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.     

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).     

Investigating the stationarity of insurance premiums: international evidence

This article explores whether there is support for the stationarity hypotheses of life and non-life insurance premiums during the period 1979–2007 for 40 heterogeneous countries. The stationarity of insurance premiums affects insurance companies’ prediction on their future inflow of premium income, which affects the liquidity of insurance companies and their investment plans and thus is relevant to the insurers’ operation. This article employs the advanced nonlinear panel unit-root test with a sequential panel selection method to classify the entire panel into two groups: stationary countries and non-stationary countries. We apply Monte Carlo simulations to derive empirical distributions of the test, which allows us to correct for the finite-sample bias and to consider the cross-country effects. We find relatively stationary life insurance premiums in countries from the following groups: high-income, Europe, and common law origin; relatively stationary non-life insurance premiums exist in the following groups: low-income, Middle East and Africa, and common law origin. Evidence herein shows that different classifications, including income levels, geographic regions, regionally or economically integrated blocs, and legal system, affect the stationarity of life and non-life insurance premiums.     

Financing Gaps of Public Pension Schemes and Market Potential for the Private Retirement Market

Abstract

Increasing longevity, declining birth rates, and high unemployment severely threaten the financial basis of many public pension plans. These problems are most pronounced in continental Europe, where public pension plans tend to be relatively generous and are usually funded on a pay-as-you-go basis. Given the demographic development, future pension payments exceed the expected contribution payments. The resulting financing gaps can be seen as implicit public debts (net pension liabilities), which often exceed the value of GDP figures and are in many cases higher than the explicit public debt figures. If people would decide to cover these financing gaps via life insurance, life insurance premiums would triple in Germany, more than double in Italy, and double in Canada and France. The increase would be only moderate in the U.S. and particularly small in the U.K.     

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.     

New standard regulations regarding allocation to the safety reserve in Sweden

Abstract

This paper describes a statistical investigation of observed loss ratios and run-offs for a number of Swedish insurance companies within different lines of business. The main aim of the investigation was to revise existing upper limits for allocation to the so-called safety reserve, which is an untaxed contingency reserve. The effort was successful in that new rules were established by the Swedish Supervisory Authority in accordance with the results of the investigation. This paper also contains an exposition of the general principles underlying the Swedish safety reserve.     

中国保险需求地区差距的实证研究

本文分别构建了我国地区人身险和财产险影响因素的实证模型,使用1996年～2008年的省际面板数据,重点采用动态系统GMM估计方法,检验人身险和财产险需求地区差异的动态形成机制。研究发现：与人身保险需求相比,财产保险需求近年来的“习惯形成”特征更为显著,收入水平的增长更有利于加快当前财产保险市场的发展;东部省份的经济发展...     

Pure Versus Mutual Health Insurance: Evidence From Swedish Historical Data

Using data from voluntary Swedish health insurance societies 1902‐1910, this article analyzes the coexistence of pure and mutual insurance societies where pure societies are characterized by charging ex ante premiums only while mutuals in addition charge ex post assessments. On average, mutual insurance societies are found to be larger and to offer greater insurance coverage per member. Pure insurance societies have, on average, higher insurance coverage per day, greater mean levels of moral hazard controls, a higher mean number of policy categories, and greater longevity.     

Post-war mortality among industrial insured lives in Norway

Abstract

The results of mortality investigations among industrial insured lives with weekly premiums in the Norwegian life insurance company Fram for the period 1931/40 and for the period 1940/46 have earlier been published in this journal.l It is now possible to render the main results of the continued investigation for the post-war years 1946/50.     

Stochastic Orderings of Convex-Type for Discrete Bivariate Risks

New classes of order relations for discrete bivariate random vectors are introduced that essentially compare the expectations of real functions of convex-type of the random vectors. For the actuarial context, attention is focused on the so-called increasing convex orderings between discrete bivariate risks. First, various characterizations and properties of these orderings are derived. Then, they are used for comparing two similar portfolios with dependent risks and for constructing bounds on several multilife insurance premiums.     

Use of a Markov Model to Estimate Long-Term Insured Lives’ Mortality Risk Associated With BRCA1 and BRCA2 Gene Mutations

Abstract

There is uncertainty regarding the degree of insurance risk associated with BRCA1/2, the gene mutations associated with breast cancer. Most reports to date have been based on high-risk populations selected from families with multiple and/or early-onset cancers; more favorable data have been reported in studies without this selection bias.

This paper discusses use of a Markov model to estimate mortality risk associated with BRCA1/2 gene mutations in female life insurance applicants. The goal is to derive a range of risk estimates based on different assumptions of breast and ovarian cancer incidence. A particular strength of the model is that transition probabilities after cancer diagnosis vary with age and cancer stage, as do excess hazard rates.

Data calculated by the model indicate that no single mortality curve characterizes risk for all life insurance applicants with a BRCA1/2 mutation. Rather, mortality risk depends on breast and ovarian cancer incidence rates and subsequent mortality rates, and on the method used to deal with competing breast and ovarian cancer incidence and mortality rates. Further refinement of risk estimates will depend on better incidence data and on resolution of complex statistical problems, such as informative censoring.

Widespread use of genetic information by insurance consumers could have important economic implications. For companies that sell individually underwritten products, profitability might decrease. Consumers might find higher prices and reduced availability, with a corresponding decrease in quantity of insurance purchased. Insurance and consumer ramifications would vary by cover, with living-benefit products, such as critical-illness insurance, most adversely affected. Societal choices are limited. Given assumptions in the cited scenario, it is likely premiums would rise and quantity of insurance purchased would decrease even with no change in existing social policy; attempted legal or regulatory remedies would further accentuate price increases and reductions in quantity purchased.     

Insurance contracts portfolios with heterogenous parametric life distributions

In this paper we consider two portfolios: one of m endowment insurance contracts and one of m whole life insurance contracts. We introduce the majorization order, Schur functions, and parametric families of distribution functions. We assume that the owners of the portfolios are exposed to different members of a known parametric family of distributions and study the effect of this stochastic heterogeneity on the premiums and death benefits of the insurance contracts. We show that the premiums paid in both contracts are Schur concave and that the death benefit awarded in the whole life contract is Schur convex. We provide upper and lower bounds for the premiums and for the death benefit, and compute the bounds for four parametric families of distribution functions used frequently in the Actuarial Sciences.     

Insurance economics

Abstract

Background

Insurance accounting is generally speaking based upon the idea that a comparison shall be made between “premiums earned” and “claims incurred”. Even if there are exceptions in different countries and in different classes of business the method where premiums earned and claims incurred are compared is so widely used that we will take this method as our starting point for a discussion of the shortcomings, if any, of insurance accounting.     

New bases for non-cancellable sickness insurance in Sweden

Abstract

Non-cancellable sickness and disability insurance—in Sweden known as long-term sickness insurance—has been carried on in Sweden since the beginning of the twentieth century; first by Eir since 1911, then by Valkyrian from 1912, and by Salus, a special company for physicians, since 1929. An account of the technical methods employed by Eir in sickness insurance is given in a paper which was read before the Ninth International Congress of Actuaries in 1930.1 In several important respects a new epoch has been established as regards sickness insurance in Sweden. On 1 January 1955 compulsory sickness insurance was introduced; and thus an essential part of the demand for sickness insurance was covered. At the same time three of the life assurance companies, Thule, Svenska Liv, and Städernas Liv have also begun to carryon the type of sickness insurance which had previously been effected only by the three companies mentioned above, and whose activities are restricted to sickness insurance. The apprehensions that might have been felt respecting the possible glut of the market were not confirmed; on the contrary, the interest in long-term sickness insurance appears to be increasing.     

Research in collective risk theory

Abstract

An insurance company can be considered as an adjustment institution for the policyholders. The individual risks of the policyholders are taken over by the company at the price of a comparatively small stake, the premium. This is so calculated that the premiums from all the policyholders will, according to statistical experience, on the average cover the company's payments for claims. With respect to unfavourable random deviations from the average, the premiums contain security loadings. For the same purpose the company also makes other precautions. The most important of these are reinsurance and the building up of adjustment funds. On the other hand, extensive precautions increase the price of the insurance. Therefore the objective fixing of the precautions in order to get a satisfactory solidity as well as a reasonable price constitutes a weighing problem, demanding a measure of the effect of diverse precautions.     

Valuation of Equity-Linked Insurance and Annuity Products with Binomial Models

Abstract

In this paper we develop a valuation method for equity-linked insurance products. We assume that the premium information of term life insurances, pure endowment insurances, and endowment insurances at all maturities is obtainable within a company or from the insurance market. Using a method similar to that of Jarrow and Turnbull (1995), we derive three martingale probability measures associated with these basic insurance products. These measures are agedependent, include an adjustment for the mortality risk, and reproduce the premiums of the respective insurance products. We then extend the martingale measures to include the financial market information using copulas and use them to evaluate equity-linked insurance contracts and equity-indexed annuities in particular. This is different from the traditional approach under which diversification of mortality risk is assumed. A detailed numerical analysis is performed for various existing equity-indexed annuities in the North American market.     

Pricing and Capital Allocation for Multiline Insurance Firms

We study multiline insurance companies with limited liability. Insurance premiums are determined by no‐arbitrage principles. The results are developed under the realistic assumption that the losses created by insurer default are allocated among policyholders following an ex post, pro rata, sharing rule. In general, the ratio of default costs to expected claims, and thus the ratio of premiums to expected claims, vary across insurance lines. Moreover, capital and related costs are allocated across lines in proportion to each line's share of a digital default option on the insurer. Our results expand and generalize those derived elsewhere in the literature.     

An Actuarial Analysis of Participating Life Insurance

An actuarial model is developed to reveal the intrinsic nature of participating life insurance. The basic safe-side criterion is examined. It is established how the first-order prospective net premium reserve includes safety margins or bonus loadings, and it is demonstrated how the bonus loadings are currently released. It is demonstrated how surplus may be distributed and accumulated as a terminal bonus in an equitable way. The level premium is divided into a variable recurrent single premium and a variable natural premium, and an alternative to the prospective net premium reserve is examined. A capitalization of future safety margins or bonus loadings, which are related to past premiums and the paid-up benefit, may allow the insurance company a considerable increase in investment freedom. The theory is illustrated by numerical results.     

On the probability of ruin in the collective risk theory for insurance enterprises with oly negative risk sums

Abstract

1. The determination of the probability that an insurance company once in the future will be brought to ruin is a problem of great interest in insurance mathematics. If we know this probability, it does not only give us a possibility to estimate the stability of the insurance company, but we may also decide which precautions, in the form of f. ex. reinsurance and loading of the premiums, should be taken in order to make the probability of ruin so small that in practice no ruin is to be feared.     

An optimal stopping problem in risk theory

Abstract

In classical risk theory often stationary premium and claim processes are considered. In some cases it is more convenient to model non-stationary processes which describe a movement from environmental conditions, for which the premiums were calculated, to less favorable circumstances. This is done by a Markov-modulated Poisson claim process. Moreover the insurance company is allowed to stop the process at some random time, if the situation seems unfavorable, in order to calculate new premiums. This leads to an optimal stopping problem which is solved explicitly to some extent.