Basic concepts in life assurance mathematics

Abstract

1. Introduction.

In this paper the basic concepts of the life insurance mathematics will be discussed. Due to the fact that the importance of the probability calculus as a hasis for the actuarial science has repeatedly been disclaimed in recent literature (See e.g. Ernst ZWinggi (1]), the present author feels that there is a justification for reconsidering the fundamental ideas of the actuarial science.     

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.     

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.     

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.)     

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.     

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.     

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).     

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.     

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.     

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.     

Author’s Reply: Skewness and Stock Option Prices - Discussion by Terence Chan,Michel Jacques,Heinz H. Mu¨ller,Geérard Pafumi,Elias S.W. Shiu,and Serena Tiong,July 1997

Abstract

In recent years, the combined effects of deregulation in financial services, along with advances in telecommunications and information technology, are forcing far-reaching changes upon the insurance industry. The result is the industry is becoming more competitive. The emerging role of electronic commerce (e-commerce) is particularly important and interesting to study.

I offer a brief survey of the role of e-commerce in the insurance industry. The paper is organized in the following manner: Section 1 summarizes Internet trends and discusses various related public policy issues; Section 2 addresses online insurance supply and demand; Section 3 discusses the economics of disintermediation and reintermediation and explains how this applies to e-commerce in the insurance industry. Finally, Section 4 offers a set of concluding remarks.     

Generalized Life Insurance: Ruin Probabilities

We study ruin probabilities for generalized life insurance programs. These programs include among others whole life and long term care contracts. Clearly, in such programs the claims in successive years are dependent, hence the structure of our problem is different from that of ruin probabilities in general insurance where claims over time are independent. First, we develop algorithms calculating the ruin probabilities for life and LTC insurance programs. Further, upper and lower bounds for these probabilities are derived. These new bounds take into account the joint distribution of claims over time.     

Exponential inequalities for ruin probabilities in the Cox case

Abstract

We consider an insurance model where the underlying point process is a Cox process. Using a martingale approach we obtain extensions of the classical Lundberg inequality.     

Market Price of Insurance Risk Implied by Catastrophe Derivatives

Abstract

Insurance derivatives facilitate the trading of insurance risks on capital markets, such as catastrophe derivatives that were traded on the Chicago Board of Trade. Simultaneously, insurance risks are traded through reinsurance portfolios. In this paper we make inferences about the market price of risk implied by the information embedded in the prices of these two assets.     

Reciprocal reinsurance treaties seen as a two-person co-operative game

Abstract

1.1. In 1930 Professor Cramer wrote: “The object of the theory of risk is to give a mathematical analysis of the random fluctuations in an insurance business, and to discuss the various means of protection against their inconvenient effects” ([6], page 7). This definition has obviously been adequate, since Cramer still subscribes to it when 25 years later he makes a comprehensive survey of the subject [7]. However, the mild complaint Cramer made in 1930 that “practical insurance business has hitherto made little or no application of the results offered by the mathematical theory of risk” still has some validity. The very impressive results achieved by the mathematical theory of risk during the last thirty years have certainly found practical applications, but not so many as one would expect, considering that the theory proposes to analyse the very foundations of the insurance business.     

How Does Information Disclosure Affect Bank Systemic Risk in the Presence of a Deposit Insurance System?

ABSTRACT

This article establishes a dynamic game with incomplete information to theoretically analyze the influence mechanism of information disclosure on systemic risk in the presence of a deposit insurance system. To verify the mechanism, we use panel data on 247 global banks in 41 countries during the period 2006 to 2015 in an empirical analysis. Our article finds that a high degree of information disclosure can reduce deposit insurance premiums and weaken the negative incentive from a bailout by regulatory authorities. Moreover, the effect of deposit insurance on financial stability is not apparent, but the synergistic effect of deposit insurance and information disclosure reduces bank systemic risk. Furthermore, different deposit insurance designs affect bank behavior, so it is crucial for bank supervisors to create proper deposit insurance systems, which are helpful in strengthening market discipline and preventing moral hazard thus contributing to a stable financial environment. Therefore, under the deposit insurance system, regulatory authorities should strive to improve the standard of information disclosure to ensure systemic stability.     

Life Expectancy in the Future

Abstract

The public responsibility of life insurance actuaries has changed from supervisory compliance with detailed state laws to certifying adherence to more general regulatory objectives complemented by actuarial standards of practice.     

Weighted Pricing Functionals With Applications to Insurance

Abstract

We explore the role of weighted distributions in pricing insurance risks. In particular, we relate the distributions to actuarial and economic premium calculation principles and in this way provide a unifying methodology for constructing new principles and analyzing known ones.     

Pricing Dynamic Insurance Risks Using the Principle of Equivalent Utility

We introduce an expected utility approach to price insurance risks in a dynamic financial market setting. The valuation method is based on comparing the maximal expected utility functions with and without incorporating the insurance product, as in the classical principle of equivalent utility. The pricing mechanism relies heavily on risk preferences and yields two reservation prices - one each for the underwriter and buyer of the contract. The framework is rather general and applies to a number of applications that we extensively analyze.