To Sustain a Vital and Vibrant Actuarial Profession

Abstract

Insurance markets are different from most other markets. Insurance markets have an inherent self-destructive tendency that can cause market failure. However, insurance markets not only exist, they thrive. This paper explores the essential role that actuaries play in countering problems that can cause market failure. Armed with our mathematical and business skills and strong sense of professionalism, actuaries are essential to the successful growth of insurance companies and insurance markets. The breakdown of barriers among segments of the financial services industry creates an opportunity for actuaries to apply these same skills to noninsurance financial institutions. Actuaries have a strong claim to becoming the profession the public relies upon to ensure that an adequate balance is kept between profits and solvency. The foundation of this claim is not the superiority of our intellectual tools. It is the advantages to society of actuaries as a well-defined, recognized group of trustworthy and professional financial managers.     

Survival analysis of pension scheme mortality when data are missing

Missing data is a problem that may be faced by actuaries when analysing mortality data. In this paper we deal with pension scheme data, where the future lifetime of each member is modelled by means of parametric survival models incorporating covariates, which may be missing for some individuals. Parameters are estimated by likelihood-based techniques. We analyse statistical issues, such as parameter identifiability, and propose an algorithm to handle the estimation task. Finally, we analyse the financial impact of including covariates maximally, compared with excluding parts of the mortality experience where data are missing; in particular we consider annuity factors and mis-estimation risk capital requirements.     

Reference mortality K2004 of personal life insurance policies in Finland

This article presents the reference mortality model K2004 approved by the Actuarial Society of Finland and the technique that was implemented in developing it. Initially, I will present the historical development of individual mortality rates in Finland. Then, the requirements posed for a modern mortality modelling will be presented. Reference mortality model K2004 is based on total population mortality rates, which were adjusted to correspond with that portion of the population that has a life insurance policy. First, the model presents a margin of the observed life insurance mortality rate in the total population with a Lee-Carter method together with a forecast, where the downward trend in mortality rates is expected to continue at the rate illustrated since the 1960s. Then, the mortality rate has been adjusted into life insurance mortality per age so that it corresponds to the differences observed between total population and the portion of population that has a life insurance during 1991–2001. Finally, a cohort and gender-specific functional margin will be presented to obtained data.     

Outlier analysis and mortality forecasting: The United Kingdom and Scandinavian countries

The Lee-Carter model and its variants have been extensively employed by actuaries, demographers, and many others to forecast age-specific mortality. In this study, we use mortality data from England and Wales, and four Scandinavian countries to perform time-series outlier analysis of the key component of the Lee-Carter model – the mortality index. We begin by employing a systematic outlier detection process to ascertain the timing, magnitude, and persistence of any outliers present in historical mortality trends. We then try to match the identified outliers with imperative events that could possibly justify the vacillations in human mortality levels. At the same time, we adjust the effect of the outliers for model re-estimation. A new iterative model re-estimation method is proposed to reduce the chance of erroneous model specification. The empirical results indicate that the outlier-adjusted model could achieve more efficient forecasts of variables such as death rates and life expectancies. Finally, we point out that the Lee-Carter forecasts are especially vulnerable to outliers near the forecast origin, and discuss the potential limitations of the application of the Lee-Carter model to mortality forecasting.     

Loss Reserves and the Employment Status of the Appointed Actuary

Abstract

Property/casualty (P/C) insurers are required to establish loss reserves for unpaid losses at the time that the loss has occurred or is reasonably expected to have occurred. We examine factors that may impact the accurate setting of loss reserves. These include the level of rate regulation faced by the insurer and the incentives to underestimate or overestimate reserves to improve financial ratios or improve solvency scores, to reduce earnings, to defer taxes, or to smooth earnings volatility in order to meet shareholder expectations. The employment status of the Appointed Actuary, that is, whether the Appointed Actuary is an employee of the firm or a consultant, may also impact reserve accuracy. Using a variety of regression models with data from 1995 to 2010, we examine the impact of these factors on the accuracy of reserves posted by Canadian P/C insurers. Our results provide no evidence of systematic differences in the magnitude or direction of loss reserve errors between insurers that use company actuaries versus those that use consultant actuaries. However, we find that for both consultant and company actuaries positive reserve errors are associated with increases in global stock market returns and decreases in unanticipated inflation. The insurance market cycle impacts reserve errors for company actuaries and not consultant actuaries. As well, our results indicate that as the proportion of short-tailed business increases in a company, consultant actuaries are more likely to over-reserve. Similar to many previous studies using U.S. data, we do not find strong evidence regarding insurers’ incentives to deliberately overstate or understate reserves: Loss reserves are relatively unbiased estimates of the true losses paid. Thus these findings should be welcome news to the actuarial profession in Canada and to the prudential regulator: The Appointed Actuary, regardless of employment status, provides objective and unbiased estimates of insurers’ largest liability.     

Developing Mortality Improvement Formulas

Abstract

Longevity improvements have contributed to widespread underfunding of pension plans and losses in insured annuity portfolios. Insurers might reasonably expect some upside from the effect of lower mortality on their life business. Although mortality improvement scales, such as the Society of Actuaries Scale AA, are widely employed in pension and annuity valuation, the derivation of these scales appears heuristic, leading to problems in deriving meaningful measures of uncertainty. We explore the evidence on mortality trends for the Canadian life insurance companies, data, using stochastic models. We use the more credible population data to benchmark the insured lives data. Finally, we derive a practical, model-based formula for actuaries to incorporate mortality improvement and the associated uncertainty into their calculations.     

Generalized Frasier Claim Rates Under Survivorship Life Insurance Policies

Abstract

This paper proposes two modifications to the well-known Frasier formula, often used in the pricing, design, and valuation of survivorship life insurance policies: (1) allowing lapse rates to change after the first death and (2) reflecting simultaneous exposure to the same hazards, such as infectious diseases and common accidents, and possibly higher mortality among survivors. The purpose is to improve the pricing and valuation of survivorship life insurance. The paper will be of interest to actuaries doing pricing, GAAP valuation, self-support certifications, and to illustration actuaries. The results are important to reinsurers and direct writers. The paper includes numerical examples and compares the claim rates with and without the suggested modifications. The modified survivorship claim rates are considerably higher than those developed using pure Frasier, emphasizing the importance of learning to use these or similar methods.     

Strategies for Dividend Distribution: A Review

Abstract

In today’s world of financial uncertainty, one major public concern is to assess (and possibly improve) the stability of companies that take on risks. Actuaries have been aware of that issue for a very long time and have a great experience in modeling the activity of a risk business. During the first part of the twentieth century, they focused on the probability of ruin to assess the stability of their company. In his seminal paper of 1957 Bruno de Finetti criticized this approach and laid the foundations of what would become an increasingly popular topic: the study of dividend strategies. The contributions made by actuaries in that field constitute a substantial body of knowledge, whose interest is relevant not only to insurance but also to a much broader range of areas of practice. In this paper we aim at a taxonomical synthesis of the 50 years of actuarial research that followed de Finetti’s original paper.     

Pricing implications of trends in population mortality and underwriting effectiveness

Pricing actuaries try to anticipate insured lives mortality rates for decades into the future by considering historic relationships between population and insured lives mortality and trends in population mortality. The degree to which underwriting might decrease insured lives mortality relative to population mortality is of particular importance. A comparison of trends in population and insured mortality is presented to illustrate historic relationships. Two theories for future life expectancy trends are: 1) no foreseeable limit to life expectancy, and 2) life expectancy limited by biological forces. Factors that may increase or decrease the future effectiveness of underwriting are reviewed.     

Some mathematical aspects of price optimisation

Calculation of an optimal tariff is a principal challenge for pricing actuaries. In this contribution we are concerned with the renewal insurance business discussing various mathematical aspects of calculation of an optimal renewal tariff. Our motivation comes from two important actuarial tasks, namely (a) construction of an optimal renewal tariff subject to business and technical constraints, and (b) determination of an optimal allocation of certain premium loadings. We consider both continuous and discrete optimisation and then present several algorithmic suboptimal solutions. Additionally, we explore some simulation techniques. Several illustrative examples show both the complexity and the importance of the optimisation approach.     

Dynamic Financial Analysis: Classification, Conception, and Implementation

Dynamic financial analysis (DFA) models an insurance company's cash flow in order to forecast assets, liabilities, and ruin probabilities, as well as full balance sheets for different scenarios. In the past years DFA has become an important tool for the analysis of an insurance company's financial situation. In particular, it is a valuable instrument for solvency control, which is now becoming important as regulators encourage insurance companies to determine risk-based capital using internal risk management models. This article considers three aspects: First, we discuss the reasons why DFA is of special importance today. Second, we classify DFA in the context of asset liability management and analyze its fundamental concepts. As a result, we identify several implementation problems that have not yet been adequately considered in the literature, and therefore our third aspect is a discussion of these areas. In particular we consider the generation of random numbers and the modeling of nonlinear dependences in a DFA framework.     

Actuaries at the Dawn of the Computer Age

The NAAJ is honoring the Society of Actuaries in 1999, its golden anniversary year, by publishing a series of articles on the contributions of actuaries to the development of ideas. In this issue, we look at the advent of the use of computers in insurance operations. We begin with a short essay by James C. Hickman and conclude with comments by the actuaries who were there when computers entered the world of business, changing it forever.     

The Evolving Role of the Actuary in Financial Reporting of Insurance

Abstract

The demands that financial reporting of insurance companies present to actuaries are great and growing. With the prospects of change in the rules for financial reporting becoming more likely and insurance products becoming more complex, it is desirable to examine the evolving roles of the actuary and the actuarial profession. This paper describes these changes and the value that actuaries bring to financial reporting. The challenges presented are significant. As the methods of assessing and managing risk change are becoming more complex, the best efforts of the profession and individual actuaries will be needed to ensure that the actuary’s role is enhanced and expanded. Not only will the techniques used evolve, but the audiences served by the actuary will become even more demanding. The actuarial profession is better situated than other professions to meet these demands.     

The Actuary’s Role in Managed Care

Abstract

Financial risk is moving to center stage in the $1-trillion U.S. health-care market. The growth of managed care has created new forms of risk and has shifted this risk from insurance companies, which have long dealt with it successfully, to health-care providers and other organizations that have not traditionally accepted the same type and amount of risk. Health-care actuaries have the expertise to help these institutions, and the nation, protect their financial well-being.

Actuaries specialize in the evaluation, quantification, and management of risk. Actuarial models of health-care costs, which help evaluate risk, offer management a window to the managed care world. With these models and other tools, health-care actuaries help organizations succeed in today’s health-care environment by showing how the financial and functional elements of an organization relate to risk.

This report discusses the evolution of the health-care industry and the role that the healthcare actuary has played in that evolution. Eight case studies outline actuarial approaches to assessing risk in the era of managed care by discussing situations affecting five groups: providers, employers, regulators, public policy organizations, and HMOs. Built on experience gained in hundreds of cases, these studies show the range of tasks encountered by managed care actuaries and outline approaches that can help balance risks in today’s health-care system.     

Discussion of the paper by Aven and Myre

The paper is an interesting contribution to the development of actuarial statistics. Loss of profits insurance presents some peculiar problems that have received little attention from actuaries and—as far as I know—the model framework proposed by the authors has not formerly been applied to actuarial problems.     

Computerised detection and stochastic forecast of age, period and cohort effects

In this study, we adapt and apply suitable methods of image processing and computer vision to actuarial science. In particular, we design a multistage algorithm based on the well known Canny operator with a view to detecting abrupt changes in incremental mortality development factors by age over time. These edges indicate the boundaries between areas of higher and lower mortality improvements. The computerised detection algorithm allows for a more objective judgement concerning the existence of specific mortality patterns. Furthermore, we propose a stochastic mortality forecast model that may be viewed as a Lévy process. First, objectively identified mortality patterns are removed from the matrix of mortality improvement rates. We then forecast residual mortality development factors by applying a non-parametric block bootstrap simulation. Finally, future age, period and cohort effects are superimposed on a simulation basis. Notably, our stochastic mortality model is capable of incorporating specific stress scenarios such as mortality shocks.     

Obesity,Mortality, and the Obesity Paradox

The percentage of the population who are obese has grown dramatically on a worldwide basis over the last several decades, although the growth in the prevalence of obesity has slowed recently at a high level in the United States. Although there have been numerous studies of the effect of this trend on mortality, the findings have been inconsistent and controversial, in part because of methodological differences and the complexity of the relationships between obesity and mortality. The objective of this article is to discuss the issues surrounding these relationships and to shed light on the likely effects of the obesity epidemic on mortality. Of particular interest is the so-called obesity-mortality paradox, where mortality experience is lower for overweight and in some cases obese individuals than for those of normal weight. Although more recent studies of the relationship between mortality and obesity seem to indicate those who are obese have experienced a reduced percentage of additional mortality, this may in part be due to the shorter average time those currently obese have been exposed to their condition, the heterogeneity of the normal and obese populations, measurement issues including treatment of smokers and those who are ill, and study design limitations. An increased number of premature deaths may arise as more individuals who are obese are exposed for a longer period to excess adiposity. Although public policy issues surrounding obesity are being addressed with a great deal of activity and publicity, they have and will continue to prove quite challenging for both individuals and society to manage and overcome. The prevalence of obesity has had and will continue to have a significant effect on the mortality experience in most areas of actuarial practice. As a result, it is important for actuaries to enhance their understanding of these effects.     

New Swedish mortality table for annuity insurance

Abstract

The processive lowering of the general death rate during a considerable time past, which in spite of a temporary check such as the Spanish Flu epidemic of the years 1918–1920 is yet plainly evident, is a phenomenon of great significance for life insurance in general, and especially for life annuity insurance. Attention has been devoted to this trend by insurance men, and attempts have been made in several quarters to design mortality tables that could be regarded as affording ample security for the latter type of insurance. (Reference may in this connection be made to articles in ?Skandinavisk Aktuarietidskrift?, XII, p. 239 and XV, p. 45.)     

The argument for more future-oriented planning

Planning, and practically all forms of decisionmaking, are concerned with the future. The future, unless we adopt deterministic philosophies, is uncertain and therefore difficult to plan for. Through the processes of change it is likely to be different from the past; existing and past knowledge and experience are only a partial guide to decisionmaking. The inclusion of a future dimension based on careful thought about possible future development offers a new tool to the decisionmaker that should not be overlooked.     

Social security, life insurance and annuities for families

In this paper we ask whether an aspect of social security, namely its role as a provider of insurance against uncertain life spans, is welfare enhancing. To this end we use an OLG model where agents have a bequest motive and differ in sex and marital status and where families are formed and destroyed and their characteristics evolve (exogenously) according to U.S. demographic patterns of marriage, divorce, fertility and mortality. We compare the implications of social security under a variety of market structures that differ in the extent to which life insurance and annuities are available. We find that social security is a bad idea. In economies where the private sector provides annuities and life insurance, it is a bad idea for the standard reason that it distorts the intertemporal margin by lowering the capital stock. In the absence of such securities social security is still a very bad idea, only marginally less so compared with economies with annuities and life insurance. We also explore these issues in a world where people live longer and we find no differences in our answers. As a by-product of our analysis we find that the existence of life insurance opportunities for people is important in welfare terms while that of annuities is not.