ICBE 2007

Gabriela Atanasiu, Genoveva Perju

Technical University of Iasi, Romania

Identifying the risk from the average expected Identifying the risk from the average expected annualized losses at earthquakeannualized losses at earthquake

ICBE 2007

Magnitude Description of Effect

less than 3.4

Usually felt by only a few people near the epicenter.

3.5 - 4.2 Felt by people who are indoors and some outdoors; vibrations similar to a passing truck.

4.3 - 4.8 Felt by many people; windows rattle, dishes disturbed, standing cars rock.

4.9 - 5.4 Felt by everyone; dishes break and doors swing, unstable objects overturn.

5.5 - 6.1 Some damage to buildings; plaster cracks, bricks fall, chimneys damaged.

6.2 - 6.9 Much building damage; houses move on their foundations, chimneys fall, furniture moves.

7.0 - 7.3 Serious damage to buildings; bridges twist, walls fracture, many masonry buildings collapse.

7.4 - 7.9 Causes great damage; most buildings collapse.

greater than 8.0

Causes extensive damage; waves seen on the ground surface, objects thrown into the air.

ICBE 2007

ICBE 2007

Earthquakes - 1996Earthquakes - 1996

ICBE 2007

Hawaii is the state at greatest risk for a tsunami. They get about one a year, with a damaging tsunami happening about every seven years. Alaska is also at high risk. California, Oregon and Washington experience a damaging tsunami about every 18 years.

Damage at the Mauna Kea Beach Resort: (a) structural damage at an elevator shaft and (b)

severe cracking at expansion joint

Tsunami Damage, Indian Ocean December 26, 2004

ICBE 2007

Forecasting TheoryForecasting Theory

- Moving Average

Risk

ICBE 2007

Identifying the risk from the average expected annualized losses at earthquakeIdentifying the risk from the average expected annualized losses at earthquake

• (Porter et.others , 2004 )

• where: • V denotes value exposed to loss (e.g., replacement cost

of the building);• s refers to some seismic intensity measure;• y(s) is the mean seismic vulnerability function, defined

here as the average level of loss as a fraction of V given an occurrence of s;

• v(s) is the average annual frequency of experiencing shaking intensity s.

0( ) ( )

sEAL V y s v s ds

∞

== ∫

ICBE 2007

Identifying the risk from the average expected annualized losses at earthquakeIdentifying the risk from the average expected annualized losses at earthquake

• are the mean values of the seismic vulnerability function respectively of the annual frequency of experiencing a shaking intensity s.

• We consider one medium probability of loss occurrence

at a medium value of the shaking magnitude.

8

1( ) ( )

=7 * ( )* ( )

sEAL V y s v s ds

V y c v c=

= ∫

( ) and ( )y c v c

( )= [1 0.75 0.5 0.33 0.25]y c

ICBE 2007

Identifying the risk from the average expected annualized losses at earthquakeIdentifying the risk from the average expected annualized losses at earthquake

Loss probability

Frequency

100% 75% 50% 33% 25%

1/1 (1.0) 7 V 5.25 V 3.5 V 2.31V 1.75V

½ (0.5) 3.5 V 2.65 V 0.25 V 0.17 V 0.13 V

1/3 (0.33) 2.33 V 0.25 V 0.165 V 0.11 V 0.08 V

¼ (0.25) 1.75 V 0.19 V 0.125 V 0.08 V 0.06 V

1/5 (0.2) 1.4 V 0.15 V 0.1 V 0.07 V 0.05 V

1/6 (0.16) 1.12 V 0.12 V 0.08 V 0.05 V 0.04 V

1/7 (0.14) 0.98 V 0.11 V 0.07 V 0.05 V 0.04 V

1/8 (0.12) 0.84 V 0.09 V 0.06 V 0.04 V 0.03 V

1/9 (0.11) 0.77 V 0.08 V 0.055 V 0.04 V 0.03 V

1/10 (0.1) 0.7 V 0.08 V 0.05 V 0.03 V 0.03 V

ICBE 2007

Identifying the risk from the average expected annualized losses at earthquakeIdentifying the risk from the average expected annualized losses at earthquake

Loss probability Frequency

100% 75% 50% 33% 25%

1/1 (1.0) Unacceptable risk

Unacceptable risk

Unacceptable risk

Unacceptable risk

Unacceptable risk

½ (0.5) Unacceptable risk

Unacceptable risk

Medium risk

Medium risk

Medium risk

1/3 (0.33) Unacceptable risk

Medium risk

Medium risk

Medium risk

Low risk

¼ (0.25) Unacceptable risk

Medium risk

Medium risk

Low risk Low risk

1/5 (0.2) Unacceptable risk

Medium risk

Low risk Low risk Low risk

1/6 (0.16) Unacceptable risk

Medium risk

Low risk Low risk Low risk

1/7 (0.14) High risk Medium risk

Low risk Low risk Low risk

1/8 (0.12) High risk Low risk Low risk Low risk Low risk 1/9 (0.11) High risk Low risk Low risk Low risk Low risk 1/10 (0.1) High risk Low risk Low risk Low risk Low risk

ICBE 2007

ConclusionsConclusions

• The seismic risk with low frequency of occurrence and low proximity of loss should be ignored and therefore not insured. We refer here to losses below 10% of the initial value of the building that in any case are not covered by insurance because of deductibles.

• In case of an earthquake occurrence of once in every year the risk is unacceptable and disinvestment should be considered as option.

• For frequencies of occurrence of once in one year and once in two years the seismic risk cannot be mitigated through diversification and therefore unacceptable for insurer too.

• The only insurable risk is the medium towards high level of seismic risk. If the expected losses exceed 80% of the initial investment the decisions of risk mitigation should involve disinvestment or governmental aid.