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Health and Business Workshop 30 November 2017, UNSW Sydney Modelling Health Status and Long Term Care Insurance Michael Sherris Professor of Actuarial Studies, School of Risk and Actuarial Studies, UNSW Sydney Chief Investigator, CEPAR

Modelling Health Status and Long Term Care Insurance · Modelling Health Status and Long Term Care Insurance Michael Sherris Professor of Actuarial Studies, School of Risk and Actuarial

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Page 1: Modelling Health Status and Long Term Care Insurance · Modelling Health Status and Long Term Care Insurance Michael Sherris Professor of Actuarial Studies, School of Risk and Actuarial

Health and Business Workshop

30 November 2017, UNSW Sydney

Modelling Health Status

and

Long Term Care InsuranceMichael Sherris

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

UNSW SydneyChief Investigator, CEPAR

Page 2: Modelling Health Status and Long Term Care Insurance · Modelling Health Status and Long Term Care Insurance Michael Sherris Professor of Actuarial Studies, School of Risk and Actuarial

CoverageProjects

Focus is Post Retirement and Older Ages• Health Status and Retirement Income Streams – Life Annuities,

Pooled Annuities• Long Term Care Insurance – Modelling Functional Disability Risks,

LTCI Product design, Insurer Pricing and Capital• Housing and Long Term Care Insurance – Individual retirement

Financing, Reverse Mortgages, Life annuities

Industry Partners and Collaborators

Page 3: Modelling Health Status and Long Term Care Insurance · Modelling Health Status and Long Term Care Insurance Michael Sherris Professor of Actuarial Studies, School of Risk and Actuarial

Health Status and Retirement Income Streams – Life Annuities, Pooled Annuities

Models for health status and mortality heterogeneity and implications for retirement income stream products

• Frailty and Markov Ageing Models – calibration to population mortality data

• Markov ageing models calibrated to cross sectional health status data and longitudinal population mortality data – applied to annuity pricing, adverse selection and tail risks of life insurers

• GLMM for health risk factors using individual level HRS data – pricing underwritten life annuities, risks and capital requirements for life insurers

• Mortality heterogeneity and health status and impact on mutual risk pooling products – GSA’s, pooled annuities – equitable methods of determining annuity payments

Page 4: Modelling Health Status and Long Term Care Insurance · Modelling Health Status and Long Term Care Insurance Michael Sherris Professor of Actuarial Studies, School of Risk and Actuarial

Frailty and Markov Physiological Ageing Models

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

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

Source: Shu and Sherris (2010)

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

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

Page 5: Modelling Health Status and Long Term Care Insurance · Modelling Health Status and Long Term Care Insurance Michael Sherris Professor of Actuarial Studies, School of Risk and Actuarial

Life Annuity Portfolio Mix

-1,500-1,000

-5000

5001,0001,5002,000

25 30 35 40 45

Ann

uity

Por

tfolio

years since start of contract

Best Health Only

mean ±1 standard deviation 5th percentile

-1,500-1,000

-5000

5001,0001,5002,000

25 30 35 40 45

Ann

uity

Por

tfolio

years since start of contract

Mixed

mean ±1 standard deviation 5th percentile

Writing a portfolio representative of the population – less profitable and more risky

Markov ageing model

Le Bras model –lower mean and less volatility

Sherris, M. and Q. Zhou (2014). ‘Model Risk, Mortality Heterogeneity, and Implications for Solvency and Tail Risk,’ in P. B. Hammond, R. Maurer, and O. S. Mitchell, eds., Recreating Sustainable Retirement: Resilience, Solvency, and Tail Risk. Oxford, U.K.: Oxford University Press, pp. 113–133.

Page 6: Modelling Health Status and Long Term Care Insurance · Modelling Health Status and Long Term Care Insurance Michael Sherris Professor of Actuarial Studies, School of Risk and Actuarial

Models of Mortality Heterogeneity – Annuity Pricing 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.

Page 7: Modelling Health Status and Long Term Care Insurance · Modelling Health Status and Long Term Care Insurance Michael Sherris Professor of Actuarial Studies, School of Risk and Actuarial

Long Term Care Insurance – Modelling Functional Disability Risks, LTCI Product design, Insurer Pricing and Capital

Models for functional disability, LTC insurance products• Multiple state models for functional disability and mortality - calibrated

to HRS data• Incorporating systematic trends and uncertainty into multiple state

models and implications for healthy life expectancy – calibrated using HRS data

• International comparison of functional disability and long term trends in disability

• LTC product design, pricing and capital• Models and product innovations using Australian individual data

Page 8: Modelling Health Status and Long Term Care Insurance · Modelling Health Status and Long Term Care Insurance Michael Sherris Professor of Actuarial Studies, School of Risk and Actuarial

Multi-State Life Tables for Functional DisabilityDisability & 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.

Page 9: Modelling Health Status and Long Term Care Insurance · Modelling Health Status and Long Term Care Insurance Michael Sherris Professor of Actuarial Studies, School of Risk and Actuarial

Multi-State Life Tables for Functional Disability

US Mortality rates from HRS data

Higher male mortalityHigher disabled

mortality

Mortality transition Intensities –Males on left and Females on right

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

Page 10: Modelling Health Status and Long Term Care Insurance · Modelling Health Status and Long Term Care Insurance Michael Sherris Professor of Actuarial Studies, School of Risk and Actuarial

Multi-State Life Tables for Functional Disability

Male transition rates by age – HRS data

Female transition rates by age – HRS data

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

Page 11: Modelling Health Status and Long Term Care Insurance · Modelling Health Status and Long Term Care Insurance Michael Sherris Professor of Actuarial Studies, School of Risk and Actuarial

Functional Disability Life Table and LTC Insurance

- Disability (functional) free life expectancy- Estimated from HRS data

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

Page 12: Modelling Health Status and Long Term Care Insurance · Modelling Health Status and Long Term Care Insurance Michael Sherris Professor of Actuarial Studies, School of Risk and Actuarial

LTC Insurance Liabilities and Capital

Shao A. W., Sherris, M and Fong, H. Y., (2017), Product Pricing and Solvency Capital Requirements for Long-Term Care Insurance, Scandinavian Actuarial Journal, Vol 2017, Issue 2, 175-208. http://dx.doi.org/10.1080/03461238.2015.1095793

Page 13: Modelling Health Status and Long Term Care Insurance · Modelling Health Status and Long Term Care Insurance Michael Sherris Professor of Actuarial Studies, School of Risk and Actuarial

Distribution of Functional Disability including Trends and Uncertainty

Li, Z., Shao, W. A., and Sherris, M. (2017), The Impact of Systematic Trend and Uncertainty on Mortality and Disability in a Multistate Latent Factor Model for Transition Rates, North American Actuarial Journal, 2017, 1-17, doi: 10.1080/10920277.2017.1330157

Page 14: Modelling Health Status and Long Term Care Insurance · Modelling Health Status and Long Term Care Insurance Michael Sherris Professor of Actuarial Studies, School of Risk and Actuarial

Housing and Long Term Care Insurance – Individual Retirement Financing, Reverse Mortgages, Life annuities

Individual retirement planning incorporating life annuities, long term care insurance and housing

• Long term care insurance impact on demand for life annuities, role of reverse mortgages in unlocking illiquid housing equity

• Bequest motive reduces demand for life annuities but what about impact of bequest on long tem are insurance demand?

• To what extent does housing crowd out demand for long term care insurance?

• Impact of lack of liquidity, asset rich cash flow poor retirees because of house equity, on demand for annuities and long term care insurance? Role for reverse mortgages?

• Product innovations – combining reverse mortgage with LTCI, combining life annuity with LTCI

Page 15: Modelling Health Status and Long Term Care Insurance · Modelling Health Status and Long Term Care Insurance Michael Sherris Professor of Actuarial Studies, School of Risk and Actuarial

LTC Insurance and Reverse Mortgages

Shao, W. A., Chen, H. and Sherris, M. (2017), To Borrow or Insure? Long Term Care Costs and the Impact of Housing. Working Paperunder Review

Demand for reverse mortgages in presence of illiquid housing and LTCI

Page 16: Modelling Health Status and Long Term Care Insurance · Modelling Health Status and Long Term Care Insurance Michael Sherris Professor of Actuarial Studies, School of Risk and Actuarial

LTC Insurance and Reverse Mortgages

Shao, W. A., Chen, H. and Sherris, M. (2017), To Borrow or Insure? Long Term Care Costs and the Impact of Housing. Working Paperunder Review

Page 17: Modelling Health Status and Long Term Care Insurance · Modelling Health Status and Long Term Care Insurance Michael Sherris Professor of Actuarial Studies, School of Risk and Actuarial

LTC Insurance and Demand for Life Annuities

Xu, M., Alonso-Garcia, J., Shao, W. A. and Sherris, M. (2017), Demand for Annuities and Long-term Care Insurance with RecursiveUtility: Impact of Housing, Unpublished Working Paper.

Page 18: Modelling Health Status and Long Term Care Insurance · Modelling Health Status and Long Term Care Insurance Michael Sherris Professor of Actuarial Studies, School of Risk and Actuarial

Industry Partners and Collaborators

Industry Partners in CEPAR and on Linkage Grants• PwC• APRA• AMP• World Bank• Netspar• SOA

Collaborators

• Prof Annamaria Olivieri (University of Parma), Prof Ermanno Pitacco(University of Trieste), Dr Adam Shao (Milliman), Dr Hua Chen (Temple University), Dr Ramona Meyricke (Suncorp)

• Research students and postdocs at UNSW

Page 19: Modelling Health Status and Long Term Care Insurance · Modelling Health Status and Long Term Care Insurance Michael Sherris Professor of Actuarial Studies, School of Risk and Actuarial

[email protected]://www.cepar.edu.au/

Michael SherrisCEPAR, Risk and Actuarial Studies

UNSW Business SchoolUNSW

http://papers.ssrn.com/author=410919

Page 20: Modelling Health Status and Long Term Care Insurance · Modelling Health Status and Long Term Care Insurance Michael Sherris Professor of Actuarial Studies, School of Risk and Actuarial

References

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.

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

Sherris, M. and Q. Zhou (2014). ‘Model Risk, Mortality Heterogeneity, and Implications for Solvency and Tail Risk,’ in P. B. Hammond, R. Maurer, and O. S. Mitchell, eds., Recreating Sustainable Retirement: Resilience, Solvency, and Tail Risk. Oxford, U.K.: Oxford University Press, pp. 113–133.

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

Fong, J.HY, Sherris, M. and Yap, J., (2017), Forecasting Disability: Application of a Frailty Model, Scandinavian Actuarial Journal, Vol 2017, Issue 2, 125-147. http://dx.doi.org/10.1080/03461238.2015.1092168

Page 21: Modelling Health Status and Long Term Care Insurance · Modelling Health Status and Long Term Care Insurance Michael Sherris Professor of Actuarial Studies, School of Risk and Actuarial

References

Shao A. W., Sherris, M and Fong, H. Y., (2017), Product Pricing and Solvency Capital Requirements for Long-Term Care Insurance, Scandinavian Actuarial Journal, Vol 2017, Issue 2, 175-208. http://dx.doi.org/10.1080/03461238.2015.1095793

Li, Z., Shao, W. A., and Sherris, M. (2017), The Impact of Systematic Trend and Uncertainty on Mortality and Disability in a Multistate Latent Factor Model for Transition Rates, North American Actuarial Journal, 2017, 1-17, doi: 10.1080/10920277.2017.1330157

Xu, M., Sherris, M. and Meyricke, R., (2017), Systematic Mortality Improvement Trends and Mortality Heterogeneity: Insights from Individual Level HRS data Working Paper under Review.

Shao, W. A., Chen, H. and Sherris, M. (2017), To Borrow or Insure? Long Term Care Costs and the Impact of Housing. Working Paper under Review.

Xu, M., Alonso-Garcia, J., Shao, W. A. and Sherris, M. (2017), Demand for Annuities and Long-term Care Insurance with Recursive Utility: Impact of Housing, Unpublished Working Paper.

Page 22: Modelling Health Status and Long Term Care Insurance · Modelling Health Status and Long Term Care Insurance Michael Sherris Professor of Actuarial Studies, School of Risk and Actuarial

Questions and Discussion