Genetic Testing, Insurance Underwriting and
Adverse Selection
Pradip Tapadar
University of Kent
Global Conference of Actuaries, Mumbai, India
19-21 February, 2012
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Agenda
1
Introduction
2
Risk aversion
3
Adverse selection
4
A Simple Two-state Model
5
Critical Illness Insurance Example
6
References
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Introduction
Agenda
1
Introduction
2
Risk aversion
3
Adverse selection
4
A Simple Two-state Model
5
Critical Illness Insurance Example
6
References
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Introduction
Background
Background
Single-gene disorders: Huntington’s disease, Alzheimer’s disease.
Multifactorial disorders: Cancer, Cardiovascular disease.
The UK Biobank project:
Over 500,000 recruited from England, Scotland and Wales.
Age-range 40-69: Follow-up period 30 years.
DNA extraction from blood sample as and when required.
“The main aim of the study is to collect data to enable the
investigation of the separate and combined effects of
genetic and environmental factors (including lifestyle,
physiological and environmental exposures) on the risk
of common multifactorial disorders of adult life.”
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Introduction
Genetics and Insurance Regulations
Genetics and Insurance Regulations
Insurance underwriting and setting premium rates.
Information asymmetry and adverse selection.
Genetic risk, environmental risk and insurance.
Insurance regulatory developments in the UK:
1997: HGAC asks Government to impose a moratorium.
1999: GAIC formed to scrutinise use of genetic tests.
2000: GAIC approves use of genetic tests for HD for life insurance
contracts over £500,000.
2001: ABI withdraws all applications – agrees a 5-year moratorium.
2005: Moratorium extended until 2011.
2011: Moratorium extended until 2017.
Q: Taking economic and epidemiological issues into account,
under what circumstances is adverse selection likely to occur
with sufficient force to be problematic?
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Risk aversion
Agenda
1
Introduction
2
Risk aversion
3
Adverse selection
4
A Simple Two-state Model
5
Critical Illness Insurance Example
6
References
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Risk aversion
Basic assumptions
Basic assumptions
Consider an individual with:
initial wealth: W ;
exposed to an adverse risk with probability q;
on adverse event would incur a loss: L;
utility function U(w ), which is:
? an increasing function of wealth;
? with decreasing marginal utility.
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Risk aversion
Utility function
U(W−L)
Utility
U(W)
Utility function
W−L
W
Wealth
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Risk aversion
Expected utility of a gamble
U(W)
Expected utility of a gamble
Expected utility
U(W−L)
Utility
qU(W − L) + (1 − q)U(W)
W−L
W
Wealth
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Risk aversion
A risk-averse individual with insurance
U(W)
A risk-averse individual with insurance
Utility
U(W − qL)
U(W−L)
Fair premium
qL
W−L
W−qL
W
Wealth
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Risk aversion
Comparing insurance against a gamble
U(W)
Comparing insurance against a gamble
U(W − qL)
Preference for insurance
U(W−L)
Utility
qU(W − L) + (1 − q)U(W)
W−L
W−qL
W
Wealth
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Risk aversion
Tolerance for a higher than fair premium
U(W)
Tolerance for a higher than fair premium
U(W − qL)
Tolerance limit
Utility
qU(W − L) + (1 − q)U(W)
Extra
premium
U(W−L)
∆
W−L
W − (qL + ∆)
Fair premium
qL
W−qL
W
Wealth
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Adverse selection
Agenda
1
Introduction
2
Risk aversion
3
Adverse selection
4
A Simple Two-state Model
5
Critical Illness Insurance Example
6
References
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Adverse selection
Uniform premium for all strata
Uniform premium for all strata
Suppose:
There are two risk groups.
Low-risk group’s risk of adverse event q0 .
High-risk group’s risk of adverse event q1 .
Suppose further:
The insurer is not allowed access to private information, and
is forced to charge the same average premium, q̄, for both groups.
Q: Assuming that the insurance purchasers are aware of their
own risk, under what circumstances will the low-risk
individuals stop purchasing insurance, triggering adverse
selection?
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Adverse selection
Within tolerance limits – no adverse selection
U(W)
Within tolerance limits – no adverse selection
U(W−L)
Utility
q0U(W − L) + (1 − q0)U(W)
Extra
premium
Fair
premium
∆
q0L
Average
premium
q×L
W−q×L
W−L
W
Wealth
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Adverse selection
Outside tolerance limits – adverse selection
q0U(W − L) + (1 − q0)U(W)
U(W−L)
Utility
U(W)
Outside tolerance limits – adverse selection
Extra
Fair
∆
q0L
Average
premium
q×L
W−q×L
W−L
W
Wealth
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A Simple Two-state Model
Agenda
1
Introduction
2
Risk aversion
3
Adverse selection
4
A Simple Two-state Model
5
Critical Illness Insurance Example
6
References
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A Simple Two-state Model
The Model
The Model
λ
-
A
B
Model assumptions:
Insured event represented by transition from state A to state B.
Two risk groups with different transition intensities λ.
Relative risk: k =
λ1
λ0
⇒ q1 = 1 − (1 − q0 )k .
Proportion of population in each risk-group is known.
The threshold relative risk, above which adverse selection takes place,
can now be analysed.
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A Simple Two-state Model
Threshold relative risk
Threshold relative risk
3
4
q0 = 0.5
1
2
q0 = 0.1
0
Threshold relative risk
5
50% in low−risk group
0
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Loss ratio (L W)
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A Simple Two-state Model
Threshold relative risk
8
6
4
q0 = 0.5
2
q0 = 0.1
90% in low−risk group
0
Threshold relative risk
10
Threshold relative risk
0
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Loss ratio (L W)
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A Simple Two-state Model
Immunity from Adverse Selection
Immunity from Adverse Selection
0.9 1
0.5
q0 = 0.1
q0 = 0.5
0
Threshold population
The population proportions above which the low-risk group will buy
insurance at the average premium regardless of the relative risk:
0
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Loss ratio (L W)
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A Simple Two-state Model
Summary
Summary
Observations
For low loss ratios, even small relative risks cause people to opt against
insurance.
At high loss ratios, threshold relative risk increases.
A sufficiently high proportion of low risk individuals ensures that adverse
selection never occurs whatever the relative risk.
Higher risk-aversion ⇒ Higher threshold relative risk.
Conclusions
Adverse selection in the 2-state insurance model does not appear unless:
purchasers insure a small proportion of wealth;
the elevated risks implied by genetic information are implausibly high;
the size of the low-risk stratum is unrealistically small.
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Critical Illness Insurance Example
Agenda
1
Introduction
2
Risk aversion
3
Adverse selection
4
A Simple Two-state Model
5
Critical Illness Insurance Example
6
References
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Critical Illness Insurance Example
A Critical Illness Insurance Model
A Critical Illness Insurance Model
λ12 (x) State 2 Heart Attack
λ13 (x) State 3 Cancer
*
State 1 Healthy
P Tapadar (University of Kent)
λ14 (x) State 4 Stroke
H
@HH
@ HH
@
HH
@
HH
j State 5 Other CI
@ λ15 (x) H
@
@
@
@
λ16 (x) @
R State 6 Dead
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Critical Illness Insurance Example
Heart Attack Rates
Heart Attack Rates as a % of Total CI Rates
1
Male
Female
Ratio
0.8
0.6
0.4
0.2
0
0
10
20
30
40
50
60
70
80
Age (years)
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Critical Illness Insurance Example
Summary
Summary
Observations
Critical illnesses other than heart attacks creates a minimum premium;
. . . and dilutes the impact of genetic risk on heart attack.
The threshold relative risks are much higher for males than females.
Adverse selection appears to be possible only for smaller losses and
extremely low levels of risk aversion.
Adverse selection does not appear at all at realistic risk-aversion levels.
Conclusions
The results suggest that in circumstances that are plausibly
realistic, private genetic information relating to risks only available
to consumers does not lead to adverse selection.
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References
References
References
Macdonald, A.S. & Tapadar, P. (2010)
Multifactorial Genetic Disorders and Adverse Selection:
Epidemiology Meets Economics.
Journal of Risk and Insurance, 77:1, 152–182
Macdonald, A.S., Pritchard, D.J. & Tapadar, P. (2006)
The impact of multifactorial genetic disorders on critical illness
insurance: A simulation study based on UK Biobank.
ASTIN Bulletin, 36, 311–346
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