Life Tables and Insurance Applications

[Pages:21]Mortality in Australia: Marking the 150th Anniversary of the First Australian Life Table

13 November 2017, Melbourne Town Hall

Life Tables and Insurance Applications

Michael Sherris Professor of Actuarial Studies, School of Risk and Actuarial Studies,

UNSW Sydney Chief Investigator, CEPAR

Early Life Table Insurance Applications

? In the early third century, Roman Praetorian prefect Aemilius Macer and praetorian prefect Domitius Ulpianus (Ulpian) constructed life tables used as an annuities table for determining tax based on age and the annuity value.

? John Graunt (1620-1674) was the first to produce a life table based on the Bills of Mortality of London. The Bills of Mortality included details of the deaths each week and the cause of death.

? Johann de Witt (1625-1672), the Prime Minister of the Netherlands, used the chances of death to value Life Annuities issued by the government.

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Early Life Table Insurance Applications

? Edmond Halley (1656-1742), of Halley's Comet fame, developed a mortality table from the bills of mortality of the town of Breslau and used his table of mortality to calculate values of life annuities.

? Abraham de Moivre (1667-1754) developed the first treatment of probability in English, the Doctrine of Chances, and applied the theory of probability to problems related to annuities on human lives in his Annuities upon Lives.

? James Dodson (1710?1757) was a British mathematician, actuary and innovator in the insurance industry. He used mortality rates based on the Bills of Mortality for the City of London for the period 1728-50 to compute long term insurance premiums used by The Equitable.

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Life Tables and Insurance Applications

? Morris Birkbeck Pell (1827?1879) was a mathematician, professor, lawyer and actuary.

? In 1854 he had become actuarial consultant to the Australian Mutual Provident Society

? In 1870 he was a director and consulting actuary of the Mutual Life Association of Australasia.

? He published papers 'On the Rates of Mortality and Expectation of Life in New South Wales' (1867) and 'On the Constitution of Matter' (1871).

? He also published in the Journal of the Institute of Actuaries, London, 'On the Distribution of Profits in Mutual Insurance Societies' (1869) and 'On the Institute of Actuaries' life tables' (1879) among other papers.

Source: Australian Dictionary of Biography

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Data for Life Tables

Individual data

? Risk factors: Age, sex, smoking status, education, occupation, ethnicity, income, geographical location, marital status

? Cause of death ? Survey data (HRS) ? Government administrative

data

Population by country

? Aggregate deaths by age, gender, period, cohort

? Aggregate cross sectional health data

? Prevalence of health conditions

? Mortality rates by Causes of death

? Human Mortality Database

Life insurance, pension fund and annuity pools

? Aggregation of deaths and exposures by underwriting risk factors

? Effect of selection ? Insured lives ? Annuitants ? Pensioners ? Role of Actuarial

associations (CMIB, SoA)

Frailty and Markov Physiological Ageing Models

Life insurers "select" lives using underwriting allowing for heterogeneity in individual mortality

Frailty Model ? 1945 Australian Male Cohort with varying levels of frailty

Markov Physiological Age Model ? Distribution of Physiological Ages for a 65 year old Australian male

Su, S. and Sherris, M. (2012), Heterogeneity of Australian Population Mortality and Implications for a Viable Life Annuity Market, Insurance: Mathematics and Economics, 51, 2, 322?332

Source: Shu and Sherris (2010)

6 Life Tables for Insurance allowing for Risk Factors

GLMM can allow for both underwriting risk factors and residual variability (frailty)

Heterogeneity still significant after underwriting

Insurer can adjust annuity prices by pricing using adjusted mortality reflecting risk profiles and a frailty factor

Meyricke, R., and Sherris, M. (2013), The determinants of mortality heterogeneity and implications for pricing annuities. Insurance: Mathematics and Economics, 53, 2, 379?387.

7 Multi-State Life Tables for Functional Disability

Disability & recovery transition Intensities ? Males on left, Females on right U.S. HRS (Health and

Retirement Study) data: - Rates of becoming LTC

disabled are significantly higher for women than men. - Force of disability > mortality hazard for females of all ages. - Distinct age patterns of recovery. - Used to produce life tables by health state

Fong, H. Y., Shao W., and Sherris, M. (2015), Multi-State Actuarial Models of Functional Disability, North American Actuarial Journal, 19:1, 41-59.

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