a case study for an Italian Region
3. Numerical experiments
For Option 1, where the burden of losses is equally distributed over the population, the annual premium is equal to the flat rate of 0.02 monetary units (m. u.) per cubic meter of building (in per cent term, i.e., t x
100
πj , j=1,...,m, t∈[ T0, ]).
For Option 2, Fig. 2 shows the distribution of municipality-specific premiums based on average damage in each municipality (or according to the municipality-specific risk exposure factor).
There is a prevailing number of municipalities (about 220) that have to pay 0.02-0.03 m. u., which is close to the flat rate of 0.02, as in Option 1. About 20 municipalities are at no risk at all (0 rate). Municipalities more exposed to the risk, have to pay 0.04 and higher rates (more than 50 municipalities).
0 20 40 60 80 100 120 140 160 180 200
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 More
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Fig. 2. Distribution of municipality-specific premiums (per m3 building volume at municipality, in per cent terms).
Fig. 3 shows the distribution of the insurers’ reserve at premiums of Options 1 and 2. The reserve is cumulated over a 50 year time span. The volume of capital is defined by the horizontal axis. The probability of insolvency (when the risk reserve accumulated until the occurrence of the catastrophe is not enough to compensate incurred losses) is indicated on the
right-hand ordinate axis. As is seen, there is a rather high probability of ‘small’ insolvency (values –90, -40 occurred 190 and 90 times out of 500 simulations). High solvency (more than 500 m. u.) occurred in about 10 per cent of the simulations. The insolvency would represent the cost to the government in guaranteeing the reserve fund.
Fig. 4 shows the distribution of premiums for Option 3. According to this principle, most of the municipalities (190) have to pay close to the flat rate of 0.02-0.03 m. u. per cubic meter of building. Rates of 0.04 and higher have to be paid by about 100 municipalities. In this case the highest premium rate is 0.5, which, in comparison to the highest rate of 1.2 of Option 2, is much lower. The distribution of the insurer's reserve in Fig. 5 indicates also the improvement of the insurer’s stability: the frequency of insolvency is reduced to 3 out of 500 performed simulations.
0 50 100 150 200 250
-138.9 -91.7 -44.5 2.8 50.0 97.2 144.4 191.6 238.8 286.0 333.2 380.4 427.6 474.8 522.0 569.2 616.4 663.6 710.8 758.0 805.2 852.4 More 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Fig. 3. Distribution of insurer’s reserve for Options 1 and 2 (in thousands monetary units over 50 years).
0 20 40 60 80 100 120 140 160 180 200
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 More
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Fig. 4. ‘Fair’ premiums according to model (1)-(2), or gainer-looser equilibrium (per m3 building volume at municipality, in per cent terms).
0 50 100 150 200 250
-23.2 51.0 125.3 199.5 273.7 347.9 422.2 496.4 570.6 644.8 719.1 793.3 867.5 941.8 More 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Fig. 5. Distribution of insurer’s reserve for Option 3 (in thousands monetary units over 50 years).
0 0.2 0.4 0.6 0.8
1 21 41 61 81 101 121 141 161 181 201 221 241
Flat (0.02) Location-specific ’Fair’
Fig. 6. Comparison of Options: flat, municipality-specific, and ‘fair’ premiums.
Fig. 6 is very illustrative. For each municipality it shows the optional premiums to be paid: the flat premium rate of 0.02, the Option 2 municipality-specific rate, and the ‘fair’ premium of Option 3. Many municipalities in all three options have to pay the premium rate, which is about the flat rate (0.015-0.03). For quite a number of municipalities in Options 2 and 3, the rate significantly exceeds the flat rate. Options 2 and 3, therefore, identify the municipalities, which are most exposed to the risks. For these municipalities special attention should be given as to whether they are able to pay such high risks. The model here incorporates average wealth (households’ income) in municipalities, which can be regarded as additional constraint on the municipalities ‘solvency’ (overpayments). Option 3 allows to take such individual constrains into account and work out the premium rate optimal both for insurer and for municipalities.
4. Conclusions
The case study based on a comprehensive geographically distributed data set has demonstrated the ability of the methodology developed at IIASA to analyse and compare different policy options for risk sharing in the case study region. The methodology is able to incorporate different kinds of hazard and vulnerability models, and to deal with various kinds of dependencies.
Future work should
include probability distributions for vulnerability, instead of point value, as in the present study;
investigate the trade-off between structural mitigation measures and insurance strategies for an integrated risk management;
include a people's behaviour model with respects their willingness to make use of possible incentives to reduce vulnerability, and/or to buy insurance. In this case the live- savings aspects of retrofitting should also be considered;
introduce dynamics of reconstruction, and superimposing seismic crises.
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