Technical basis for collective (Group) pensions insurance in Norway — K 1946

I. Introduction.

In 1933 O. Aabakken in this journal ¹ Olav Aabakken: “A New Basis of Calculation for Collective Pensions Insurance in Norway”. 1933. dealt with the collective (group) pensions insurance in Norway and especially with the technical basis — K 1931 — which was adopted in 1931 by the life offices in common for this branch of insurance. This basis was worked out from the experiences since 1917, when collective pensions insurance was introduced in Norway. When the National old-age insurance was introduced in 1936, the life offices adopted some new collective pensions benefits which could be employed in the cases where an adjustment to the National old age insurance was desirable. O. Böe has described the mode of adjustment. ² Olav Böe: “Relations between Collective Pensions Insurance, Employer's Pension Funds and National Insurance in Norway”. Transactions of the Eleventh International Congress of Actuaries, Paris 1937.      

The mortality among industrial insured lives in Norway 1931–1940

Abstract

Industrial insurance was introduced in Norway in 1903 by The Norwegian Life Insurance Company FRAM which was alone in this branch of life insurance activity until 1918, when The Life Insurance Company Norske Folk adopted industrial insurance also. Later on other companies too have started industrial insurance, but Fram is still by far the largest industrial insurance company in Norway, and to-day works with industrial insurance with weekly, monthly and daily premiums (calendarpremium).     

Optimal Annuitization Policies

Abstract

At, or about, the age of retirement, most individuals must decide what additional fraction of their marketable wealth, if any, should be annuitized. Annuitization means purchasing a nonrefundable life annuity from an insurance company, which then guarantees a lifelong consumption stream that cannot be outlived. The decision of whether or not to annuitize additional liquid assets is a difficult one, since it is clearly irreversible and can prove costly in hindsight. Obviously, for a large group of people, the bulk of financial wealth is forcefully annuitized, for example, company pensions and social security. For others, especially as it pertains to personal pension plans, such as 401(k), 403(b), and IRA plans as well as variable annuity contracts, there is much discretion in the matter.

The purpose of this paper is to focus on the question of when and if to annuitize. Specifically, my objective is to provide practical advice aimed at individual retirees and their advisors. My main conclusions are as follows:

? Annuitization of assets provides unique and valuable longevity insurance and should be actively encouraged at higher ages. Standard microeconomic utility-based arguments indicate that consumers would be willing to pay a substantial “loading” in order to gain access to a life annuity.

? The large adverse selection costs associated with life annuities, which range from 10% to 20%, might serve as a strong deterrent to full annuitization.

? Retirees with a (strong) bequest motive might be inclined to self-annuitize during the early stages of retirement. Indeed, it appears that most individuals—faced with expensive annuity products—can effectively “beat” the rate of return from a fixed immediate annuity until age 75?80. I call this strategy consume term and invest the difference.

? Variable immediate annuities (VIAs) combine equity market participation together with longevity insurance. This financial product is currently underutilized (and not available in certain jurisdictions) and can only grow in popularity.     

Insurance Fraud

Insurance fraud is a major problem in the United States at the beginning of the 21st century. It has no doubt existed wherever insurance policies are written, taking different forms to suit the economic time and coverage available. From the advent of “railway spine” in the 19th century to “trip and falls” and “whiplash” in the 20th century, individuals and groups have always been willing and able to file bogus claims. The term fraud carries the connotation that the activity is illegal with prosecution and sanctions as the threatened outcomes. The reality of current discourse is a much more expanded notion of fraud that covers many unnecessary, unwanted, and opportunistic manipulations of the system that fall short of criminal behavior. Those may be better suited to civil adjudicators or legislative reformers. This survey describes the range of these moral hazards arising from asymmetric information, especially in claiming behavior, and the steps taken to model the process and enhance detection and deterrence of fraud in its widest sense. The fundamental problem for insurers coping with both fraud and systemic abuse is to devise a mechanism that efficiently sorts claims into categories that require the acquisition of additional information at a cost. The five articles published in this issue of the Journal of Risk and Insurance advance our knowledge on several fronts. Measurement, detection, and deterrence of fraud are advanced through statistical models, intelligent technologies are applied to informative databases to provide for efficient claim sorts, and strategic analysis is applied to property‐liability and health insurance situations.     

Some reflections on different disability models

Abstract

As a retired actuary of life and health insurance the author has wished to summarize his experience and reflections about different systems of disability insurance. He wants to show how the premium technique of the “classic” Hamza process presented in 1900 as a model of the invalidity insurance technique without any element of recovery can be described for an active person by three alternative formulas of expected value of a disability indemnity. His of interest to observe that the second of these formulas can be applied to the technique of sickness insurance based on the probability of being sick. This technique is also used in British and Norwegian long term disability insurance. The third formula leads after modification to the Swedish sickness annuity technique and, further, to the technique of basic continuance tables used in U.S.A. In describing the classic process the author has used the discontinuous approach, but otherwise the continuous approach with integrals instead of sums has been preferred.

Methods of calculating the premium for “waiver of premium” have in this paper only been touched upon as a result of a modification of the sickness annuity technique. It has been found necessary to refrain from the opportunity to illustrate the interesting development of the invalidity technique according to Schoenbaum and later to Simonsen who introduced a series of transition probabilities between different states of activity and disablement.     

About a duration index for life insurance contracts

Abstract

In this paper, after having defined the duration for a “generic” life insurance contract, we bring out some of its properties. We also prove that, in some cases, duration is a natural extension of well-known duration indices.     

A proposal for a new basis of life insurance calculations in Norway

Abstract

The basis used by Norwegian life insurance companies for the calculation of premiums and reserves is, as regards insurances, The Institute of Actuaries Life Tables H ^M (20 British Life Offices tables) with interest at 4 per cent. This basis has been used by Norwegian companies for more than thirty-five years and has proved entirely safe.     

Sickness experience of Framtiden

Abstract

Introduction.

Livförsäkringsbolaget Framtiden, ömsesidigt (the Life Insurance Co. “The Future”, Mutual), to the policyholders of which I have the honour of devoting my actuarial work, is a relatively new enterprise. It was founded in 1911. Its main work is industrial life insurance with monthly premiums. All industrial policies include the waiver of premiums on disablement by sickness or accident for at least four weeks. Disablement lasting more than four weeks involves the waiver of premiums from the beginning of the disablement. For industrial policies issued in late years, the payment of premiums is limited to 65 years of age. Besides ordinary endowment (or whole life) policies, many childrens' insurances are written, including some or other insurance of the bread-winner, at all events the waiver of premiums till the 20th birthday of the child, if the supporter should die before that time, and for the periods during this time when the supporter is disabled by sickness or accident for at least four weeks. It has been tried to propagate more protective forms of children's policies, but it has partly failed, owing to lack of interest from agents and public. Nevertheless, it has been possible to exclude pure childrens' tariffs, and so in almost every policy issued, there is a moment of sickness insurance. In late years, this holds true also for the ordinary branch. The mass of experience collected is thus by no means unimportant, despite the smallness of the Company, as compared with foreign Companies. The experience is, moreover, collected during a relatively short period of time, giving a rather homogeneous material.     

Withdrawal among Norwegian Life Assured 1910–1935

Introduction.

In the series of statistical experiences of the Norwegian life assurance companies report No. IV was issued some time ago. ¹ “Frivillig avgang blant norske livsforsikrede og dödeligheten blant forsikrede med fripolise 1910–1935”. Oslo 1943. The report, which was prepared at the Statistical Bureau of the Norwegian Life Assurance Companies, comprises 2 subjects: 1. Withdrawal among Norwegian life assured

2. Mortality among assured with paid-up policies (free policies) both during the period 1910–1935.

     

Elderly empowerment,fertility, and public pensions

The economic role of elderly people is underestimated in the context of the debate on pension reforms. This is because, as healthy life expectancy increases, the elderly become more active not only in the labor market but also in household production. Using a three-period overlapping-generations model in which grandparents allocate time between labor and informal childcare (“grandparenting”), we analyze the interaction among grandparenting, fertility, elderly labor, and public pensions. We obtain two analytical results. First, increasing the pension contribution rate increases grandparenting. Second, elderly labor force participation rates are negatively (positively) related to the fertility rates among countries with small (large) public pensions. The nonlinear relationship between elderly labor and fertility is empirically supported.

     

Issues in the Drive to Measure Liabilities at Fair Value

This paper compares the discussion on liability measurement in Accounting The0y Monograph 10 with the liability measurement requirements in recent international proposals on accounting for financial instruments. Rather than conducting a detailed review of the Monograph, the paper examines three major issues which wawant amplifjing, extending or criticising: What is “fair value”? Why fair value liabilities? Should fair value include an entity's own credit risk? The focus is on financial liabilities such as “plain vanilla” debt; other financial liabilities, such as insurance obligations, pensions, wawanties and environmental damage restoration involve additional considerations and are therefore not considered.     

Modeling Severity and Measuring Tail Risk of Norwegian Fire Claims

The probabilistic behavior of the claim severity variable plays a fundamental role in calculation of deductibles, layers, loss elimination ratios, effects of inflation, and other quantities arising in insurance. Among several alternatives for modeling severity, the parametric approach continues to maintain the leading position, which is primarily due to its parsimony and flexibility. In this article, several parametric families are employed to model severity of Norwegian fire claims for the years 1981 through 1992. The probability distributions we consider include generalized Pareto, lognormal-Pareto (two versions), Weibull-Pareto (two versions), and folded-t. Except for the generalized Pareto distribution, the other five models are fairly new proposals that recently appeared in the actuarial literature. We use the maximum likelihood procedure to fit the models and assess the quality of their fits using basic graphical tools (quantile-quantile plots), two goodness-of-fit statistics (Kolmogorov-Smirnov and Anderson-Darling), and two information criteria (AIC and BIC). In addition, we estimate the tail risk of “ground up” Norwegian fire claims using the value-at-risk and tail-conditional median measures. We monitor the tail risk levels over time, for the period 1981 to 1992, and analyze predictive performances of the six probability models. In particular, we compute the next-year probability for a few upper tail events using the fitted models and compare them with the actual probabilities.     

The Impact of Surplus Distribution on the Risk Exposure of With Profit Life Insurance Policies Including Interest Rate Guarantees

This article analyzes the numerical impact of different surplus distribution mechanisms on the risk exposure of a life insurance company selling with profit life insurance policies with a cliquet‐style interest rate guarantee. Three representative companies are considered, each using a different type of surplus distribution: a mechanism, where the guaranteed interest rate also applies to surplus that has been credited in the past, a slightly less restrictive type in which a guaranteed rate of interest of 0 percent applies to past surplus, and a third mechanism that allows for the company to use former surplus in order to compensate for underperformance in “bad” years. Although at the outset all contracts offer the same guaranteed benefit at maturity, a distribution mechanism of the third type yields preferable results with respect to the considered risk measure. In particular, throughout the analysis, our representative company 3 faces ceteris paribus a significantly lower shortfall risk than the other two companies. Offering “strong” guarantees puts companies at a significant competitive disadvantage relative to insurers providing only the third type of surplus distribution mechanism.     

The mortality among industrial insured lives in Norway during the war

In the Norwegian life insurance company Fram a continuous mortality investigation takes place in connection with the yearly valuation of policies issued with weekly premiums. The investigation gives the aggregate mortality, the unit is the policy and the year of observation is the calendar year. A detailed account of the method used has been given by Fredrik Borch in his paper: “The mortality among industrial insured lives in Norway 1931–1940” in this journal 1943. The most important results of the investigation from the years 1940–1946 are rendered below.     

A practical solution to the problem of ultimate ruin probability

Abstract

It was the Swiss actuary Chr. Moser who, in lectures at Bern University at the turn of the century, gave the name “self-renewing aggregate” to what Vajda (1947) has called the “unstationary community” of lives, namely where deaths at any epoch are immediately replaced by an equivalent number of births. It was Moser too (1926) who coined the expression “steady state” for the stationary community in which the age distribution at any time follows the life table (King, 1887). With such a distinguished actuarial history, excellently summarized by Saxer (1958, Ch. IV), it behoves every actuary to know at least the definitions and modus operandi of today's so-called renewal (point), or recurrent event, processes.     

Fair Valuation of a Guaranteed Life Insurance Participating Contract Embedding a Surrender Option

In this article we deal with the problem of pricing a guaranteed life insurance participating policy, sold in the Italian market, which embeds a surrender option. This feature is an American‐style put option that enables the policyholder to sell back the contract to the insurer at the cash surrender value. Employing a recursive binomial formula patterned after the Cox, Ross, and Rubinstein (1979) discrete option pricing model we compute, first of all, the total price of the contract, which also includes a compensation for the participation feature (“participation option,” henceforth). Then this price is split into the value of three components: the basic contract, the participation option, and the surrender option. The numerical implementation of the model allows us to catch some comparative statics properties and to tackle the problem of suitably fixing the contractual parameters in order to obtain the premium computed by insurance companies according to standard actuarial practice.     

Appraisement of under-average lives in Norway

Abstract

When it was proposed in 1917 to proceed to insurance of »under-average lives» in Norway through the company Norske Folk we had very little statistical data to build upon. There existed no Norwegian or Scandinavian statistics in this field. Some American statistics were, it is true, available, but in many cases these could not be applied direct to Norwegian conditions. However, we could not let ourselves be deterred by this, but proceeded to feel our way forward as well as possible, having constantly ascertained by means of summary annual calculations of mortality that the actual mortality for the aggregate number of insured lay somewhat below the expected figure. The intention was, however, to investigate the mortality in some of the different groups of under-average lives, as soon as the order of magnitude within these groups had become such as to render such investigation possible. The first investigation was made in 1936 for the period from 1917 to the anniversary date in 1935. The results of the mortality inquiry were submitted at the Congress of Actuaries in Paris in 1937. ¹ Olav Aabakken: The Insurance of Under-average Lives in Norway, Statistical Investigations.      

Principle of equivalent utility and universal variable life insurance pricing

In this paper we study the pricing problem for a class of universal variable life (UVL) insurance products, using the idea of principle of equivalent utility. As the main features of UVL products we allow the (death) benefit to depend on certain indices or assets that are not necessarily tradable (e.g., pension plans), and we also consider the “multiple decrement” cases in which various status of the insured are allowed and the benefit varies in accordance with the status. Following the general theory of indifference pricing, we formulate the pricing problem as stochastic control problems, and derive the corresponding HJB equations for the value functions. In the case of exponential utilities, we show that the prices can be expressed explicitly in terms of the global, bounded solutions of a class of semilinear parabolic PDEs with exponential growth. In the case of general insurance models where multiple decrements and random time benefit payments are all allowed, we show that the price should be determined by the solutions to a system of HJB equations, each component corresponds to the value function of an optimization problem with the particular status of the insurer.     

A credibility theory for automobile bonus systems

Summary

This paper deals with the problem of designing experience rating systems of the bonus type, commonly used in automobile insurance. On the basis of a simple model the mean squared deviation between a policy's expected claim amount and its premium in the nth insurance period as n→∞, is taken as a measure of the efficiency of a bonus system. It is shown that to any set of bonus rules (which determines the bonus class transitions of the policies), there is an optimal premium scale, which coincides with the one proposed by Pesonen in 1963. Thus the problem of choosing an efficient bonus system reduces to choosing efficient bonus rules. Examples are given of comparison between different bonus rules. In one example the present Norwegian bonus system is compared to alternative systems. Comments are made on earlier papers on bonus systems. The credibility theoretic foundation is laid in a separate section.     

Risk as perceived by the German public: pervasive risks and “switching” risks

In 2001, a major project on the perception and evaluation of risks in southern Germany was conducted consisting of survey data as well as of semi‐structured interviews. With reference to the psychometric paradigm, this article analyzes public risk perception, pointing out the perceived risk semantic for nuclear energy, GM‐food, mad cow disease (BSE), crime, global climate change, mobile telephony and its radiation risks. These hazards reveal different patterns of risk perception and different levels of risk acceptability. Secondly, a comparison of qualitative and quantitative findings will be conducted: qualitative analyses indicate that the results of quantitative rating scales on the perception, evaluation and acceptance of technical and environmental hazards might be misleading since the public's focus on risks as elicited by open association stimuli relies much more on ‘everyday‐life’ and ‘pervasive’ risks than for instance on hazards emerging from new technologies. The relevance of technological risks tends to be dependent on the context: If explicitly mentioned in newscasts, in debates or listed in questionnaires memories, fears or other immediate responses become activated, yet they may be forgotten a short time later. We have called this phenomenon “switching effect” and the respective risks “switching risks”. In standardized opinion polls such ‘switching effects’ may evoke firm judgments, even if the importance in the interviewee's mental representation seems marginal.