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.     

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).     

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.     

Intergenerational Transfers and Insurance Policy Design

Abstract

Group health insurance policies offering an identical benefit package to every member of the group result in lower expected health benefits for younger cohorts than older cohorts. The dispersion in insurance benefits across age groups differs among insurance policies. Simulation results presented in this paper demonstrate that a shift from comprehensive health insurance to high-deductible health insurance decreases the share of expected benefits going to younger cohorts. An estimated 81.5% of the 23-to-32-year-old cohort is expected to receive less than $500 in health benefits during a year for one prototypical high-deductible health plan. Low expected benefits for younger relatively healthy cohorts could increase the number of younger individuals who eschew health coverage. Age-rated premiums are probably the most straightforward way to stimulate demand for high-deductible health plans among younger healthier individuals.     

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.     

The new technical basis of the Swedish life insurance companies

Abstract

During the past year most of the Swedish life insurance companies have agreed upon instituting common technical basis for the calculation of premiums, policy reserves, surrender values and prospective bonus (returns of premiums). Chiefly the same basis also has been adopted by two companies outside the agreement, and with one exception all Swedish life insurance companies now use the same premiums.     

The price,quality and distribution of mortgage payment protection insurance: A hedonic pricing approach

Mortgage payment protection insurance (hereafter MPPI) provides varying combinations of accident, sickness and unemployment insurance and is used to protect the mortgage payments of policyholders in the event of a fall in income. Despite alleviating housing market failures, this service has been heavily criticised for providing poor value for money and being associated with unhelpful sales techniques especially when sold jointly with a mortgage in the UK. Consequently, the Competition Commission (2009) ruled that after February 2011 MPPI should not be sold jointly with mortgage lending within seven days of the credit transaction. We examine whether this prohibition was justified and if the form of distribution, either jointly with the mortgage or independently influences the premium levels. This assessment uses a hedonic pricing approach with details and premiums of MPPI policies in 2010 and 2012. Despite the success in reducing MPPI premium levels, we conclude that the Competition Commission judgement has raised concerns as to mortgagee protection.     

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.     

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.     

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.     

Adult Polycystic Kidney Disease and Critical Illness Insurance

Abstract

Adult polycystic kidney disease (APKD) is a single-gene autosomal dominant genetic disorder leading to end-stage renal disease (ESRD, meaning kidney failure). It is associated with mutations in at least two genes, APKD1 and APKD2, but diagnosis is mostly by ultrasonography. We propose a model for critical illness (CI) insurance and estimate rates of onset of ESRD from APKD using two studies. Other events leading to claims under CI policies are included in the model, which we use to study (a) extra premiums under CI policies if the presence of an APKD mutation is known, and (b) the possible costs arising from adverse selection if this information is unavailable to insurers. The extra premiums are typically very high, but because APKD is rare, the possible cost of adverse selection is low. However, APKD is just one of a significant number of single-gene disorders, and this benign conclusion cannot be assumed to apply to all genetic disorders taken together. Moreover, ignoring known genetic risks in underwriting sets a precedent that could have unintended consequences for the underwriting of nongenetic risks of similar magnitude.     

Reinsurance premium principles based on weighted loss functions

ABSTRACT

In this paper, we propose new reinsurance premium principles that minimize the expected weighted loss functions and balance the trade-off between the reinsurer's shortfall risk and the insurer's risk exposure in a reinsurance contract. Random weighting factors are introduced in the weighted loss functions so that weighting factors are based on the underlying insurance risks. The resulting reinsurance premiums depend on both the loss covered by the reinsurer and the loss retained by the insurer. The proposed premiums provide new ways for pricing reinsurance contracts and controlling the risks of both the reinsurer and the insurer. As applications of the proposed principles, the modified expectile reinsurance principle and the modified quantile reinsurance principle are introduced and discussed in details. The properties of the new reinsurance premium principles are investigated. Finally, the comparisons between the new reinsurance premium principles and the classical expectile principle, the classical quantile principle, and the risk-adjusted principle are provided.     

Statistical study of waivers of premiums on disablement

Abstract

At the request of the author, the Managing Director of Livförsäkringsbolaget Framtiden, ömsesidigt (the Swedish Mutual Life Insurance Co. ? Future?), gave him an opportunity to make an investigation into the waivers of premiums on disablement. This investigation which at first was suggested by the Chief Mathematician of the Company, K. G. Hagstroem D. Sc., was meant to contain a study of the experience of a single year, 1932. With regard to view points put forward by the author, the original scheme was essentially widened to give a complete study of the whole experience ever since the foundation of the Company. The author wishes to express his gratitude to the Managing Director for placing a working staff at his disposal for carrying out this plan. He also wants to thank Dr. Hagstroem for his appreciation of the views advanced. The author, furthermore, has pleasure to express his thanks to the entire staff of the Company, for aiding him in his work in many ways, and in this connection he wants especially to mention Mr. Erik Grune, the manager of the actuarial department. Finally, he wishes to thank his many collaborators, especially Miss Elsa Fredricsson and Stig Cronvali, M. Bc. for their assistance.     

12-Year Experience Following Bone Marrow Transplantation with Emphasis on Acute and Chronic Leukemia

Abstract

Actuaries use a variety of approximations in calculating reserves. Among the methods used by actuaries for policies with modal premiums are fully discrete reserves, fully continuous reserves, discounted continuous reserves (equivalent to the apportionable premium case), and semicontinuous reserves. In this paper I discuss the relationships between these methods. I also examine the practical approximations commonly used and the way in which unearned premiums and deferred premiums are incorporated into this framework.     

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.     

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.     

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.     

Forecasting mortality

Abstract

The work of actuaries is concerned with estimating the future on the basis of past experience. The calculation of a premium to be charged for a given risk implies a forecast of the future but so far as mortality is concerned we have generally been content to examine past experience and assume that the results will be repeated. Judged as forecasts our estimates have sometimes been wide of the mark and owing to an almost continuous improvement in mortality actuaries have been assuming heavier rates of mortality than have been experienced. We may defend the use of past experience by saying that it is on the safe side when we are calculating premiums and we may argue that it is the best practical method; but an alternative is to make a more accurate forecast and then allow in our calculations a margin for chance deviations, emergencies, etc. Moreover the assumption that the past will be repeated has not been uniformly safe; it has led to bad results in annuity business and may prove unfortunate in social insurance, pension funds, and even sickness insurance. For some of these purposes we should either work on an estimate of future rates of mortality or, which comes to much the same thing, take a sufficient margin to cover the error involved in our assumptions.     

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.

     

Product pricing and solvency capital requirements for long-term care insurance

This paper presents a comprehensive assessment of premiums, reserves and solvency capital requirements (SCRs) for long-term care (LTC) insurance policies using Activities of Daily Living and US data. We compare stand-alone policies, whole life insurance policies with LTC benefit riders (LTC insurance combined with whole life insurance), life care annuities (LTC insurance combined with annuities) and shared LTC insurance in terms of net premium cost and SCRs. Net premiums and best-estimate reserves for base LTC insurance policies are determined using Thiele’s differential equation. Product features such as the elimination period and the maximum benefit period are compared using a simulation-based model. We show how a maximum benefit period can reduce costs and risks for LTC insurance products. SCRs for longevity risk and disability risk are based on the Solvency II standard formula. We quantify the extent to which whole life insurance policies with LTC benefit riders and life care annuities provide lower SCRs than stand-alone LTC insurance policies.