produce small oscillations around perfect balance between contribution revenue and pension expenditure manageable with a small buffer fund.

We consider a profitable, risky setting with two separate, correlated asset and liability processes (first introduced by Gerber and Shiu, 2003). The company that is considered is allowed to distribute excess profits (traditionally referred to as dividends in the literature), but is regulated and is subject to particular regulatory (solvency) constraints. Because of the bivariate nature of the surplus formulation, such distributions of excess profits can take two alternative forms. These can originate from a reduction of assets (and hence a payment to owners), but also from an increase of liabilities (when these represent the wealth of owners, such as in pension funds). The latter is particularly relevant if distributions of assets do not make sense because of the context, such as in regulated pension funds where assets are locked until retirement. In this paper, we extend the model of Gerber and Shiu (2003) and consider recovery requirements for the distribution of excess funds. Such recovery requirements are an extension of the plain vanilla solvency constraints considered in Paulsen (2003), and require funds to reach a higher level of funding than the solvency level (if and after it is triggered) before excess funds can be distributed again. We obtain closed-form expressions for the expected present value of distributions (asset decrements or liability increments) when a distribution barrier is used.

In this paper, we review changes in the insurance industry due to new risk-based regulations such as Solvency 2 and Swiss Solvency Test. The move from corporate management based on cash-flow to risk-based management is described and discussed through its consequences on capital management, economic valuation and the internal model. We discuss the limits and difficulties of enterprise risk management and its effect on the organisation of companies and the role of actuaries in insurance. The risk/return relation is becoming a central element of the company’s management slowly supplanting the traditional accounting view.

The European-centric Solvency II and Australian-centric Life and General Insurance Capital regimes are two examples of risk-based approaches to capital determination and risk management for life insurers. Both consist of a three-pillar structure covering capital, risk management and disclosure requirements. We apply the capital requirements of each regime to three synthetic sets of insurance policies, including a risk, annuity and combined portfolios, and consider the impact on capital arising from three separate and relatively severe stress events. Results highlight the relatively capital intensive nature of annuities, the differences between different capital regimes, the significance of solvency II’s matching adjustment and the robustness of each regime to both pandemic and economic stresses. Results also highlight the nature of diversification benefits from within each capital regime, on overall capital requirements.

In the New South Wales Supreme Court decision of Anglican Development Fund Diocese of Bathurst v Palmer in December 2015, a single judge of the court held that a large amount of money which had been lent to institutions in the Anglican Diocese of Bathurst, and guaranteed by a letter of comfort issued by the then bishop of the diocese, had to be repaid by the bishop-in-council, including (should it be necessary) levying the necessary funds from the parishes. The lengthy judgment contains a number of interesting comments on the legal personality of church entities and may have long-term implications (and not merely in Australia) for unincorporated, mainstream denominations and their contractual and tortious liability to meet orders for payment of damages. The article discusses the decision and some of those implications.

The life annuity business is heavily exposed to longevity risk. Risk transfer solutions are not yet fully developed, and when available they are expensive. A significant part of the risk must therefore be retained by the life insurer. So far, most of the research work on longevity risk has been mainly concerned with capital requirements and specific risk transfer solutions. However, the impact of longevity risk on shareholder value also deserves attention. While it is commonly accepted that a market-consistent valuation should be performed in this respect, the definition of a fair shareholder value for a life insurance business is not trivial. In this paper, we develop a multi-period market-consistent shareholder value model for a life annuity business. The model allows for systematic and idiosyncratic longevity risk and includes the most significant variables affecting shareholder value: the cost of capital (which in a market-consistent setting must be quantified in terms of frictional and agency costs, net of the value of the limited liability put option), policyholder demand elasticity and the cost of alternative longevity risk management solutions, namely indemnity-based and index-based solutions. We show how the model can be used for assessing the impact of different longevity risk management strategies on life insurer shareholder value and solvency.

We show how estimators for the chain ladder prediction error in Mack's (1993) distribution-free stochastic model can be derived using the error propagation formula. Our method allows for the treatment of the general case of the prediction error of the loss development result between two arbitrary future horizons. In the well-known special cases considered previously by Mack (1993) and Merz and Wüthrich (2008), our estimators coincide with theirs. However, the algebraic form in which we cast them is new, considerably more compact and more intuitive to understand. For example, in the classical case treated by Mack (1993), we show that the mean squared prediction error divided by the squared estimated ultimate loss can be written as ∑jû2j, where ûj measures the (relative) uncertainty around the jth development factor and the proportion of the estimated ultimate loss that it affects. The error propagation method also provides a natural split into process error and parameter error. Our proofs identify and exploit symmetries of “chain ladder processes” in a novel way. For the sake of wider practical applicability of the formulae derived, we allow for incomplete historical data and the exclusion of outliers in the triangles.

With the advent of formal regulatory requirements for rigorous risk-based, or economic, capital quantification for the financial risk management of banking and insurance sectors, regulators and policy-makers are turning their attention to the pension sector, the other integral player in the financial markets. In this paper, we analyse the impact of applying economic capital techniques to defined benefit pension schemes in the United Kingdom. We propose two alternative economic capital quantification approaches, first, for individual defined benefit pension schemes on a stand-alone basis and then for the pension sector as a whole by quantifying economic capital of the UK’s Pension Protection Fund, which takes over eligible schemes with deficit, in the event of sponsor insolvency. We find that economic capital requirements for individual schemes are significantly high. However, we show that sharing risks through the Pension Protection Fund reduces the aggregate economic capital requirement of the entire sector.

In this paper, we develop a theoretical basis for drawing up a “Swedish” type actuarial balance sheet for a defined benefit pay-as-you-go (DB PAYG) scheme with retirement and disability benefits. Our model enables us to obtain the system's expected average turnover duration, measure the scheme's solvency and explore the phenomenon identified as “pension reclassification”, a widespread practice that masks the system's real status unless further pension information becomes available. The model is clearly linked to actuarial practice in social security and gives partial support to the practical adaptation of Swedish methodology carried out by OSFI (2012) in applying the concept of the contribution asset to the Canadian Pension Plan (CPP) balance sheet, which includes disability and survivor benefits.

The aim of this paper is to make an assessment of the 2011 reform of the public pension system in Spain using the Swedish pension system as a benchmark, although some reference to the US pension system is also made. The paper focuses on the reform, explaining its aims, breaking down the main contents, critically examining the official view and describing the expected ageing of the Spanish population. This approach complements the quantitative analyses performed by other researchers and will enable us to assess the reformed system with the focus on four main areas: actuarial fairness, actuarial transparency, solvency and communication with the public. The main conclusion is that the reform was a wasted opportunity given that Spain did not take advantage of the lessons learned in Sweden, it did not include any elements for improving the management of pay-as-you-go systems, and there is no sound basis for claiming that the system's sustainability is assured in the medium term, the long term or even the short term. The new parametric reforms currently under consideration in Spain are targeted to correct some of the pension system's design faults that have been highlighted in this paper.

Stochastic modeling of mortality/longevity risks is necessary for internal models of (re)insurers under the new solvency regimes, such as Solvency II and the Swiss Solvency Test. In this paper, we propose a mortality model which fulfills all requirements imposed by these regimes. We show how the model can be calibrated and applied to the simultaneous modeling of both mortality and longevity risk for several populations. The main contribution of this paper is a stochastic trend component which explicitly models changes in the long-term mortality trend assumption over time. This allows to quantify mortality and longevity risk over the one-year time horizon prescribed by the solvency regimes without relying on nested simulations. We illustrate the practical ability of our model by calculating solvency capital requirements for some example portfolios, and we compare these capital requirements with those from the Solvency II standard formula.

This paper provides a detailed quantitative assessment of the impact of capital and default probability on product pricing and shareholder value for a life insurer providing life annuities. A multi-period cash flow model, allowing for stochastic mortality and asset returns, imperfectly elastic product demand, as well as frictional costs, is used to derive value-maximizing capital and pricing strategies for a range of one-year default probability levels reflecting differences in regulatory regimes including Solvency II. The model is calibrated using realistic assumptions. The sensitivity of results is assessed. The results show that value-maximizing life insurers should target higher solvency levels than the Solvency II regulatory one-year 99.5% probability under assumptions of reasonable levels of policyholder's aversion to insolvency risk. Even in the case of less restrictive solvency probabilities, policyholder price elasticity and solvency preferences are shown to be important factors for a life insurer's value-maximizing strategy.

The Management Board of the UK Actuarial Profession is undertaking a thought leadership cross-practice research project on the use of discount rates by UK actuaries. The timing for this research is particularly appropriate as there is a convergence of interest in discount rates from within and outside of the Profession. Discount rates are at the heart of most actuarial calculations and are of significant public interest. As part of this project the Management Board wants a full and open debate on the significant issues and this paper is the next step in stimulating that debate, giving another opportunity to influence the future direction of the project.

The Management Board set up a small cross-practice steering committee to drive the project. The Discount Rate Steering Committee identified five areas of work that would be needed to achieve the project's overall objectives:

1. (1) A survey of current practices.

2. (2) A survey of existing research and debate.

3. (3) Developing a common language for communicating discount rates and risk.

4. (4) Developing a common framework for the future where appropriate.

5. (5) Considering the impact of any changes.

Although the Profession does not set standards for technical work it still has a significant role for undertaking research in the public interest which supports the competence of its members and the furtherance of actuarial science.

Chinu Patel and Chris Daykin were commissioned to undertake the first part of this work and they presented their preliminary output at a forum of thought leaders across the Profession and externally on 23 March 2010. Their report “Actuaries and Discount Rates” was subsequently published in May 2010 and presented the results of their initial research into past and current practice in the setting of discount rates in the UK, and a survey of existing research and debate. A summary of that report is included in Section 2 of this paper.

Following consultation both within and outside the Actuarial Profession, this interim paper now takes forward the ideas and initial steps developed by Patel & Daykin and looks at developing a common language and framework for using discount rates in actuarial work. The Discount Rate Steering Committee is making a number of recommendations to the Profession which are intended to help actuaries speak clearly and with authority in future debates about discount rates and to support actuaries in communicating impartially and effectively. The recommendations are set out in Section 6 of the report following the development of the framework in Sections 3–5. As part of further developing the recommendations to the Profession, the Discount Rate Steering Committee is seeking views from stakeholders from inside and outside of the Profession. This will be undertaken throughout January and February 2011 and, as part of this process, the report will be presented at sessional research events in Edinburgh (17 January 2011) and London (31 January 2011). The Discount Rate Steering Committee is committed to seeking feedback on the recommendations and hopes this paper will give those inside and outside the Profession an opportunity to add to the dialogue so that as wide a range of potential views as possible is heard.

In this paper, the steering committee has concentrated on the more technical aspects of developing a framework for communicating discount rates and associated risks and the report is aimed primarily at actuaries. But the committee is mindful of the need to help actuaries communicate more clearly with those outside the Profession. During the first half of 2011, the steering committee will therefore concentrate on producing a document in less technical language to help non-actuaries understand the issues around the selection and use of discount rates and to help actuaries in their communication with stakeholders.

This article considers the amount of economic capital that defined benefit (DB) pension schemes potentially need to cover the risks they are running. A real open scheme, the Universities Superannuation Scheme, is modelled and used to illustrate our results and, as expected, economic capital requirements are large. We discuss the appropriateness of these results and what they mean for the DB pension scheme industry and their sponsors. The article is particularly pertinent following the recent European Commission Green Paper on the future of European pensions systems, its call for advice on reviewing the Institutions for Occupational Retirement Provision Directive and the introduction of the Basel 2 and Solvency 2 risk-based regulatory regimes for banking and insurance, respectively.

This paper looks at the problems of assessing, for solvency purposes, the capital requirements of a non-life insurer in the context of the United Kingdom. It considers how these capital requirements might vary according to the different risks to which an insurer is subject and how this Risk-Based Capital (RBC) might be measured in practice, using as a case study the RBC formula recently introduced in the United States of America. The paper also discusses the application of RBC concepts to the problem of internal capital allocation, to assist in measuring an insurer's rate of return to shareholders by business unit, as well as the more obvious regulatory application. The advantages and disadvantages of a formula-based approach to capital requirements for solvency purposes are discussed in comparison with possible alternative approaches to insurance supervision.

This paper explores an approach to assessing the adequacy of capital resources for non-life insurance companies. It examines the range of risks faced by these companies and the factors that influence the analysis of their impact on an organisation's financial condition. The paper considers how the actuarial profession may contribute to this process, with particular reference to the regulatory regime envisaged in the United Kingdom.

The theoretical basis for, and practical application of, the discounted income method for valuing UK pension fund assets is discussed, with particular reference to the widely adopted application to variable income (equity type) assets, as proposed by Day & McKelvey (1964), in the context of both the management and compliance objectives of pension fund valuation. An alternative methodology is proposed in which consistency with assets, liabilities, and market values is demanded, with smoothing of the valuation result achieved on an explicit rather than implicit basis. It is then demonstrated that the explicit smoothing parameter can be set so as to achieve the historic smoothness framework for establishing pension fund investment policy.

In conclusion the paper suggests greater emphasis on market-related methodologies for compliance valuations and leaves open the choice of methodology for management valuations and monitoring purposes, on the grounds that there is a large subjective element in any realistic basis. However, it is demonstrated that while smoother than unadjusted market-related methods, other aspects of the dynamics of the funding level under the method of Day & McKelvey can be perverse and it is suggested that this method should not be allowed to dictate investment decisions.