2002 50 2 259 278 c 2002 1 2 2002 2 14 2002 6 17 73 PML 1. 1997 1998 Swiss Re 2001 Canabarro et al. 1998 2001 1 : 651 0073 1 5 1 IHD 3 2 110 0015 3 3 3
260 50 2 2002, 2. 1 1 2 10 1 1.
261 1. 3. 3.1 2 1 A B PML Probable Maximum Loss 50 10 0.002105 475 X Y 3 2.
262 50 2 2002 2 PML 3.2 2 3 2 3 a H(a) x f H(x) (3.1) H(a) = Z a f H(x)dx i 3.
263 f F (x, i) a F (a, i) (3.2) F (a, i) = Z a 0 f F (x, i)dx i C(i) L(a) (3.3) L(a) = n 1 X i=1 C(i){F (a, i) F (a, i +1)} + C(n)F (a, n) n i 3.3 1 2 PML PML 1 2 A B L A L B µ A µ B σ A σ B L P µ P σ P (3.4) (3.5) µ P = µ A + µ B σp 2 = σa 2 + σb 2 +2ρσ Aσ B ρ L A L B ρ =1 (3.6) σ 2 P =(σ A + σ B) 2 σ P = σ A + σ B PML PML 3.5 ρ =1 PML 1 1 3 2 2000a, 2000b 2000 2001 1999
264 50 2 2002 3 4 Annaka and Yashiro 2000 2 4 4.
265 1 1 5 5. 6.
266 50 2 2002 6 1 4 200 0 1 3.4 1 7 i l P (i) 7.
267 (3.7) l P (i) =l P (i) l(i) l P (i) l P (i) l(i) (3.8a) (3.8b) l(i) = min[l u,f 1(l P (i))] (l P (i) >l 0) l(i) =0 (l P (i) l 0) l 0 l u f 1( ) (3.9a) (3.9b) l(i) =f 2(M(i)) C (M(i) M 0) l(i) =0 (M(i) <M 0) M(i) i C M 0 f 2( ) 2 p p p (3.10a) (3.10b) p = L ovl /L rpt p = A ovl /A rpt L rpt L ovl A rpt A ovl p =1 p =0 8 4. 4.1 1 0.05 73
268 50 2 2002 8. 9. 1 100 7300 9 2 1
269 2. 2000 1 2 C 0 =0.2 80 gal C 0 1.0 400 gal 1 2 1 1998 1.5 1998 0.7 2 3 2000 5 10 30 100 2 4 Annaka and Yashiro 1998 10 3 (4.1) log A =0.61M +0.00501h 2.203 log(d)+1.377 d =( 2 +0.45h 2 ) 0.5 +0.22 exp(0.699m) A h M 0.5 5
270 50 2 2002 10. 3.
271 11. 11 1 2 1 20 km 3 1 50 km 6 1 f 2( ) 12 3 a M =6.9 25 M =7.4 100 b c M =7.1 7.6 M =7.3 7.8 7 PML 13 200 1/475 PML PML 249.38 3.42
272 50 2 2002 12. 13. PML 292 730 4 10 4.2 1 PML 4 PML PML PML 200 PML 2 14 4 12 b 8 1
273 4. PML 292 3 1 2 1 15 b M7.6 15 M7.8 8.2 2 3 1 2 14 2 3 1 2 3 14 16 14 10 =730 14
274 50 2 2002 14. 4 15. 1 3 14 3 17 14 16 2 4 =292 M7.8 8.2 100
275 16. 10 17. 4 M7.8 0.002 0.002 18 14 16 17 0.002 14 16 2 3 4 PML
276 50 2 2002 18. 10 19. PML 4 19 M 0 M 0 4 0.04 a 3 4 0.1
277 c 1 PML 5. 73 PML 1 PML 1/475 PML 2 0.002 PML 3 4 Annaka, T. and Yashiro, H. 1998. A seismic source model with temporal dependence of large earthquake occurrence for probabilistic seismic hazard analysis in Japan, Risk Analysis (eds. C. A. Brebbia and J. L. Rubio), 233 242, WIT Press, Southampton, U.K. Annaka, T. and Yashiro, H. 2000. Uncertainties in a probabilistic model for seismic hazard analysis in Japan, Risk Analysis II ed. C. A. Brebbia, 369 378, WIT Press, Southampton, U.K. Canabarro, Eduardo, Anderson, Richard R., Finkemeier, Markus and Bendimerad, Fouad 1998. Analyzing Insurance-linked Securities, Fixed Income Research, Goldman Sachs, New York. 1998. 1998 PD 15 20. 2000a. 11 275 278. 2000b. JCOSSAR2000 205 208. 2001. 5 21 23. 1999. 47 1 27 30. 1998. 2000. PML 12 2 69 76. 2001. 12 41 46. Swiss Re 2001. Capital market innovation in the insurance industry, Swiss Re SIGMA Series, No. 3, Zürich.
278 Proceedings of the Institute of Statistical Mathematics Vol. 50, No. 2, 259 278 (2002) An Analysis for Securitizing of Seismic Risk Harumi Yashiro (Asian Disaster Reduction Center; The Tokio Marine and Fire Insurance Co., Ltd.) Sei ichiro Fukushima (Tokyo Electric Power Services Co., Ltd.) In recent years, some risk analysis methods have been proposed for quantitative evaluations of risk. However although it is important for carrying out effective risk management, the treatment of quantified risk has not been considered sufficiently. This paper proposes a seismic portfolio analysis method considering the effect of risk transfer such as securitization, which has been adopted to the portfolio of 73 buildings in Tokyo. Through its application, the following findings are obtained: the grid has a relatively large effect on the PML (probable maximum loss) although the forfeiture rate of principal does not, risk transfer is more effective from the viewpoint of investment for risk with a smaller grid and a higher trigger level that is the minimum magnitude for forfeiture, and some combinations of grid and forfeiture rate can be identical to each other regardless of principal. Key words: Portfolio of buildings, risk management, seismic risk, risk transfer, securitization of risk.