The paper addresses some of the practical and theoretical issues raised by the move to a market consistent calculation of realistic liabilities and solvency capital for with-profits business. It also proposes some changes to the presentation of the realistic balance sheet, which the authors believe will provide greater transparancy, and more closely reflect the way in which with-profits business should be managed in future.

The focus of the paper is non-profit lifetime annuities in the UK. Annuity insurers have been faced with, or have initiated, an unprecedented amount of change during the last decade, and rapid change is still continuing. We draw out implications for the actuarial management of the business, arising from the evolution of: longevity risk assessment and management, investment strategy and operations, financial reporting, and enterprise risk management. We discuss Solvency II in some technical depth, analysing the proposed rules for technical provisions and solvency capital requirement.

The Management Board of the UK Actuarial Profession has identified enterprise risk management (ERM) as an area of growth, particularly within the financial sector. It is an area which offers opportunities for actuaries, working with other disciplines, to move out of their traditional sectors of employment, with the skill set required fitting well with an actuary's training and practical focus.

Members of the Profession also highlighted ERM as one of the two main areas where they wanted the Profession to focus their research efforts in the membership survey in 2009. Consequentially the Management Board allocated funds to support research projects in ERM in 2010–2011 and has worked with the ERM Practice Area Committee to identify the topics that they feel most suited to external research where the outputs will have a broad strategic value to the financial services sector.

Referring again to Art. 4 of Gompertz's treatise, let us denote by a0dx the actual probability of dying in the infinitely small time dx, at the initial age of the mortality table, and by axdx the abstract chance of death (in the time dx) at the end of x years; that is to say, the chance considered “independently of” (as Gompertz expresses it) or as “abstracted from” the deterioration resulting from increased age, then, according to Gompertz's law, the actual probability of dying, in the time dx, at the latter age will be axqxdx, in which expression q only is an arbitrary constant denoting the rate of deterioration. If, in axqxdx, we put x=0, it becomes a0dx, which coincides with the expression first assumed. Hence, Gompertz's law, which supposes that “the “vital force or recuperative power loses equal proportions in equal “times”, is expressed, in its general form, by the equation μxdx=axqxdx, or, which is the same thing, by μx=axqx.

Deep neural network models have substantial advantages over traditional and machine learning methods that make this class of models particularly promising for adoption by actuaries. Nonetheless, several important aspects of these models have not yet been studied in detail in the actuarial literature: the effect of hyperparameter choice on the accuracy and stability of network predictions, methods for producing uncertainty estimates and the design of deep learning models for explainability. To allow actuaries to incorporate deep learning safely into their toolkits, we review these areas in the context of a deep neural network for forecasting mortality rates.

The calculations which I have made respecting the rates of mortality in New South Wales are founded upon the returns of the Registrar-General for the years 1860-75, and upon two censuses taken in the years 1861 and 1871. There is every reason to believe that the returns of births and deaths are as accurate as can be expected in any case, and that the results of the censuses are as trustworthy as is usually the case. The returns for the year 1876 were not published when I commenced the calculations; and I have not gone farther back than 1860, because during the year before, Queensland with a considerable population was separated from New South Wales, producing of course an awkward break in the registrations.

When deriving a demographic basis from experience data it is useful to know (i) what uncertainty surrounds that basis, and (ii) the financial impact of that uncertainty. Under the Solvency II regime in the EU, insurers must hold capital against a number of risks. One of these is mis-estimation risk, i.e. the uncertainty over the current rates of mortality and other biometric risks experienced by a portfolio. We propose a general method for assessing mis-estimation risk, and by way of illustration we look at how mis-estimation risk can be assessed for a portfolio of pensions in payment from a UK pension scheme. We find that the impact of mis-estimation risk varies according to the risk factors included in a model, and that the inclusion of some necessary risk factors increases the financial impact of mis-estimation risk. In particular, the inclusion of risk factors which improve the model’s fit and financial applicability can lead to an increase in the mis-estimation risk. We also find that a full-portfolio valuation is preferable to using model points when assessing mis-estimation risk.

This paper takes an overview of the various financial risks which need to be managed in banking. It then looks in detail at the specific areas of operational risk, market risk and pricing loans. A cash flow model is then developed, which takes explicit account of the various financial factors which should influence the interest rate charged. The model is applied to price loans with various features. The results of the model are shown, and weaknesses in the model and possible areas for further work indicated.

Reserving is important to our profession as it is a core activity for actuaries. The members of the General Insurance Reserving Issues Taskforce (GRIT) have been considering how actuaries can improve the way in which we do reserving in general insurance. We gathered our thoughts and recommendations together in a Consultation Paper which has been discussed widely in the profession. We are very grateful to everyone who shared their views and comments with us, particularly those who gave us written feedback. We have considered carefully all the feedback which we received and adapted our final report in response to this.

Given the scope and importance of our remit, it is perhaps not surprising that this is not a short paper. We hope that Section 1 provides a reasonable summary.

Generally, our view is that there are many things on which our profession should focus. However, it is also important to remind ourselves of the positive items of feedback which we heard from our stakeholders. In addition to many suggestions for things to do better, we consistently heard the message that actuaries play an extremely valuable role in general insurance.

This is a major testimony to the progress which the actuarial profession has made in recent years in its ability to contribute to the general insurance industry. Perhaps it is because of this progress that now is an appropriate time for us, as a profession, to take a hard look at what we do in reserving, and ask ourselves whether there are any things which we could do differently. We hope that GRIT's report will facilitate this debate.

GRIT's recommendations fall under the following key themes:

— Providing more transparency to our reserving methods and helping our stakeholders have more insight into the key reserving assumptions and decisions.

— Providing more information on uncertainty in our reserve estimates. In particular, we recommend that actuaries provide a quantitative indication of the range of outcomes for future claim payments, and that our profession defines a common vocabulary for communicating uncertainty.

— Understanding better the business we are reserving. We suggest a range of analyses and activities for doing this.

— Applying our standard actuarial reserving methods more consistently. We identify a list of specific areas where we believe that there is scope for improvement. Also, we believe that the actuarial training syllabus should be extended, and this leads to consideration of whether a more specialised general insurance actuarial qualification is needed.

— Understanding the implications of the underwriting cycle, which, we believe, influences the behaviour of claims development in a way that our reserving models do not currently capture. We suggest what we believe may be the foundations of a potentially more cycle proof methodology, but this is an area which we believe will require much more research.

— Helping actuaries understand how behaviour can affect the reserve estimation process, particularly in the face of uncertainty. We make various suggestions in this area, including helping actuaries manage pressure from third parties.

We are convinced that, for our profession to implement these suggestions, it will require a concerted change management strategy and set of actions to embed changes into the way in which actuaries work. We believe that this will include:

— increasing the level of debate and research in the profession on claims reserving;

— a broader communication programme with the general insurance industry, covering, amongst other things, uncertainty and data quality;

— a sub-group of the GI Board with a specific focus on reserving, responsible for implementing GRIT's recommendations and dealing with new issues as they arise; and

— our profession resolving the conflicting pressures which will arise out of the extra work required for reserving by the GRIT recommendations.

There is one specific item where we have not made a recommendation. It has been suggested to us that many of the standard reserving methods in common use, such as the chain ladder, are not sophisticated, and that more sophisticated mathematical and statistical methods should be a priority. We do not agree with this. Whereas, in the longer term, this might be an important issue for our profession, we believe that the current focus for actuaries should be in the areas set out in this paper, such as understanding the business better.

GRIT believes that the issues which we have identified are important for the future of our profession and the contribution which we can make to the general insurance industry.

A well-known feature of the great H1N1 influenza pandemic of a century ago is that the highest mortality rate was amongst young adults. The general explanation has been that they died from an over-reaction of their active immune systems. This explanation has never been very satisfactory because teenagers also have very active immune systems. Recent virological research provides a new perspective, which is important for life and health insurers. There is now strong recent scientific evidence for the principle of antigenic imprinting, where the highest antibody response is against influenza virus strains from childhood. The peak ages of 1918 pandemic mortality correspond to a cohort exposed to the H3N8 1889–1890 Russian influenza pandemic. The vulnerability of an individual depends crucially on his or her exposure to influenza during their lifetime, especially childhood. Date of birth is thus a key indicator of pandemic vulnerability. An analysis of the implications is presented, with focus on those now in their fifties, who were exposed to the H3N2 1968 Hong Kong influenza.

The Age-Period-Cohort-Improvement (APCI) model is a new addition to the canon of mortality forecasting models. It was introduced by Continuous Mortality Investigation as a means of parameterising a deterministic targeting model for forecasting, but this paper shows how it can be implemented as a fully stochastic model. We demonstrate a number of interesting features about the APCI model, including which parameters to smooth and how much better the model fits to the data compared to some other, related models. However, this better fit also sometimes results in higher value-at-risk (VaR)-style capital requirements for insurers, and we explore why this is by looking at the density of the VaR simulations.

For life insurers in the United Kingdom (UK), the risk margin is one of the most controversial aspects of the Solvency II regime which came into force in 2016.

The risk margin is the difference between the technical provisions and the best estimate liabilities. The technical provisions are intended to be market-consistent, and so are defined as the amount required to be paid to transfer the business to another undertaking. In practice, the technical provisions cannot be directly calculated, and so the risk margin must be determined using a proxy method; the method chosen for Solvency II is known as the cost-of-capital method.

Following the implementation of Solvency II, the risk margin came under considerable criticism for being too large and too sensitive to interest rate movements. These criticisms are particularly valid for annuity business in the UK – such business is of great significance to the system for retirement provision. A further criticism is that mitigation of the impact of the risk margin has led to an increase in reinsurance of longevity risks, particularly to overseas reinsurers.

This criticism has led to political interest, and the risk margin was a major element of the Treasury Committee inquiry into EU Insurance Regulation.

The working party was set up in response to this criticism. Our brief is to consider both the overall purpose of the risk margin for life insurers and solutions to the current problems, having regard to the possibility of post-Brexit flexibility.

We have concluded that a risk margin in some form is necessary, although its size depends on the level of security desired, and so is primarily a political question.

We have reviewed possible alternatives to the current risk margin, both within the existing cost-of-capital methodology and considering a wide range of alternatives.

We believe that requirements for the risk margin will depend on future circumstances, in particular relating to Brexit, and we have identified a number of possible changes to methodology which should be considered, depending on circumstances.

Cyber Operational Risk: Cyber risk is routinely cited as one of the most important sources of operational risks facing organisations today, in various publications and surveys. Further, in recent years, cyber risk has entered the public conscience through highly publicised events involving affected UK organisations such as TalkTalk, Morrisons and the NHS. Regulators and legislators are increasing their focus on this topic, with General Data Protection Regulation (“GDPR”) a notable example of this. Risk actuaries and other risk management professionals at insurance companies therefore need to have a robust assessment of the potential losses stemming from cyber risk that their organisations may face. They should be able to do this as part of an overall risk management framework and be able to demonstrate this to stakeholders such as regulators and shareholders. Given that cyber risks are still very much new territory for insurers and there is no commonly accepted practice, this paper describes a proposed framework in which to perform such an assessment. As part of this, we leverage two existing frameworks – the Chief Risk Officer (“CRO”) Forum cyber incident taxonomy, and the National Institute of Standards and Technology (“NIST”) framework – to describe the taxonomy of a cyber incident, and the relevant cyber security and risk mitigation items for the incident in question, respectively.Summary of Results: Three detailed scenarios have been investigated by the working party:

• ∙ Employee leaks data at a general (non-life) insurer: Internal attack through social engineering, causing large compensation costs and regulatory fines, driving a 1 in 200 loss of £210.5m (c. 2% of annual revenue).

• ∙ Cyber extortion at a life insurer: External attack through social engineering, causing large business interruption and reputational damage, driving a 1 in 200 loss of £179.5m (c. 6% of annual revenue).

• ∙ Motor insurer telematics device hack: External attack through software vulnerabilities, causing large remediation / device replacement costs, driving a 1 in 200 loss of £70.0m (c. 18% of annual revenue).

• ∙ While the presented scenarios are deemed material at this point in time, the threat landscape moves fast and could render specific narratives and calibrations obsolete within a short-time frame.

• ∙ There is a lack of historical data to base certain scenarios on and therefore a high level of subjectivity is used to calibrate them.

• ∙ No attempt has been made to make an allowance for seasonality of renewals (a cyber event coinciding with peak renewal season could exacerbate cost impacts)

• ∙ No consideration has been given to the impact of the event on the share price of the company.

• ∙ Correlation with other risk types has not been explicitly considered.

The paper explores the framework for the development of actuarial education in the future. The main aims are to broaden the profession while maintaining standards and to achieve global qualifications by working with other actuarial bodies. The suggested way forward would mean several changes from existing practice.

It was in June 1931 that the Council honoured me with an invitation to submit a paper on this subject, the intention being that it should be read at the Ordinary Meeting in April 1932.

1.1. An earlier paper by the author has attempted to describe the theories of multi-state life tables and inhomogeneous Markov chains in their application to the study of morbidity as introduced by Pollard. It is the purpose of this paper to extend the model to describe the relationship between the incidence and prevalence of a disease. The implications of certain assumptions about the presence of mortality and of differentials in the level of mortality are also discussed.

For some while there has been a growing awareness from both internal and external stakeholders that the governance and risk management in United Kingdom (U.K.) insurance companies needed to be enhanced. The proposed European Union Solvency II Directive makes this very explicit and the current economic turmoil has put a much stronger emphasis on the whole process: it is being seen as the right thing to do, rather than simply a regulatory requirement. In this paper, we set out the background to and recent history of governance for U.K. insurance companies, and consider how enterprise risk management can bring together the various control frameworks needed to support that governance. Whilst no two companies are the same, and hence the solutions to these issues will vary, there are several common themes linked to successful implementation. Similarly, various barriers to success are identified, together with solutions to resolve them.

The term ‘investment risk’ is often used loosely, and frequently confused with the notion of short-term price volatility, particularly for equity instruments. For the long-term investor, however, what is most apposite is the ability to meet future real cash flows as they become due. This paper addresses the concept of economic fundamentals of long-term investment, the objectives of long-term investors (and how these differ from those of short-term investors), the notion of real value shortfall risk, what is meant by an investor’s risk capacity (as opposed to risk appetite) and liquidity management considerations. Subsequently, some of the constraints and barriers to appropriate risk measurement and management are considered, in particular the regulatory and behavioural biases that are overlaid on fundamental asset/liability management. Various alternative approaches to measuring risk, and their appropriateness for purpose, are outlined, in the hope of further informing the discussion and thereby helping to accelerate productive change.