I know that I don’t know what you doInformational asymmetry from the insurer’s point of view

Orsolya RétallérCorvinus University of Budapest

Theoretical background

TÁMOP-4.2.2/B-10/1-2010-0023

Informational asymmetry in the insurance market

• Competitive market – single period(Rotschild and Stiglitz, 1976)

• Monopol market – single period(Stiglitz, 1977)

• Competitive market – multi period(Cooper and Hayes, 1987 and Kuntreuther and Pauly, 1985)

• Monopol market – multi period(Dionne, 1983 and Dionne and Lassere, 1985)

My goal:

Making adverse se

lection visi

ble

Assumptions

TÁMOP-4.2.2/B-10/1-2010-0023

General Assumptions

• No influence on the risk• Insurance is not mandatory• Insurer is in monopol position• Initial number of policyholders• Policyholders are not distinguished• Insured asset worth 1• Maximum number of losses per year: 1• Amount of loss is independent from the number of losses• 10 period of time

Model structure

TÁMOP-4.2.2/B-10/1-2010-0023

Permanent data

• Continuous Risk• Type of Risk• Discrete Risk

Period-dependent data

• Policyholder Dummy• Presumed Risk• Loss Dummy• Amount of Loss• Actual Risk

A series of simulations

Initial number of policyholders: 1,000

Premium principle: net premium principle

Maximal risk: 100%

Premium tolerance: 5%

TÁMOP-4.2.2/B-10/1-2010-0023

Initial Frequencies Distribution of

Amount of Losses

Moral Hazard Policyholder’s Risk

Assumption

Adverse Selection Model

A series of simulations

TÁMOP-4.2.2/B-10/1-2010-0023

Initial Frequencies Distribution of

Amount of Losses

Moral Hazard Policyholder’s Risk

Assumption

Adverse Selection Model

• Not specified1• 80-5-5-5-5%2• 5-5-5-5-80%3

A series of simulations

TÁMOP-4.2.2/B-10/1-2010-0023

Initial Frequencies Distribution of

Amount of Losses

Moral Hazard Policyholder’s Risk

Assumption

Adverse Selection Model

A series of simulations

• Bernoulli1• Pareto2• Gamma3• Lognormal4

TÁMOP-4.2.2/B-10/1-2010-0023

Initial Frequencies Distribution of

Amount of Losses

Moral Hazard Policyholder’s Risk

Assumption

Adverse Selection Model

• No moral hazard1• Significant moral hazard2

A series of simulations

TÁMOP-4.2.2/B-10/1-2010-0023

Initial Frequencies Distribution of

Amount of Losses

Moral Hazard Policyholder’s Risk

Assumption

Adverse Selection Model

• Aware of the risk1• Developing over time2

A series of simulations

TÁMOP-4.2.2/B-10/1-2010-0023

H4H1 H2H3The number of policyholders is

decreasing over time.

The premium is increasing over time.The cumulative profit for 10

periods is negative.

The lower the discrete risk is, the faster the group terminates the contract.

Hypotheses

TÁMOP-4.2.2/B-10/1-2010-0023

ResultsInitial Frequencies

1 2 3 4 50

2

4

6

8

10

Fall-out by typesNot specified initial

frequencies

Type

Num

ber

of

peri

ods

1 2 3 4 50

2

4

6

8

10

Fall-out by types80-5-5-5-5%

Type

Num

ber

of

peri

ods

1 2 3 4 50

2

4

6

8

10

Fall-out by types5-5-5-5-80%

Type

Num

ber

of

peri

ods

1 2 3 4 5 6 7 8 9 100

200

400

600

800

1000

Number of PolicyholdersBernoulli Distribution

Number of periods

Num

ber

of

Policyhold

ers

1 2 3 4 5 6 7 8 9 100

200

400

600

800

1000

Number of PolicyholdersGamma Distribution

Number of periods

Num

ber

of

Policyhold

ers

1 2 3 4 5 6 7 8 9 100

200

400

600

800

1000

Number of PolicyholdersPareto Distribution

Number of periods

Num

ber

of

Policyhold

ers

1 2 3 4 5 6 7 8 9 100

200

400

600

800

1000

Number of PolicyholdersLognormal Distribution

Number of periods

Num

ber

of

Policyhold

ers

ResultsDistribution of Amount of Losses

2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

PremiumNo Moral Hazard

Number of periods

Pre

miu

m

2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

PremiumSignificant Moral Hazard

Number of periods

Pre

miu

m

ResultsMoral Hazard

TÁMOP-4.2.2/B-10/1-2010-0023

1 2 3 4 5 6 7 8 9 10750

800

850

900

950

1000

Number of PolicyholdersAware of the Risk

Number of periods

Num

ber

of

Policyhold

ers

1 2 3 4 5 6 7 8 9 10750

800

850

900

950

1000

Number of PolicyholdersDeveloping over time

Number of periods

Num

ber

of

Policyhold

ers

ResultsPolicyholders’ Risk Assumptions

TÁMOP-4.2.2/B-10/1-2010-0023

H1The number of policyholders is decreasing over time.

Results of Hypotheses

TÁMOP-4.2.2/B-10/1-2010-0023

1 2 3 4 5 6 7 8 9 10750

800

850

900

950

1000

Number of PolicyholdersAware of the Risk

Number of periods

Num

ber

of

Policyhold

ers

1 2 3 4 5 6 7 8 9 10750

800

850

900

950

1000

Number of PolicyholdersDeveloping over time

Number of periods

Num

ber

of

Policyhold

ers

ResultsPolicyholders’ Risk Assumptions

TÁMOP-4.2.2/B-10/1-2010-0023

H1The number of policyholders is decreasing over time.

Results of Hypotheses

TÁMOP-4.2.2/B-10/1-2010-0023

H2The premium is increasing over time.

Results of Hypotheses

TÁMOP-4.2.2/B-10/1-2010-0023

2 3 4 5 6 7 8 9 100.47

0.48

0.49

0.5

0.51

0.52

0.53

0.54

0.55

0.56

0.57

Premiumwhen the policyholders’ risk

assumption is developing over time

Number of periods

Pre

miu

m

TÁMOP-4.2.2/B-10/1-2010-0023

H2The premium is increasing over time.

Results of Hypotheses

TÁMOP-4.2.2/B-10/1-2010-0023

H3The cumulative profit for 10 periods is negative.

Results of Hypotheses

TÁMOP-4.2.2/B-10/1-2010-0023

2 3 4 5 6 7 8 9 10

-2

-1

0

1

2

3

4

Profitwhen the majority of the policyholders

is in the low risk type

Number of periods

Pro

fit

TÁMOP-4.2.2/B-10/1-2010-0023

H3The cumulative profit for 10 periods is negative.

Results of Hypotheses

TÁMOP-4.2.2/B-10/1-2010-0023

H4The lower the discrete risk is, the faster the group terminates the contract.

Results of Hypotheses

TÁMOP-4.2.2/B-10/1-2010-0023

ResultsInitial Frequencies

1 2 3 4 50

2

4

6

8

10

Fall-out by typesNot specified initial

frequencies

Type

Num

ber

of

peri

ods

1 2 3 4 50

2

4

6

8

10

Fall-out by types80-5-5-5-5%

Type

Num

ber

of

peri

ods

1 2 3 4 50

2

4

6

8

10

Fall-out by types5-5-5-5-80%

Type

Num

ber

of

peri

ods

H4The lower the discrete risk is, the faster the group terminates the contract.

Results of Hypotheses

TÁMOP-4.2.2/B-10/1-2010-0023

Conclusions

TÁMOP-4.2.2/B-10/1-2010-0023

• Adverse selection might have major influences on the• Number of policyholders• Premium• Loss expenses• Premium income• Profit

• Gender directive – role of adverse selection is enhancing• Simulations as tools for observing adverse selection

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To download my paper and model please visit:

TÁMOP-4.2.2/B-10/1-2010-0023

https://sites.google.com/site/orsiretaller/kutatas-research