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1 c PML Swiss Re 2001 Canabarro et al : IHD
2 ,
3 A B PML Probable Maximum Loss X Y 3 2.
4 PML a H(a) x f H(x) (3.1) H(a) = Z a f H(x)dx i 3.
5 263 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 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 a, 2000b
6 Annaka and Yashiro
7
8 i l P (i) 7.
9 267 (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 =
10
11 C 0 = gal C gal Annaka and Yashiro (4.1) log A =0.61M h log(d) d =( h 2 ) exp(0.699m) A h M 0.5 5
12
13 km km 6 1 f 2( ) 12 3 a M = M = b c M = M = PML /475 PML PML
14 PML PML 4 PML PML PML 200 PML b 8 1
15 PML b M M =730 14
16 =292 M
17 M PML
18 PML 4 19 M 0 M a
19 277 c 1 PML PML 1 PML 1/475 PML PML 3 4 Annaka, T. and Yashiro, H 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), , WIT Press, Southampton, U.K. Annaka, T. and Yashiro, H Uncertainties in a probabilistic model for seismic hazard analysis in Japan, Risk Analysis II ed. C. A. Brebbia, , WIT Press, Southampton, U.K. Canabarro, Eduardo, Anderson, Richard R., Finkemeier, Markus and Bendimerad, Fouad Analyzing Insurance-linked Securities, Fixed Income Research, Goldman Sachs, New York PD a b. JCOSSAR PML Swiss Re Capital market innovation in the insurance industry, Swiss Re SIGMA Series, No. 3, Zürich.
20 278 Proceedings of the Institute of Statistical Mathematics Vol. 50, No. 2, (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.
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