Session 36 PD, Practical Lessons From the Living to 100 Symposium V

Moderator: Jean-Marc Fix, FSA, MAAA

Presenters:

Jean-Marc Fix, FSA, MAAA Andrew Chong Jenkins, FSA, CERA, MAAA

Kai Kaufhold

Practical Lessons from the

Living to 100 Symposium

Jean-Marc Fix, Optimum ReAndrew Jenkins, Protective Life

Kai Kaufhold, Advanced Reinsurance Services

Session 36

• Jean-Marc: Causes of death and mortality trend pitfalls

• Kai: Modeling• Andrew: Communicating mortality information

Order

• Comparability• Independence• Extrapolation

danger

Cause of Deaths Pitfalls

Country ICD 7 to 8 ICD 8 to 9 ICD 9 to 10

USA 1968 1979 1999

Japan 1968 1979 1995

France 1968 1979 2000

Italy 1968 1979

England and Wales 1968 1979 2001

Australia 1968 1979 1998

Sweden 1969 1987 1997

Switzerland 1969 1995

Singapore 1969 1979

Norway 1969 1986 1996

Comparability

Table 1b Causes of death mortality: what do we know of their dependence, S Gaille and M Sherris

Comparability: Circulatory

Figure 2 (a) and 3(a) Causes of death mortality: …, S Gaille and M Sherris

Males USA

Comparability: Cancer

Figure 2 (b) and 3(b) Causes of death mortality: …, S Gaille and M Sherris

Males USA

Comparability: Respiratory

Figure 2 (c) and 3(c) Causes of death mortality: …, S Gaille and M Sherris

Males USA

Comparability: External Causes

Figure 2 (d) and 3(d) Causes of death mortality: …, S Gaille and M Sherris

Males USA

Comparability: Infectious and Parasitic

Figure 2 (e) and 3(e) Causes of death mortality: …, S Gaille and M Sherris

Males USA

• Dependence between causes combining to overall mortality

• Impact of changes in one component may affect different country differently

Independence

Causes of death mortality: what do we know of their dependence, S Gaille and M Sherris

• Causes of death data is sparse in life insurance• When using population data, need to look a

some confounding impacts: how much improvement is due to lower smoking prevalence?

• Obesity example: more prevalence (especially at the very young ages) but better cardiovascular mortality…

Extrapolation Danger

Obesity and mortality , Sam Gutterman

• A new angle: modal age at death

• A relook at an old angle: using what we are used to using …

Mortality Trend Pitfalls

Old wolf pit trap, Germany by Georg WassmuthPermission CC‐BY‐SA‐3.0‐DE

Mortality Rectangularization

Modal age at death: mortality trends in England and Wales 1841‐2010, Emily Clay

Mortality Compression?

Modal age at death: mortality trends in England and Wales 1841‐2010, Emily Clay

1951

1961

19711981 1991

2001

2010

Modal Age at Death

Modal age at death: mortality trends in England and Wales 1841‐2010, Emily Clay

• Age specific rate of mortality change with age kx

• kx = ln (mx)-ln(mx-1) where mx is mortality rate• If mortality is Gompertz-like then kx is constant• If kx decrease with x: deceleration of mortality

Beware your Embedded Assumptions

• Authors looked at 24 cohorts (USA, Canada, Sweden and France, for Mm & F and for 1894, 1896 and 1898

Beware your Embedded Assumptions

Mortality trajectories at extreme old ages: a comparative study of different data sources on old‐age mortalityNS Gavrilova and LA Gavrilov

• Authors looked at 24 cohorts (USA, Canada, Sweden and France, for Mm & F and for 1894, 1896 and 1898)= no significant deceleration!

• 8 cohorts exhibit non significant deceleration• But…

Beware your Embedded Assumptions

• If you combine in 5 years age group (by using kx=[ln(mx)-ln(mx-5)]/5 where mx is 5 year mortality rate

• Then 4 cohorts are now significant for deceleration and 17 other show non-significant deceleration

… or You Might Stray

Impact Estimation

Figure 8 Age‐specific rate of mortality change with age, kx, by age interval for mortality calculation. Simulated data assuming that hazard ratios follows the Gompertz Law

Mortality trajectories at extreme old ages: a comparative study of different data sources on old‐age mortalityNS Gavrilova and LA Gavrilov

• We often assume uniform distribution of death on quinquennial intervals

• At the older ages it is not even safe to do so for ONE year age interval…

One Year Time Interval

A fast computer is

nevera substitute

for an active brain

Take Home Lesson

Models and other Fun Stuff

1. Longevity is just round the bend.• Aubrey de Grey

2. Modeling advanced ages.• Gavrilova & Gavrilov, Ouellete & Bourbeau

3. Advanced experience analysis.• Zhu & Li.

4. Ideas for trading on longevity and mortality.• Li, Chan & Li.

Inspirations

• Aubrey de Grey: “Strategies for Engineered Negligible Senescence” (SENS) www.sens.org

• Aging is a lethal disease. Prevent and reverse age-related ill-health.

• Apply principles of regenerative medicine to repair the damage of aging at the cellular and molecular level.

• Postpone aging and extend healthy life-expectancy in our lifetimes!

• LESSON 1: Actuarial models may break!

Longevity is nigh!

1. Data is key for ages 80+• Howard: “Liars, cheaters and procrastinators.”• Gavrilova & Gavrilov:

US Social Security Administration Death Master File• Ouellette & Bourbeau:

French-Canadian Centenarians (parish records)

2. Distinction between death probabilities and hazards is important: 1

12

: lim→

Modeling advanced ages.

3. Mortality law for oldest ages?• Gavrilova & Gavrilov: No deceleration on a cohort basis.• Ouellette & Bourbeau: Deceleration possible.

Gompertz law (1825): →

∞

Modeling advanced ages.

Log (force of mortality): Gompertz law (1825)

Source: Richards, Kaufhold and Rosenbusch (2013)

Modeling advanced ages.

‐3.5

‐3

‐2.5

‐2

‐1.5

‐1

‐0.5

0

0.5

80 85 90 95 100

log( m

ortality ha

zard )

Age

Actual

Linear

3. Mortality law for oldest ages?• Gavrilova & Gavrilov: No deceleration• Ouellette & Bourbeau: Deceleration

Gompertz law (1825): →

∞

Thatcher-Kannisto (1998): →

1(Perks 1932)

Modeling advanced ages.

Log (force of mortality): Perks law (1932), a.k.a Thatcher-Kannisto

Source: Richards, Kaufhold and Rosenbusch (2013)

‐3.5

‐3

‐2.5

‐2

‐1.5

‐1

‐0.5

0

0.5

80 85 90 95 100

log( m

ortality ha

zard )

Age

Actual

Linear

Logistic

Modeling advanced ages.

3. Mortality law for oldest ages?• Gavrilova & Gavrilov: No deceleration• Ouellette & Bourbeau: Deceleration

Gompertz law (1825): →

∞

Thatcher-Kannisto (1998): →

1(Perks 1932)

Beard (1959): →

Modeling advanced ages.

Log (force of mortality): Beard law (1959)

Source: Richards, Kaufhold and Rosenbusch (2013)

‐3.5

‐3

‐2.5

‐2

‐1.5

‐1

‐0.5

0

0.5

80 85 90 95 100

log( m

ortality ha

zard )

Age

Actual

Linear

Logistic

Beard

Modeling advanced ages.

3. Mortality law for oldest ages?• Gavrilova & Gavrilov: No deceleration• Ouellette & Bourbeau: Deceleration

Gompertz law (1825): →

∞

Thatcher-Kannisto (1998): →

1(Perks 1932)

Beard (1959): →

LESSON 2: Use the Force!

Modeling advanced ages.

Zhiwei Zhu, Zhi Li.: Logistic regression analysis for insured mortality experience study

• Improve use of data and create portfolio-specific tables.• Identify explanatory variables, a.k.a. risk factors.• Multivariate analysis avoids “slicing and dicing”.• Statistical analysis of goodness of fit and significance of

results.• Easy access via stats packages.

Advanced Modeling

How does it work? Parametrise the mortality curve:Let‘s say:

Substitute for : ⇔ ln

, ,…

⋯

1 ⋯

⇔ logit ≔ ln 1 ⋯

Logistic Regression

Linear Regression

MultivariateLinear Regression

Advantages:• Ready access experience analysis tool.• Find and test risk factors:

• Age, gender, selection, smoker status, UW class, time, product type, policy face amount.

Disadvantages:• Restriction on shape.• Grouped data.• Lapses and discontinuities difficult to handle.

LESSON 3: Use all your data!

Logistic Regression

1. Pick any parametric mortality law.Gompertz, Makeham, Perks, Beard, etc.

2. Model the observed lifetime of each individual in continuous time.

3. Maximum Likelihood parameter estimation.

Survival Models

Pick a mortality law: “Makeham−Beard” (Beard, 1959)

1

continuous-time force of mortality.Calculate survival probability:

Survival Models

Likelihood of observing lifetimes in portfolio of lives:

∝

0, 1,

log log

Maximize log with respect to , , , ∈ 1, … , .

Survival Models

Fit a model for each individual by estimating , , ,

…

:

0, 1,

Do the same for , , .

Survival Models

Logarithmic force of mortality by gender

Source: Richard, Kaufhold and Rosenbusch (2013)

Survival Models

‐6

‐5

‐4

‐3

‐2

‐1

0

1

65 70 75 80 85 90 95 100

log ( force of m

ortality )

Age

Actual Female

Actual Male

Model Female

Model Male

Advantages1. Use all data

• Continuous time/age, survivors and deaths

2. Graduate smooth table with flexible shape.3. Automatically weight observations

• Maximum likelihood vs. least mean squares

Disadvantages1. More maths required.

Survival Models

Li, Chan, Li: The CBD Mortality Indices.

• Mortality and longevity risk hedging.

• Non-parametric indices:• London Life and Longevity Market Association: LifeMetrics Index

• Deutsche Börse: Xpect Index

• Proposal: model-based index• Compare to VIX implied volatility indices at CBOE

• Improve information content

• Requirement: Index must be new-data-invariant.

Ideas for trading mortality risk.

M1: The Lee-Carter Model

ln ,

M2: The Renshaw-Haberman Model

ln ,

M3: The Age-Period-Cohort Model

ln ,

Candidate models

M5: The Cairns-Blake-Dowd (CBD) model

ln ,

1 ,̅

M6: The CBD model with a cohort effect

ln ,

1 ,̅

M7: The CBD model with cohort and quadratic effects

ln ,

1 ,̅ ̅

Candidate models

Candidate modelsModel M1: The New‐Data‐Invariant property is NOT satisfied

Estimates of the time‐varying parameters in Model M1Population: English and Welsh malesSample periods: 1950 to 1989, 1994, 1999, 2004, 2009

Candidate modelsModel M5: The New‐Data‐Invariant property is satisfied

Estimates of the time‐varying parameters in Model M5Population: English and Welsh malesSample periods: 1950 to 1989, 1994, 1999, 2004, 2009

The Cairns‐Blake‐Dowd model:

ln ,

1 ,̅

The 1st CBD index ( )Represents the level of the mortality curve (after transformation)A reduction in  means an overall mortality improvement.

The 2nd CBD index ( )Represents the slope of the logit‐transformed mortality curveAn increase in  means that mortality at younger ages improves more rapidly than that at older ages

Interpretation

Interpretation

Interpretation K1 and K2 risks

Example 1: England & Wales

The centroid moves to the upper‐left

The area becomes larger over time

The portions falling into the lower quadrants are similar in size

Example 2: Canada

Narrower and taller

More tilted

The area falling into the lower‐left‐hand quadrant is smaller

1. Models may break!

2. Use the force!

3. Use all your data!

4. Models can be used to trade risk.

Inspirations & Lessons

54

Communicating Longevity Risk

55

Customers

Senior Management

Chief Risk Officer

Public Policymakers

Identifying Your Stakeholders

Am I going to outlive my savings?

Can we translate risk into opportunity?  

How long can people live?  Will it be costly?

How do we fund our public pensions?

• Customers do not understand probabilities – make it binary.

• Studies show consumers consistently underestimate their life expectancy.1

• Ask the question: What are the chances you will live to age X or more?

• Make it visual – leverage retirement planning tools that incorporate life expectancy.

• Example: www.troweprice.com/ric

• Focus on the bottom line – reduce spending, invest to remove risk (e.g. annuities).

56

Longevity Risk for Customers

1Source: “Subjective Survival Probabilities and life tables: Evidence from Europe”, Franco Peracchi and Valeria Perotti

• Customer profiles help company leaders understand their oldest customers.

• Longevity Genes Project2

• Align customer needs with product solutions: annuities, income riders, etc.

57

Longevity Risk for Senior Management

2Source: The Longevity Genes Project, Dr. Nir Barzilai, http://www.einstein.yu.edu/centers/aging/longevity‐genes‐project/

• Summarize your changing life tables into life expectancy at key ages.

• Equate ages.

• What if all our customers live 1 year longer?

58

Longevity Risk for Senior ManagementLife expectancy at birth for males3

In 1950 65.4

In 1970 67.0

In 1990 71.9

In 2010 76.4

Current age and age of equivalent mortality 50 years ago for U.S. males4

60 53

70 63

3Source: Human Mortality Database, www.mortality.org4Source: “The Advancing Frontier of Survival: With a Focus on the Future of US Mortality”, James W. Vaupel

• How volatile are adult life expectancies?• Compressing versus shifting.

• Can we look beyond the U.S.?

• Lack of expert consensus on the range of mortality improvement factors.

• 1% (UK Public Pension) to 3% (expert estimates) and beyond (biomedical gerontologists).

• Improvement & population relationship. 59

Longevity Risk for the CRO

• Focus on the total population “Big Picture.” • Improvement by age matters.5

• Reduced mortality under age 35 lower cost.• Reduced mortality over age 35 higher cost.

• Birth rate needs to be presented in parallel.• Importance of retirement age assumption.• Public funding needed to understand new

drivers of old age mortality.• Example: Alzheimer's.

60

Longevity Risk for Public Policymakers

5Source: “Declining Mortality (Increasing Longevity): At What Rate?”, Steve Goss, Office of the Chief Actuary, U.S. S.S.A

Jean-Marc is Vice President, Research and Development at Optimum Re in Dallas, TX.He is responsible for the evaluation of new concepts involving product development or underwriting. His special areas of interest are all things mortality and critical illness both in the US and Canada.Prior to joining Optimum in 1997, Jean-Marc has worked at a number of reinsurer and direct life insurance companies, mostly in the area of product development.

Jean-Marc Fix, FSA, MAAA

Jean-Marc is a frequent speaker at life insurance, underwriting and medical directors meetings and is currently involved with a number of industry activities, including:

SOA Living to Age 100 Symposium Program Committee Joint AAA/SOA team on guaranteed and simplified issue mortality Joint AAA/SOA Underwriting Criteria Team SOA Reinsurance Section Research Team

Jean-Marc received a BA in Mathematics from Whittier College in California

Kai is managing director of Ad Res Advanced Reinsurance Services GmbH in Cologne, Germany. He manages projects in the fields of biometric experience analysis and mortality projection as well as life reinsurance. Prior to founding Ad Res in 2011, Kai worked for Manulife Reinsurance in Toronto and in Cologne. From 2006 to 2011 he was in charge of Manulife’s European life retrocession business, after having had roles in life reinsurance pricing, product development and marketing.

Kai Kaufhold, Aktuar DAV

Kai is a member of the German actuarial association (DAV) and of the IAA Life Section, and enjoys discussing biometric risk analysis and reinsurance where ever he goes. He received an M.Sc. in physics from the University of Cologne.

Andrew is VP of Annuity Product Development at Protective Life Insurance Co.

He is a Fellow of the Society of Actuaries, a Member of the American Academy of Actuaries, a Chartered Enterprise Risk Analyst, a Certified Product Manager, and a Certified Product Marketing Manager.

He holds a B.S. in Mathematics from the University of Texas at Austin (Hook ‘Em).

Andrew Jenkins, FSA, CERA, MAAA