Scope of Insurance Premium for Residential Houses against Seismic Risk in Japan

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1 Scope of Insurance Premium for Residential Houses against Seismic Risk in Japan J. Kanda a) and K. Nishijima b) a) University of Tokyo, Japan b) ETH, Switzerland ABSTRACT The premium for seismic insurance of houses in Japan is basically controlled by the government. Since individual structural capacities of houses are not sufficiently taken into account for the premium rating, the premium is fairly high in comparison with the existing risk. The present study compares the current seismic insurance premium and the expected seismic loss considering several levels of damages with damage cost statistics available from the Hyogoken-Numbu Earthquake for eight sites in Japan. The regional variation indicates the strong influences of the seismic hazard characteristics. The differentiation of premium considering the structural capacity is strongly recommended for improving the application ratio of seismic insurance. KEYWORDS Seismic insurance, Insurance premium, Seismic hazard, residential houses, Damage statistics, Fragility function, Loss function INTRODUCTION In Japan the seismic insurance for houses is re-insured by the government and the premium is basically controlled by the government. The seismic insurance is a part of the fire insurance as a special contract. The application rate for the seismic contract has increased since the Hyogoken-Numbu Earthquake 1995 and is approximately 35% at present. The premium was calculated from the average damages estimated from the past earthquakes during 500 years. Since 1995 the seismic insurance has been discussed in many occasions. The seismic hazard was reviewed and the insurance premium has been amended by reflecting the seismic risk. The premium in a higher zone is approximately three times that in a lower zone. On the other hand the premium for houses is not differentiated according to structural capacity differences. The tendency of relations between significant parameters in the loss function and reasonable insurance premium for houses is discussed by considering the seismic risk for individual houses based on expected annual portfolio loss.

2 We focus only on the Earthquake insurance premium for new houses properly built of steel structure and reinforced structure, because the main topic in this paper is to discuss on the consistency between the insurance premium at present and the statistics estimated from engineering experience such as expected loss or probable maximum loss based on damage statistics available. ESTIMATED LOSS FUNCTION The loss function can be estimated from the fragility functions proposed from damages by the Hyogoken-Nambu Earthquake. Murao and Yamazaki, 2000 showed typical fragility models for buildings with different constructions. These fragility functions can be applied to ordinary existing houses, while houses built according to the current Building Standard Law are estimated to have significantly higher capacity. Some houses with base isolation systems will have even higher capacity. Since sufficient information is not available for these houses, parameters in loss functions are somehow assumed based on the damages caused by Hyogoken-Nambu Earthquake. Fragility curve is assumed to be expressed in the following log-normal probability form with parameters in Table 1. lnv λi ( Damageratio) =Φ (1) ξ where V is the input earthquake ground motion on surface in velocity (cm/s), Φ is the normal distribution function, and i represents the damage state. These values are obtained after Hyogoken-Nambu earthquake for houses with grade 1, which is the basic performance grade as specified by the Law for Quality Assurance of Performance of Houses. The repair cost in Table 1 is obtained also from the Hyogoken-Numbu Earthquake as surveyed by Kanda and Hirakawa, Seismic performance for newly built houses in Japan can be categorized into three grades as the regulation specifies. Grade 1 is the ordinary level satisfying the criteria specified in the seismic regulation according to the Building Standard Law, Grade 2 is the level where 1.25 times seismic load of the regulation is applied and Grade 3 is the level where 1.5 times is applied.

3 Table 1 Parameters for log-normal fragility curve Damage state i λ ξ Repair cost (%) Slight ln Minor ln Moderate ln Severe ln Collapse ln According to the conventional contract of the earthquake insurance, the insurance is paid when the following criteria are met, If the monetary loss of elements of the relevant structure falls between 3 % and 20 %, or the house is affected by flood above floor level, 5 % of insured value is paid. (level 1) If the monetary loss of elements of the relevant structure falls between 20 % and 50 %, or 20 % to 70% of total floor is lost due to fire, tsunami, or flood, 50 % of insured value is paid. (level 2) If the monetary loss of elements of the relevant structure exceeds 50 %, or 70 % or more of total floor is lost due to fire, tsunami, or flood, 100 % of insured value is paid. (level 3) Compared with the loss due to the direct damage from earthquake motion, the probability that the house is damaged by fire, tsunami, or flood is so much smaller that only damage due directly to the earthquake motion is considered hereafter. In order to estimate some statistics of earthquake insurance, we need to relate the criteria of earthquake insurance to damage state of structure in Table 1. It seems rational to relate as level 1 to the slight and minor damage, level 2 to the severe and moderate damage, level 3 to the collapse. As a consequence, the insured loss, L, where i indicates the damage level, is obtained as the sum of the following, lnv ln50 lnv ln150 L1 = 0.05 Φ Φ (2a) i lnv ln150 lnv ln250 L2 = 0.5 Φ Φ lnv ln250 L3 = 1 Φ 0.4 (2b) (2c) Figure 1 shows the diagram of damage ratio for each stage of loss level. These loss functions can be interpreted as the ones for portfolio. The original fragility curve

4 represents the average loss ratio so that the local loss ratios may differ from average loss ratio. However, when portfolio loss is considered, the loss ratio can be rationally assumed to converge to average loss ratio by the law of large number. The portfolio loss can be used for insurance premium calculation. From this reason, thereafter we adopt the above loss functions as the ones for portfolio in a deterministic manner. SEISMIC HAZARD ESTIMATION For illustrative purposes, 8 major cities in Japan are selected, i.e. Sapporo, Sendai, Tokyo, Nagoya, Osaka, Hiroshima, Takamatsu, and Kitakyushu as shown in Figure 2. Seismic hazard analysis is conducted utilizing data and procedures proposed by Ochi et al Figure 3 shows earthquake hazard at each city. Major active faults are considered with respective occurrence probability according to a report provided by the Ministry of Education, Culture, Sports, Science and Technology, 2001 and the Gutenberg-Richer relationship for the earthquake occurrence is adopted where active fault information is not available based on the past earthquake statistics. Soil amplification factor at each site is assumed to be 2.0, which is a reference value for a relatively firm soil condition. Hazard values at Osaka, Nagoya and Takamatsu are relatively high as shown in Figure 2 as the consequence of To-kai and To-nankai Earthquakes with their fairly high occurrence probabilities. The uncertainty of attenuation formula used in the study is assumed as 0.5 in terms of the logarithmic standard deviation. Although this value is consistent to the statistics available for many earthquakes, it could be considered to be extremely high when the fault source model can be estimated and soil characteristics and path information are provided. The combination of high occurrence probability and high uncertainty of attenuation formula cause significantly high hazard results and could lead to the conservative loss estimation. This conservatism may be eliminated by applying scenario earthquakes to probabilistic hazard estimation such as proposed by Kanda et al, INSURANCE PREMIUM AND EXPECTED LOSS Table 2 shows basic insurance premium for each site for a house of reinforced concrete or steel structure. Even higher premium is determined for wooden houses. The seismic activity is considered based on the hazard evaluation and premium is differentiated for sites as listed in Table 2.

5 Table 2 Annual basic premium for RC or S Figure 4 shows the comparison between the present insurance premiums at each site and the mean insured loss estimated from engineering calculation. If a house is categorized to grade 1, 2 or 3, the insurance premium is reduced by 10 %, 20 %, 30 % respectively. The above mentioned fragility curve corresponds to the one for grade 1. From the engineering point of view it can be assumed that the resistance of the house with grade 2, 3 is stronger in terms of seismic load considered by 25 %, 50 % than the above mentioned fragility curve. Therefore the fragility curves for houses with grade 2, 3 are obtained by shifting the original fragility curves accordingly and so are insured loss functions. Table 3 shows the ratio of present premium, for each site and each grade, to expected insured loss obtained by hazard analyses and loss functions. Results of Table 3 indicates that present insurance premium in Table 2 does not fully reflect the local earthquake hazard, and what is more, the reduction of premiums by 20% or 30% for grade 2 or 3 respectively does not compensate at all for strengthened resistance of house. Table 3 (insurance premium at present) / (expected insured loss) Probable maximum loss (PML) curves for are shown in Figure percentile loss estimation was used as in the conventional PML estimation. 475 year is often considered for PML as the return period for the maximum earthquake ground motion, but the return period is treated as the variable in the figure to examine the tendency of the return period of input motion on the probabilistic loss estimation. As the tendency of the seismic activity differs from site to site, PML varies with the return period rather differently. In sites where the slope shallow as in Tokyo or Nagoya in Figure 5, damages are expected for relatively high frequency events which corresponds to the lower level

6 damages. Then this tendency can also pointed out in Figure 4, where the expected level 1 damage is relatively high in Tokyo or Nagoya. CONCLUSIONS Seismic insurance premium for houses is considered to be too high in Japan. Although insurance companies explain that the premium is determined according to the past earthquake damage statistics, the strength of present houses is not considered sufficiently for the premium determination. The present study describes numerical examples by showing the present premium and the expected loss, then the inconsistency of the local hazard and also the individual strength of houses are discussed. ACKNOWLEDGEMENT This project is partly supported by the grant from the JSPS for young scientists. REFERENCES Kanda, J. and Hirakawa, T. Failure cost estimation equivalent to multi-level limit state failure, Structural Safety and Reliability, Balkema, pp , Kanda, J. et al., Probabilistic design earthquake ground motions considering scenario earthquakes, Proc. 13 th World Conf. Earthquake Eng., Vancouver, Paper No. 2120, Ministry of Education, Culture, Sports, Science and Technology, Report on Survey of Active Faults, (in Japanese) Murao, O. and Yamazaki, F. Development of fragility curves for buildings based on damage survey data of a local government after the 1995 Hyogoiken-Numbu Earthquake, J. Struct. Constr. Eng., A.I.J. No.527, pp , (in Japanese) Ochi, S., Sakamoto, S., Takada, T. and Kanda, J. An internet-based system for seismic performance evaluation of existing buildings, 1 st ASRANet International Colloquium, Glasgow, 2002.

7 Figure 1 Diagram of damage ratio for each level Figure 2 Locations of 8 sites in Japan

8 Figure 3 Hazard curves at 8 sites Figure 4 Comparison between present insurance premium and expected insured loss from our analysis at each site

9 Figure 5 PML curve at each site

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