궷쁉뫞뉺뻇돸 닄꒭ꣷ 닄ꑇ듁 2003꙾7ꓫ Journal of Risk Management July 2003 -260 ꕸ왗ꖨꡡ뙗썂ꙁꭏ쁉ꮴ곹뭐뗻믹* Pricing Excess-of-Loss Catastrophe Reinsurance Contract: the Case in Taiwan ꩌꓥ꧷**ꅝWen-Chang Linꅞ뿠꧉견***ꅝYi-Hsun Laiꅞ 멋?굮 륌ꕨ볆꙾ꅁ쇶땍ꖨꡡ궷쁉쏒꣩꓆Ꙣꕸ왗ꑷ덑뱳꩸끑뷗ꅁꙢꖫ돵ꥼꖼꚨ보ꭥꚳ궭ꪺ뛇닎꧓ꭏ꿠뙱ꑕꅁꗑꗁ뚡끴Ꙙ걆ꦲꪺꙁꭏ쁉꒴결ꕄ굮ꕩꛦꪺ늾신궷쁉ꓨꚡꅃꖻꓥ궺ꗽ뷗굺빁Ꙙꕸ왗ꪺ걆ꦲꖨꡡ뙗썂ꙁꭏꮴ곹꒧귬뉺뭐걛멣ꅁꙁ껚뻚ꕸ왗ꙡ냏ꓑ땍ꖨꡡ맪믚띬깠닎군룪껆ꅁ꣏ꗎ랥귈뉺뷗꒤ꪺ쉥ꅝPOTꅞ볒ꮬ꣓끴빁꣤띬ꖢ꒧Ꟁ뫝꓀끴ꅁꣃ끷맯ꖨꡡ띬ꖢꪺ꽓꧊ꅁꕈꙢ꿂뫩룵아륌땻ꑕꪺ끝냈뿯뻜앶귬뉺꣓군뫢걆ꦲꖨꡡꙁꭏ쁉ꮴ곹ꪺ믹귈ꅁꕈꝀ결뗻믹ꪺ뉺뷗냲슦ꅃ떲ꩇ엣ꗜꕸ왗ꓑ땍ꖨꡡꟀ뎡꓀끴곛럭빁Ꙙꕈꪬ냑볆꒣결륳ꪺꑀ꿫꓆걦꧔맏ꅝGPDꅞ꓀끴꣓둹굺ꅃ굙ꕈ맯볆녠멁꓀끴ꯘ멣Ꟁ뎡꓀끴ꅁꭨ걆ꦲꙁꭏꮴ곹믹귈ꕩ꿠ꝃ꛴ꅁ꒧ꅁ굙ꕈ볆꓀끴ꯘ멣Ꟁ뎡꓀끴ꭨꕩ꿠낪꛴ꅃ쁈뗛ꮴ곹꒣Ꙑꑗꑕ궭깴뙚ꪺ엜꓆ꅁꙁꭏꮴ곹믹귈ꑝ녎쁈꒧ꝥꭄ뵵꧊엜ꅃ귌ꑝ땯뉻럭쉥귈뱗ꕛꅁꮴ곹믹귈ꑝ쁈꒧ꑗꅃꖻꓥꪺ뗻믹ꓨꩫ뭐떲ꩇꕩꝀ결ꖼ꣓걆ꦲ덝군ꟳꞹ돆ꖨꡡ뙗썂ꙁꭏꮴ곹꦳믹굱ꥷꪺ냑ꛒꅃ 쏶쇤꙲ꅇꖨꡡꅁ뙗썂ꙁꭏ쁉ꅁ룵아륌땻ꅃ * Ꝁ꽓ꝏ띐쇂ꑔꛬ냎ꙗ뗻뱦ꪺ쑟뙑띎ꢣꅃꖻ곣ꡳ놵꣼냪곬라곣ꡳ룉ꝕꅁ뵳뢹NSC 89-2416-H-194-055 ** 냪ꗟ꒤ꖿꑪ뻇끝냈뿄곣ꡳ꧒ꝕ뉺뇐뇂ꅁAssistant Professor, Department of Finance, National Chung Cheng University, Chia-Yi, Taiwan. *** 냪ꗟ꒤ꖿꑪ뻇끝냈뿄곣ꡳ꧒돕ꑨ꽚곣ꡳꗍꅁDoctoral Student, Department of Finance, National Chung Cheng University, Chia-Yi, Taiwan.
234 ꕸ왗ꖨꡡ뙗썂ꙁꭏ쁉ꮴ곹뭐뗻믹 Abstract Although the securitization of catastrophe risk in Taiwan had been widely advocated by scholars and regulator recently, traditional reinsurance still plays as a major risk transfer tool for the property and liability insurer because of the immaturity of catastrophe derivative market. In this paper, we first address the rationales and, subsequently, price the ongoing government excess of loss reinsurance contract in Taiwan. We fit the loss distributions by using most updated catastrophe data. More specifically, the Generalized Pareto distributionꅝGPDꅞfrom extreme value theory is undertaken to describe the tail distribution of Taiwan’s natural disaster. Our results indicate that GPD is a decent choice for loss data fitting compared to other distributions. Finally, the contract’s values are computed by mean of a pure-jump based financial option model. According to the simulation results, we find that the contract value may be underestimated if the excess of loss distribution is fitted by lognormal. Conversely, exponential distribution may overestimate the true contract value. In addition, given the computed contract values under various triggers/caps, we find that it may vary in accordance with different thresholds. Our results may serve as a supportive function on the design and pricing of government catastrophe XOL reinsurance contract in Taiwan. KeywordsꅇCatastrophe, Excess of Loss Reinsurance, Jump Process.
궷쁉뫞뉺뻇돸 닄꒭ꣷ 닄ꑇ듁 2003꙾7ꓫ235 1. ꭥꢥ ꕸ왗ꙡ덂믤궷뭐ꙡ빟쁗셣꒧ꙡ녡ꅁ녱ꑋꑃꓴꡡꅂꑅꑇꑀꙡ빟ꕈꛜ돌꫱ꪺ꿇ꝑ궷ꡡꅁ뻺꙾뎣녡꣓ꑪꑰ꒣ꑀꪺ띬ꖢꅃꓑ땍ꖨꡡ쓝꧳곛쏶띬ꖢꕂ결ꝃ쁗뉶ꅂ낪띬ꖢ꒧궷쁉ꅁ꒣꧶ꗑ뛇닎ꭏ쁉꣓꒤ꥍꅝrisk poolingꅞꅁꙁꭏ쁉Ꙗ꣓결ꭏ쁉꒽ꕱꕄ굮궷쁉신늾ꑵ꣣ꅁ귉ꝕ꧳꒣Ꙑꙡ뉺냏꣓꓀뒲궷쁉ꅝgeographical diversificationꅞꅃFrootꅝ1999ꅞꕘꅆꙁꭏ쁉맯꧳ꖨꡡ궷쁉ꅁ꽓ꝏ걏Ꙣꖨꡡ땯ꗍ륌ꯡꅁ꧶늣ꗍ꣑떹뙱꒣ꢬꅂ믹껦ꝥ뉻꒣쎭ꥷꅂꕈ꣓ꛛꭏ쁉ꑈꪺ륄뱷ꙍ쁉끦뿯뻜ꅂ썢쉟ꅂ때껄뉶떥냝썄ꅁ뻉ꛜꑀ꿫냓띾ꙁꭏ쁉녠때ꩫꚳ껄룑ꡍꖨꡡ궷쁉늾신냝썄ꅃꕴꑀꓨ궱ꅁ녎궷쁉ꗑꭏ쁉ꖫ돵꓀뒲ꛜ룪ꖻꖫ돵ꪺ꧒뿗ꖨꡡ궷쁉뗽ꣷ꓆1꫱꙾꣓붫결궷ꛦꅁ꣤쇶꣣ꚳꗦ꧶ꚨꖻꝃꅂ꧓ꭏ깥뙱낪떥쁵쉉ꅁ꣒꙰Ꙣ1992꙾과냪ꪺCBOT뙽ꥬꗦ꧶ꪺꖨꡡ듁덦ꅝcatastrophe futureꅞꅁꙝꖨꡡ볆꣮ꥷꪺ냝썄Ꙣꕛꑗ볆ꗧꕩ꿠ꚳ룵아뉻뙈ꛓ뻉ꛜ륈곹떥냝썄ꛓ꒣곆ꚨꕜꅆꚹꕾꅁꖨꡡ볆뿯뻜앶ꅝ꙰과냪 PCS optionꅞꖨꡡ뛅꣩ꅝCAT bondꅞ떥쇶Ꙣ냪ꕾꑷꚨ결녠ꢣꪺ쇗쁉ꑵ꣣ꅁ냪꒺ꓥ쑭ꑝꚳ꧒꒶닐ꅝ뎯녠ꡞꅂ녩롧뉺ꅁ1997ꅆ뱂ꣴ꽅ꅁ1997ꅆꭊꑂꓫꅁ2001ꅆ뎯뷷럗ꅁ2001떥ꅞꅁ땍ꛓ덯ꭏ쁉구ꗍꪫꅝinsurance derivativesꅞꪺ볧Ꙣ냝썄걏ꅆ땯ꛦ뭐룪ꑈꕩ꿠꙳ꚳ꒣꒽뙽꒣맯뫙룪끔ꅆ걏ꙝꖨꡡ띬ꖢ꓀끴뭐꣤냑볆ꪺ꒣뵔ꥷ궷쁉ꅁ뙩ꛓ꣏룪ꑈ꧄ꡂꅆ걏ꖫ돵ꗦ꧶ꅝ꙰늣쁉꒽ꕱꅞꪺ꒣보노떥ꅁꞡ꣏덯냓ꭾ땵듁꒺Ꙣꕸ왗꒣꧶ꚨ보ꅃꙝꚹꙢ꣨꒣깥뵷ꑕꅁꗁ뚡끴Ꙙ걆ꦲ뒣꣑ꙁꭏ쁉ꅁ꫱듁꒺꒴녎ꕄ굮ꕩꛦꪺꖨꡡ궷쁉늾신ꓨꚡꅃ ꕈꗘꭥ냪꒺덱륌ꪺꛭꙶꙡ빟ꭏ쁉Ꙁꭏꙍ쁉꧓뻡뻷꣮뿬ꩫ결꣒ꅁ륷군뇄꣺ꕼ뱨꿅꣮ꯗꅁ궺ꗽꗑ냪꒺늣쁉꒽ꕱꙀꭏꅝꑇꑑ믵ꅞꅁ닄ꑇ뱨ꭨꗑ끝많ꩫꑈ냲꧓뻡ꅝꑀꛊꑋꑑ믵ꅞꅁ닄ꑔ뱨ꅝꑇꛊ믵ꅞꙁꙷ뇆냪ꕾꙁꭏ쁉꒽ꕱꙁꭏ룪ꖻꖫ돵꓀뒲ꅁ돌ꯡꙁꗑ걆ꦲꗩ럓과ꅂꓩ꣮ꯗꅁꗑ냪깡꣓꒶ꑊꅁꕈ룑ꡍ꧓ꭏ꿠뙱꒣ꢬꙁꭏ믹껦꒣쎭ꪺ냝썄ꅃ꒣Ꙑ꧳과냪ꅁ꣤냪꒺ꙕꙡ뉺냏ꝙꚳ곛럭꒧궷쁉꓀뒲ꅁꕸ왗ꙝ결궱뽮꾶ꑰꅁꙢꫬ뱨꿅ꅝlayerꅞꭏ쁉ꝙ믝귉ꝕ냪ꕾꙁꭏ쁉ꕈ륆꣬ꙡ뉺냏ꪺ꓀뒲ꅁꕛꑗ꫱꙾꣓ꖨꡡ쁗셣ꅁ냪믚ꙁꭏ뎼Ꙗ귗ꖿ믹껦궰ꝃ꧓ꭏ뙱ꅁꙝꚹ빁럭ꪺ걆ꦲ꒶ꑊꕈ꒶ꑊꪺ곉궭ꅝtrigger or attachmentꅞ둎엣녯ꑑ꓀궫굮ꅃ믝ꪾ걆ꦲ꒶ꑊꣃꭄ걏ꗎ꣓꣺ꕎ뭐ꗁ뚡ꙁꭏ뭐룪ꖻꖫ돵쑶ꪧꅁꛓ걏뛱룉꣤꒣ꢬꪺ뎡ꗷꅃꕈꗘꭥ낪뱨걆ꦲ꧓뻡ꪺ뎡ꗷ꣓뮡ꅁꥼ때ꭏ뙏군뫢꒧뉺뷗뻚ꅁꕂ뉻ꛦ꧓뻡띬ꖢ뱨꿅ꑝꚳ궭ꅝꑀꛊ믵꒸ꅞꅁꖼ꣓ꕸ왗삳ꕩ듂쉘ꑪ꧓ꭏ뵤돲띬ꖢ뱨꿅뙩ꅁꕈ뒣꣑ꗾꗁꟳ뱳ꪺ 1 싇ꗑ룪ꖻꖫ돵룻ꑪꪺ깥뙱ꅁ뒣꣑ꭏ쁉ꮴ곹ꟳꚳ껄ꪺ궷쁉꓀뒲ꅃ
236 ꕸ왗ꖨꡡ뙗썂ꙁꭏ쁉ꮴ곹뭐뗻믹 ꓑ땍ꖨꡡꭏ믙ꅃ ꙝꚹꅁꖻꓥꕈ돌낪뱨꿅ꪺ걆ꦲꖨꡡꙁꭏ쁉ꮴ곹결끑뷗볐ꪺ2ꅁꗽ녱걆ꦲ꒶ꑊ꣮ꯗꪺꝑ맺꣓끑뷗ꅁꣃꕈꕸ왗ꙡ냏륌ꕨꓑ땍ꖨꡡ띬ꖢ룪껆3ꅁꝑꗎ랥귈뉺뷗꒤ꪺ쉥ꅝpeak over threshold, POTꅞ볒ꮬꡄ꣤띬ꖢ꒧Ꟁ뫝꓀끴ꅁꙁ떲Ꙙ끝냈뿯뻜앶굱믹ꅁ낣ꑆ뎯굺꣤뉺뷗뻚ꅁꣃ맪믚룕뫢ꡄ녯꣤끝냈Ꙙ뉺믹껦ꅁꕈ낵결ꕸ왗ꙡ냏ꖼ꣓ꯘꗟꟳꞹ뻣ꪺꓑ땍ꖨꡡ걆ꦲꙁꭏ쁉꣮ꯗ뭐굱믹꒧뉺뷗냲슦ꅃ곛룻꧳륌ꕨ냪꒺ꕾ곣ꡳꅝꩌ뇓뗘, 1994; Lewis and Murdock, 1996; Cummin, 1999떥ꅞꅁꖻꓥ낣ꑆ뎯굺걆ꦲꖨꡡꙁꭏꮴ곹ꪺ뉺ꗑꕾꅁꕄ굮ꪺ돐띳뭐끞쑭ꕝ걁ꅇ(1). 둹굺끝냈뿯뻜앶삳ꗎ꧳ꭄ샧ꝑꪺ걆ꦲꭏ쁉ꮴ곹꒧꽓꧊ꅃ(2). 떲Ꙙ랥귈꓀끴꣓둹굺꿂룵아륌땻꧳뿯뻜앶뗻믹꒤ꅃ(3). 궺ꚸꕈꕸ왗륌ꕨꓑ땍ꡡ깠맪믚룪껆꣓끴빁ꅃ뒫ꕹ룜뮡ꅁꖻꓥ꽓ꛢꙢ꧳끷맯ꕸ왗ꪺ꽓꧊ꅁ녎ꙁꭏ쁉ꮴ곹ꅂ걆ꦲꭏ쁉뭐끝냈뿯뻜앶뉺뷗덳놵ꅁꕂ삳ꗎ룻결Ꙙ빁꒧랥귈꓀끴꧳룵아띬ꖢ륌땻꒤ꅁ꧒땯깩ꪺꓨꩫ뭐녯꣬ꪺ떲ꩇꅁꕩꝀ결ꖼ꣓걆ꦲꖨꡡꭏ쁉ꮴ곹굱믹곣ꡳ꒧궫굮냑ꛒꅃ 2. ꖨꡡ뙗썂ꙁꭏ쁉ꮴ곹 걆ꦲꙢꮴ곹꒤꒧ꢤꛢ ꗑꭏ쁉ꖫ돵ꪺꢤꯗ꣓곝ꅁꖨꡡ궷쁉Ꙣꖫ돵꒺ꝥ곛럭땻ꯗꪺ꡴닎꧊ꅁꗑ꧳ꭏ쁉꒽ꕱ뭐룪ꖻꖫ돵뚡ꪺ룪끔꒣맯뫙ꅁ궱맯랥ꑪ띬ꖢꅝ꙰ꖨꡡꅞ껉ꅁꙝ결앶꽱룪ꖻ녠때ꩫꛛꗑ걹냊ꅁꗧꝙꭏ쁉ꖫ돵꒤ꪺ꒣ꞹ과뉻뙈ꅝmarket imperfectionꅞꅁ룪ꖻꖫ돵굮ꡄꪺꖲ굮돸륓뉶ꕩ꿠ꙝꖨꡡ띬ꖢꪺ땯ꗍꛓꑗꅁ뙩ꛓ꣏뿄룪ꚨꖻ뱗ꕛꅁꙁꭏ믹껦ꑝꙝ꣑떹ꑕ궰ꛓꑗ몦ꅆꝙ꣏ꡓꚳꖫ돵꒣ꞹ과ꅁ믹껦ꑝꕩ꿠ꙝꙁꭏ꒽ꕱꕩ꿠궫띳귗ꖿꖨꡡ띬ꖢ뻷뉶ꛓꑗ몦ꅃꕴꑀꓨ궱ꅁꖫ돵ꑝꕩ꿠뭻결ꭏ쁉꒽ꕱꑝ덜때ꩫ꙳겡ꢬ냷ꪺ껉뚡륆ꚨ앶꽱룪굮ꡄ돸륓뉶ꅁꝙ꣏꣤쑀띎ꕈ룻낪ꪺꚨꖻꅁꑝ때ꩫ샲녯꧒믝룪ꅃ빡뗛ꙡ뉺꧊ꪺ궷쁉꓀뒲ꅁ뛇닎ꙁꭏ쁉꒽ꕱ쇶ꓱꑀ꿫ꭏ쁉꒽ꕱ꣣ꚳ룪ꚨꖻꑗꪺ쁵뛕ꅁ땍ꛓ맯ꖨꡡ궷쁉ꅁꙐ볋ꙝ샲꣺룪ꪺꚨꖻ뉍쁶궷쁉뱗ꕛꛓ꣑떹뙱꣼궭ꅃꕈꕸ왗ꛓꢥꅁ궷쁉늾신ꕄ굮빡냪믚ꙁꭏꅁꙢꖨꡡ땯ꗍ꒧ꯡꅁ녠ꙝꙁꭏ꒽ꕱ궫띳귗ꖿꖨꡡ띬ꖢ뻷뉶ꅁ뙩ꛓ덹ꚨ믹껦ꑗ몦꣑떹뙱ꪺ꒣쎭ꥷꅃ 껚뻚Lewis Murdockꅝ1996, 1999ꅞꕈCummins et al.ꅝ1999ꅞꪺ뒣쒳ꅁꗑ걆ꦲ꒶ꑊꖨꡡ뙗썂ꙁꭏ쁉ꮴ곹ꕩ꿠ꕩ룑ꡍꚹ냝썄ꅁ과냪셰ꢹ걆ꦲ 2 ꖻꓥꣃꭄ뺨끷맯ꗘꭥ맪걉ꪺꛭꙶꙡ빟ꭏ쁉꣓끑뷗ꅁ꧒ꯘ쒳ꮴ곹ꑝꣃꭄ뺨끷맯ꛭꙶꙡ빟ꙁꭏ쁉ꅃ 3 ꖻꓥ맯ꖨꡡꥷ롱ꣃꭄ뛈ꝴꙡ빟ꅁꛓ걏걆ꦲꪺꓑꡡ띬ꖢ닎군ꅁ쏾과냪ꪺPCSꓑꡡ닎군ꅁꕏꕝꝴ믤궷ꓴꡡ떥ꅃ
궷쁉뫞뉺뻇돸 닄꒭ꣷ 닄ꑇ듁 2003꙾7ꓫ237 ꪺꙁꭏ쁉덝Ꙣꡃꚸ띬ꖢꅝper occurrenceꅞ뙗륌25 billionꪺ뎡ꗷꗑ걆ꦲ꧓뻡ꅁꑗ궭ꅝcapꅞ결50 billionꅁ꣤ꕄ굮ꪺ뷗쉉결ꅇ걆ꦲꙁꭏ쁉Ꙙ곹ꕄ굮Ꙣ뮲ꝕ냓띾ꭏ쁉ꙁꭏꚳ껄룪ꖻ꒧꒣ꢬꅁ걇ꑀ꿫ꪺꑕ궭ꅝtriggerꅞ굱ꪺ곛럭낪ꅁꕈ뵔ꭏ쇗ꝋ꽽썡ꭏ쁉ꖫ돵쑶ꪧꞡ뿅ꕈ몡ꢬꭏꑈ꒧믝ꡄꅃ곛맯꧳냓띾ꙁꭏ쁉ꅁ걆ꦲꙁꭏ쁉ꪺ쁵뛕ꯘꗟꙢ껉뚡ꓴꖭꑗꅝintertemporal or time-horizon diversificationꅞꪺ꓀뒲ꑗꅃ뒫ꕹ룜뮡ꅁ냓띾ꙁꭏ쁉ꚳꕩ꿠ꙝꑀꚸ궫ꑪ띬ꖢꛓ꽽늣ꅁꝙ꣏꒣꽽늣ꅁ꣤ꯡ쓲ꪺ룪ꚨꖻꕩ꿠ꑪ둔뒣낪ꅁꕈ교꧓ꭏ뙱빕듮ꅆꛓ걆ꦲ꺵뗛꣤쁵뙖ꪺ끝냈ꯡ곞ꅝ꿇땼ꑈꅞꅁ꣤꽽늣뻷뉶둘꫱결륳ꅝdefault freeꅞꅁꙁ뿄룪ꪺꚨꖻꅝ꣒꙰땯ꛦ꒽뛅ꅞꑝ꫱꧳때궷쁉ꝑ뉶ꅁ뮷룻냓띾ꙁꭏ쁉결ꝃꅃLewis and Murdock뭻결걆ꦲꙢꖨꡡ궷쁉ꪺ꧓꣼ꓨ궱ꅁꙢ꒣뱗ꕛ걆ꦲ뛅냈굴뻡ꪺ놡ꩰꑕꅁ꿠뱗ꕛꙁꭏ쁉ꪺ꣑떹ꅁ녱ꛓ쉘녩늣쁉꒽ꕱꪺꖨꡡ궷쁉ꪺ꧓룼꿠ꑏꅃꙝ결걆ꦲ꿠꣺녯랥ꝃꪺ귉뙕ꝑ뉶ꅁꕵ굮ꚹ뫘룪ꚨꖻꪺ쁵뛕ꅁ꿠뙗륌ꚹ뫘걆ꦲꙁꭏ군땥꒤ꕩ꿠녡꣓ꪺ껄뉶띬ꖢꅁꙁꭏ쁉ꪺ꣑떹녎ꙝꚹ엣뗛뱗ꕛꅃꕈꕸ왗ꙡ냏ꛓꢥꅁꙢꑀꥷ뱨꿅띬ꖢꕈꑗꪺꖨꡡꙁꭏ꣑떹ꖫ돵ꣃ꒣꙳ꙢꅁꙢ냪믚ꙁꭏ꣑떹뙱꣼궭ꑕꅁ걆ꦲꙁꭏ군땥ꝙ꣏Ꙣ껄뉶ꑗꚳ꧒띬ꖢꅁ꣤Ꙣꖨꡡ띬ꖢꯡ꧒땯뒧ꪺꫀ라끝둉궫꓀끴껄ꩇ녎ꟳ궫굮ꅃ ꖨꡡ쏒꣩꓆녠궱셻ꪺ돌ꑪ냝썄Ꙣ꧳걹냊꧊꒣ꢬꅁꙁꕛꑗꙁꭏꖫ돵ꪺ궭꣮ꅁ맪믚ꑗꑪꙨ볆ꪺꖨꡡ궷쁉ꞡ때ꩫꚳ껄꓀뒲ꅝFroot, 1999a; Niehaus, 2002; Cummins et al. 2002ꅞꅁꙢꖨꡡ구ꗍ꧊냓ꭾꖫ돵ꑗꅁ꙰과냪PCSꅝproperty claim serviceꅞ볆꒧볐ꪺ구ꗍꪫꣃ꒣꧶깍ꝑ쇗쁉ꅃ룪Ꙣꖫ돵ꫬ듁땯깩껉ꅁꙝꖨꡡ띬ꖢ곛쏶룪끔꣺녯꒣꧶ꕈ보노ꯗ꒣ꢬꅁ맯뙩ꑊꖫ돵꧄ꡂꅃꙝꚹ굙굮땯깩ꖨꡡ구ꗍ냓ꭾꖫ돵ꅁꓞ뙩룪ꖻꖫ돵ꪺ룪뙩ꑊꭏ쁉ꖫ돵ꅁꕈꯘꗟꖨꡡ궷쁉뫞뉺뻷꣮ꅁꝙꕩ싇ꝕ걆ꦲ꒶ꑊꝀ결꣑떹ꅁ꣏ꖫ돵보노ꚹ룪늣꒧꽓꧊뻷꣮꒧륂Ꝁꅃꛓ걆ꦲ냵ꛦꪺꙁꭏꮴ곹군땥ꪺ듁뇦ꝑ볭뉺뷗ꑗ삳결륳ꅝꗧꝙ때곕때솫ꅞꅁ듁뇦ꚨꖻꕝꝴ띬ꖢꪺ듁뇦귈뭐ꙕ뫘룳껉뚡ꑗꪺꚨꖻꅁꛓ믹껦ꑗ뛈뚷걍걆ꦲꪺ뿄룪ꚨꖻꅃꕴꕾꅁꮴ곹ꑝꕩ빁럭ꙡꕛꑊꑀꪺ궷쁉뙋ꓴ꣏꣤믹껦꿠ꟳ놵꫱ꗁ뚡ꭏ쁉ꖫ돵ꪺ믹껦ꅁꛓꚹ뙋ꓴꕩ뗸결ꖫ돵ꕩ꿠땯ꗍꗴ꛳ꖼ륷듁ꪺ엜냊ꕸ왗ꙝ룪껆꒣ꢬ꧒ꕩ꿠늣ꗍꪺ냑볆꛴군낾뭾궷쁉ꪺ룉쁶ꚨꖻꅁ걇돌ꯡꪺ믹껦삳떥꧳띬ꖢꪺ듁뇦귈ꕛꑗꛦ걆뙏ꗎ뭐썂ꕾ궷쁉뙋ꓴ4ꅃ ꮴ곹꒺깥 ꖨꡡ띬ꖢ꒧군뫢삳꣏ꗎ늣띾셠엩띬ꖢꅝindustry lossesꅞꛓꭄ꒽ꕱ귓ꝏ띬ꖢꅁꕈ궰ꝃ륄뱷궷쁉뭐끦뿯뻜ꪺ냝썄ꅁꑝꙝꚹꕩ꿠꙳Ꙣ맯귓ꝏ꒽ꕱꪺ 4 ꢣLewis Murdockꅝ1996ꅞCummins et at.ꅝ1999ꅞ.
238 ꕸ왗ꖨꡡ뙗썂ꙁꭏ쁉ꮴ곹뭐뗻믹 냲깴궷쁉ꅝbasis riskꅞ5ꅃꕴꕾꮴ곹삳ꕈ걙ꥷ듁뚡ꪺ닖뽮띬ꖢꅝaggregated lossesꅞꝀ떲뫢6ꅁ곛룻ꕈꡃꗳ결떲뫢ꅁ맯ꭏ쁉꒽ꕱꟳ꣣맪뷨쇗쁉껄ꩇꅁꕂꙝ꣏ꗎ셠엩띬ꖢꅁ걇꒣교ꚳ륄뱷ꙍ쁉냝썄ꅃꗑ꧳ꕸ왗ꙡ냏꿊ꕆ릳PCSꖨꡡ볆ꪺ셠엩띬ꖢ볆ꅁꙢꛒ뙱ꕸ왗ꙡ냏ꪺ놡ꩰꑕꅁꕩꗑꭏ쁉띾땯깩꒤ꓟꅂ늣쁉꒽라끝걆뎡ꭏ쁉ꕱ뭠뚰ꖨꡡ띬ꖢ룪껆ꅁ볒ꗩ과냪PCSꅁꯘ롭셠엩ꓑ땍ꖨꡡ볆ꅁ꣒꙰꣤군뫢ꕩ결ꅇ Lꅝindexꅞ= ꑷ땯ꗍ셠엩닖군띬ꖢꅝincurred aggregated lossesꅞ/ 100,000,000 (1) 낲덝ꡃ쉉볆믹귈덝결띳ꕸ맴ꑇꑑ롕꒸ꅁꭨꡃꑀꮴ곹Ꙣꥼꖼꛒ뱻꣤쁶ꕉꑕ궭껉ꪺ믹귈결ꅇ NT$200,000*L(Index) (2) ꙁꭏ쁉떥Ꙑ꧳ꪽ놵녎ꮴ곹뷦ꕘꅁꛓ뙒ꓨꭨ꣺녯ꑀ맯뙗륌쉥ꕈꑗ띬ꖢꪺꚳ앶ꝑꅝcontingent claimꅞꅁꑀ꿫뫙결뙗썂띬ꖢꮴ곹ꅝexcess-of-loss contract, XOLꅞꅁ걛멣ꑗ뭐뛇닎볚ꚡ뿯뻜앶곛ꅃ럭ꖨꡡ띬ꖢ뙗ꕘꑀꥷ땻ꯗꅁꝙ쉥띬ꖢꅝtriggerꅁTꅞꅁꚹꮴ곹ꪺ뷦ꓨꝙ뚷쁶ꕉꖨꡡ띬ꖢ썂ꅝLꅞꪺꑀꥷꓱ꣒ꅁꑀ꿫결놱꣮걆ꦲ꧓꣼띬ꖢꪺꑪꑰꅁꮴ곹ꚳꑀ쁶ꕉꑗ궭ꅝcapꅁCꅞꅁ럭꙾ꯗ닖뽮띬ꖢꖼ륆ꑕ궭껉꒣Ꝁ쁶ꕉꅁ럭띬ꖢ뢨Ꙣꑕ궭뭐ꑗ궭뚡껉ꅁꚹꮴ곹쁶ꕉL – Tꅁ띬ꖢ뙗륌ꑗ궭껉ꅁꮴ곹쁶ꕉ띬ꖢꑕ궭뭐ꑗ궭ꪺ깴썂C – Tꅁꝙꙁꭏꮴ곹ꪺ쁶ꕉꅝpayoffꅞ결ꅇ P=Max[0,Min(L−T,C−T)] =Max[0,L−T]−Max[0,L−C] (3) ꚹ곛럭꧳ꑀ뿯뻜뙒앶믹깴ꅝcall spreadꅞꅁ꣤냵ꛦ믹걏ꑕ궭ꅝTꅞꅁꑗ궭ꅝCꅞ곛럭꧳꧱ꅝshortꅞꕴꑀ뙒앶ꅁ냵ꛦ믹결ꑗ궭ꅃ띬ꖢꕩꕈꑒꗋ꩑룵아ꅝPoisson jumpꅞ륌땻ꫭꗜꅁ꣤꒤ꙝ결ꖨꡡ결룵아궷쁉ꅁ걇때ꩫ릳뛇닎Black & Scholes볒ꚡ꿠ꕈ덳쓲ꗦ꧶꣓ꡒ껸궷쁉ꅝcontinuous trade to hedgeꅞꅁꗧꝙꖫ돵꒧꒣ꞹꗾꅝincompletenessꅞꅁ룑ꡍꓨꚡ돌결ꑪ깡보ꪾꪺ걏Mertonꅝ1976ꅞ꧒뒣ꕘꪺꓨꚡꅆꝙ낲덝ꖨꡡ룵아맯룪ꖻꖫ돵ꛓꢥ결ꭄ꡴닎궷쁉ꅁ룪ꑈꕩ싇ꗑꙨꢤ꓆꓀뒲ꚹ궷쁉ꅁ걇돸륓뉶꒴결때궷쁉ꝑ뉶ꅃꙢ낲덝ꖨꡡ걏ꭄ꡴닎궷쁉ꑕꅁꙁꭏꮴ곹굱믹ꕩ삳ꗎ곛ꙐꝀꩫꅃ슲ꢥ꒧ꅁ걆ꦲ 5 쏶꧳ꕩ꿠뻉ꛜꪺ냲깴궷쁉ꅁLewis Murdockꅝ1996ꅞ뒣쒳ꕴꕾ굱ꗟꙁꭏ뉺뷟뇸ꗳꅁꑝ둎걏ꕵꚳ맪믚ꚳꓤꕉꓑ땍ꖨꡡ띬ꖢꅝreimbursable disaster lossesꅞ꒧Ꙙ껦늣쁉꒽ꕱꅝqualified claimantꅞꓨ꿠냵ꛦꮴ곹ꅁꕂ썂꒣녯뙗륌맪믚뷟듚ꅁꚹ뇸ꗳꕩ궰ꝃ럭띬ꖢ뺨땯ꗍꙢꞽ뎡ꙡ냏ꅁꛓ걙꒽ꕱꙢ룓냏꧓ꭏ뙱ꓖꛓꕩ꿠ꙝꚹ샲ꝑ꒧ꕩ꿠ꅁꚹꙢꕸ왗땯ꗍꪺ뻷라룻ꑰꅃ 6 ꙝ결걏늣띾띬ꖢꅝindustry lossesꅞꅁ걇ꗎ닖뽮띬ꖢ삳때ꧺ엣꒧륄뱷궷쁉뭐끦뿯뻜ꪺ냝썄ꅃ
궷쁉뫞뉺뻇돸 닄꒭ꣷ 닄ꑇ듁 2003꙾7ꓫ239 ꙁꭏꮴ곹곛럭꧳맯ꭏ쁉꒽ꕱ뷦ꕘꑀ귓럭늣띾셠ꖨꡡ띬ꖢ뙗륌ꑕ궭껉뙩ꛦꓤꕉꪺ뙒앶ꅁꣃꙐ껉꯹ꚳꑀ귓럭띬ꖢ뙗륌ꑗ궭껉ꅁꭏ쁉띾믝ꛛꛦ굴뻡ꪺ뙒앶ꅁꙝꚹ걆ꦲꪺ궷쁉볉앓덑궭꣮Ꙣꑕ궭뭐ꑗ궭뚡ꅁꛓꙢꚹ쁶ꕉ걛멣ꑕꅁꭏ쁉띾뭐ꙁꭏ띾ꕩꛛꛦꡍꥷ꣤결덗쇗ꖨꡡ띬ꖢ궷쁉꧒믝쇊뙒ꪺ돌빁ꮴ곹볆ꅃ꣒꙰걙꙾ꯗꓑ땍ꖨꡡ셠꧓ꭏ닖뽮띬ꖢ결띳ꕸ맴200믵꒸ꅁꮴ곹ꪺ띬ꖢꑕ궭ꅝꙐ뿯뻜앶ꪺ뱩곹믹ꅞ결100믵ꅁꑗ궭결200믵꒸ꅝꝙTꇗ100ꅁCꇗ200ꅞꅁ걙ꭏ쁉꒽ꕱꪺꖫ뉶결10%ꅁꛓ꣤ꛛ굴썂결10믵꒸ꅁ냪믚ꙁꭏꪺ뎡꓀결5믵꒸ꅃ럭꙾ꯗꓑ땍ꖨꡡ볆곛럭꧳200쉉ꅁꭨꡃꑀꑦꮴ곹ꪺ믹귈결 (200−100)*NT$200,000=NT$20,000,000 (4) ꖫ뉶10%ꅁꫭꗜ럭꙾ꯗꚹꭏ쁉꒽ꕱꪺꓑ땍ꖨꡡ띬ꖢ곹결20믵ꅁꚩ낣꣤ꛛ굴썂10믵꒸뭐냪믚ꙁꭏ5믵꒸ꪺ뎡꓀ꅁꚹꭏ쁉꒽ꕱꥼꚳ5믵꒸ꪺ띬ꖢꅁꭨ꣤꧒믝쇗쁉ꪺꮴ곹ꑦ볆결ꅇ 500,000,000/20,000,000=25ꅝꑦꅞ (5) ꮴ곹ꕈꑀ꙾결듁ꅁꝙꡃ귓뙗썂ꙁꭏꮴ곹쁶ꕉꭏ쁉띾ꑀ꙾꒺ꪺꙨ귓ꖨꡡ띬ꖢꅁ꧒끷맯ꪺꕄ굮궷쁉결믤궷ꅂꙡ빟ꅂꓴꡡ떥ꪺꓑ땍ꡡ깠ꅃ낣ꑆ끝걆뎡ꭏ쁉ꕱꑷ꧳ꑋꑑꑅ꙾ꑋꓫ껖ꕩꛭ깡ꙡ빟쁉ꕩ결ꑀ돦ꑀ쁉뫘ꅁꕸ왗ꙡ냏뉻뚥걱ꪺꖨꡡꭏ쁉Ꙩ뒲ꝇ꧳ꙕ뫘ꛭ깡쁉뫘꒤ꅁ꙰깡ꓵ쁉ꅂ뫮Ꙙ쁉떥ꅁ결뽗ꗟ쁉뫘ꅁꕈꕛ쁉ꪺꚡꕛꭏꅁꙝꚹ꣏녯늣띾꙾ꯗ셠띬ꖢꪺ군뫢꒤ꕝꝴꑆ꣤ꕌꭄꓑ땍ꡡ깠궷쁉ꅁ볆ꙝ덝ꚳ뇸ꗳ녎ꑀ꿫ꭄꖨꡡ궷쁉ꪺ띬ꖢ쁶ꕉ뇆낣꧳ꚹꮴ곹꒧ꕾꅁ꣏ꭏ쁉뭐ꙁꭏ띾꒣뛈맯뽗ꗟ쁉뫘ꪺꖨꡡ궷쁉볉앓Ꝁ쇗쁉ꅁꙐ껉ꛒ뱻꣤ꖦ쁉뫘ꪺ궷쁉볉앓Ꝁ결돌빁ꮴ곹쇊뙒볆ꪺ뻚ꅃꮴ곹ꪺ뙗썂띬ꖢꪺ덝ꥷꕩ냑ꛒꗘꭥꙁꭏ쁉ꖫ돵ꕩ뒣꣑ꪺꭏ썂ꑗ궭ꅁꕈ쇗ꝋ뭐ꗁ뚡ꙁꭏꖫ돵쑶ꪧꅃꙁꛒ뙱ꗘꭥꗾꕸ왗ꙡ냏ꭏ쁉띾ꪺ룪ꖻ셠썂ꅂ꧓ꭏ꿠뙱뭐걆ꦲ쁶ꕉ꿠ꑏ꣓굱ꥷꮴ곹ꑗ궭ꅁꣃꕩꪫ믹ꑗ몦뉶ꡃ꙾Ꝁ뷕뻣ꅃ 맯쇊뙒걆ꦲꙁꭏꮴ곹ꪺ뙒ꓨ삳굱ꗟ룪껦뇸ꗳꝀꑀꥷ땻Ꟈ꒧뱦걤ꅁꕈ뙩ꑀꡂ룑ꡍ끦뿯뻜냝썄ꅁ꣒꙰ꅆꕩ덗ꥷ쇊뙒믝꧳ꚹ뫘ꖨꡡꭏ쁉냓ꭾꖫ돵꒤꣣ꚳꑀꥷꚳ뉶ꅁꓨꕩꗓ뷐쇊뙒ꅁ꣏쇊뙒ꪺ궷쁉깴늧녎꒣라륌ꑪꅃꕴꕾꅁ쏶꧳륄뱷ꙍ쁉ꕩꝴ꣢ꓨ궱ꅁꑀ걏걆ꦲꙁꭏꮴ곹ꪺ쇊뙒맯걆ꦲꪺ륄뱷ꙍ쁉ꅆꖲ뚷Ꙣ굱ꗟꖨꡡ띬ꖢ볆ꕈꡄ녯꒽ꖿ7ꅁꕴꑀꭨ걏ꑀ꿫ꗁ늳Ꙣ쇊뙒ꚹ쏾ꖨꡡꭏ쁉냓ꭾꯡꕩ꿠ꪺ륄뱷ꙍ쁉ꅁ맯ꚹꕩ굮ꡄꭏ쁉꒽ꕱꙢ땯ꛦꚹ쏾ꖨꡡꭏ쁉냓ꭾꪺꙐ껉ꅁ굮ꡄꗁ늳꣤ꛭꙶ믝닅Ꙙꑀ뇸ꗳꅁ꣒꙰맯ꑧꙡꪺ꣏ 7??륌ꕨ냪ꕾCBOTꙢ땯ꛦꖨꡡ듁덦껉ꅁꝙ뒿비륊ꚹ뚵냝썄ꛓ꣏늣ꭾꖢ뇑ꅁꗘꭥꕩ냑ꛒ냪ꕾPCS optionꪺ띬ꖢ볆덝군ꅃ
240 ꕸ왗ꖨꡡ뙗썂ꙁꭏ쁉ꮴ곹뭐뗻믹 ꗎ놱꣮ꛭꙶꪺꯘ덹Ꝁ덗뵤떥ꅃ Ꙣ떲뫢ꓨ궱ꅁ럭ꖨꡡꗳ땯ꗍꯡꅁꑀ꿫Ꙣ귬굱ꪺ꣬듁ꓩꯡ믝ꕛꑗꑀ걱ꪺ띬ꖢꦵ깩듁뚡ꅝloss development periodꅞꅁ결ꢾꓮꙝꑀ덳ꛪꖨꡡ띬ꖢꪺ덳쓲닖뽮륌낪뉻뙈ꅁꕩ궭ꥷꕵꚳꙢ꙾ꯗ떲뫢ꯡꕢ꙾꒺군녯ꪺ뉺뷟띬ꖢꓨꕩ쁶ꕉꅁꚹꕩꢾꓮ낲덹뭐생ꗎꪺ놡땯ꗍꅁꗧꕩꙢꖨꡡ땯ꗍꯡꭐ꣏ꭏ쁉띾ꕛ덴꣤뉺뷟륌땻ꅃꙢ띬ꖢꦵ깩듁뚡꒤ꅁ낣ꑆ군뫢귬ꗽꮴ곹뉛뭜듁뚡ꪺꖨꡡ띬ꖢꕾꅁ믝ꕛꑗꦵ깩듁뚡꒺꧒돸ꝩꪺꖨꡡ띬ꖢ썂ꅃꙢꦵ깩듁꒺ꅁ굙ꚳ띳ꪺꖨꡡ띬ꖢ룪껆ꅁ볆꒴ꕩ귗ꖿꅁꚹꙘ곹꒴ꕩꖿ녠뙩ꛦꗦ꧶ꅁ엽꣏ꗎꚹꮴ곹ꪺ쇗쁉ꕩ뵔맪ꕈ꒧쇗쁉ꅃꛓ꙰ꭥ꧒굺ꅁ굙뇽ꕛ덴ꗁ뚡ꙁꭏꖫ돵ꪺ땯깩ꅁ꣏걆ꦲꙢꖨꡡꙁꭏꖫ돵몥몥뉈ꕘꅁꗧꕩꛒ뱻녎ꮴ곹ꕈꗁ뚡ꖫ돵ꪺ룪ꚨꖻ뷕뻣뙩ꛦ뗻믹ꅁꝙꕈꗁ뚡ꖫ돵ꪺ뉻뉶ꛓꭄ걆ꦲꪺ귉뙕ꝑ뉶꣓군뫢ꮴ곹ꪺ꒽ꖭ믹껦ꅃ 3. ꖨꡡ뙗썂ꙁꭏꮴ곹꒧뿯뻜앶뗻믹 곛쏶ꓥ쑭Ꙟ압 ꗑ꧳ꖨꡡꭏ쁉/ꙁꭏ쁉ꮴ곹ꪺ믹껦꧓ꭏ뙱륌ꕨ녠ꝥ뉻꒣쎭ꥷ8ꅁ륌ꕨꓥ쑭뗛궫꧳꣑떹믝ꡄ궱ꪺ놴끑ꅁ꣤꒤Froot and O’Connelꅝ1999ꅞ쉫ꡳꖨꡡꙁꭏ믹껦ꑗꕩ꿠걏ꙝ결ꖫ돵ꪺ꒣ꞹ과교꣏룪ꖻ걹냊꣼ꅁꗧ걏ꖨꡡ땯ꗍ띬ꖢꚳ뻷뉶뱗ꕛꅁ맪쏒엣ꗜꖨꡡꪺ덳쓲땯ꗍꪺ뵔꣏믹껦ꑗꅂ꣑떹ꑕ궰ꪺ땻ꯗ뙗륌ꑆꙘ뉺ꪺ볐럇ꅆꕴꕾꅁDong et al.ꅝ1996ꅞꕈꙢꛒ뙱ꖨꡡ맪믚맯늣쁉꒽ꕱ꽽늣꣑떹뙱ꪺ뱶암ꑕ꣓ꡄ녯ꖨꡡꭏ쁉Ꙙ뉺ꥷ믹9ꅁ Frootꅝ1999bꅞꭨ끑뷗ꑆꖨꡡꙁꭏ쁉믹껦꒣쎭ꥷꪺ귬ꙝ10ꅃCummins et alꅝ.2002ꅞꭨ꓀꩒ꑆꭏ쁉꒽ꕱ맯꧳ꖨꡡ띬ꖢ뉺뷟ꪺ쁶ꕉ꿠ꑏꅁꕩ낵결ꙁꭏꛛ꽤썂ꪺ냑ꛒꅃꙢꖨꡡ띬ꖢ꓀끴ꪺ맪쏒ꑗꅁCummins, et alꅝ.1990, 1999ꅞRootzen and Tajvidiꅝ2000ꅞ꓀ꝏ꣏ꗎꙕ뫘꒣Ꙑꪺ띬ꖢ꓀끴꣓끴빁맪믚ꖨꡡ띬ꖢ룪껆ꅁꙢꖻꓥꭨ뇄ꗎꙐRootzen and Tajvidi꒧빁Ꙙ왛듺귈ꓖꪺꑀ꿫꓆걦꧔맏꓀끴ꅁ귌녎Ꙣꑕ론뮡ꧺꅃ ꕴꑀꓨ궱ꅁ뿯뻜앶삳ꗎ꧳ꭏ쁉돌ꚭꢣ꧳Doherty and Garvenꅝ1986ꅞCumminsꅝ1988ꅞꅁꛓCumminꅝ1992ꅞShimkoꅝ1992ꅞ떥ꟳ녎뿯뻜앶ꗎ꧳ꭏ쁉/ꙁꭏ쁉ꮴ곹뗻믹ꅆꚳꝏ꧳뫫뫢볒ꮬꅁCumminsꅝ1992ꅞ돌ꚭ뒣ꕘ끝냈뿯뻜앶볒ꮬꕩꗎ꣓뗻믹ꙁꭏ쁉ꮴ곹ꅁ꣤ꯘꗟꙢ볐럇쉘뒲륌땻ꑗꅁ 8 냑럓꧓ꭏ둠샴곛쏶ꓥ쑭ꅃ 9 ꑝ둎걏깥뙱궭꣮볒ꮬꅝcapacity-based modelꅞꅃ 10 ꕝ걁룪ꖻ때껄뉶ꅂꖫ돵썢쉟ꅂꗦ꧶ꚨꖻꅂ륄뱷ꙍ쁉끦뿯뻜떥귬ꙝꅃ
궷쁉뫞뉺뻇돸 닄꒭ꣷ 닄ꑇ듁 2003꙾7ꓫ241 Cummins et al.ꅝ1999ꅞ쇶ꗎ꽓껭띬ꖢ꓀끴ꅁꣃꭄ뇄ꗎ뿯뻜앶뗻믹ꖨꡡꙁꭏ쁉ꮴ곹ꅁꛓ뇄쁒멁뗻믹ꅁ뿯뻜앶꣤ꚳꙢ꧓ꭏ듁뚡꒺둹굺꣤냊멁륌땻꒧쁵쉉ꅁ곛룻꧳ꑗ굺ꓥ쑭ꅁ귌ꕘꑆꭄ샧ꝑꪺ걆ꦲꭏ쁉ꗎꙢ끝냈뿯뻜앶ꪺ꽓껭꧊뷨ꅁꕈ꽓껭ꪺ띬ꖢ꓀끴ꅝꑝ둎걏랥귈꓀끴ꅞꗎꙢꕈ룵아륌땻결냲랡ꪺ끝냈뿯뻜앶뗻믹꒧군뫢ꅃ 뿯뻜앶볒ꮬ Ꙣ꣣룵아륌땻뿯뻜앶뗻믹ꪺ륌ꕨꓥ쑭꒤ꅁMertonꅝ1976ꅞ낲덝룵아궷쁉결ꭄ꡴닎궷쁉ꅁꗑ룪ꖻ룪늣ꥷ믹뉺뷗ꅝCAPMꅞ꣓곝ꅁꗧꝙ꣤룵아꧊믹껦룪늣뭐쏒꣩ꪺꖫ돵닕ꅝmarket portfolioꅞ때쏶ꅁ룪ꑈ꿠ꛛꛦ녎ꖨꡡ궷쁉꓀뒲ꅁ걇꧒믝돸륓결때궷쁉ꝑ뉶ꅃ굙룵아결꡴닎궷쁉ꅁꖫ돵믹껦녎라맯ꖨꡡꝀ삳ꅁꭨ뿯뻜앶뗻믹믝ꕴꝀ꣤ꕌꪺ덂뉺11ꅃ굙ꕈ걆ꦲ결ꖨꡡ궷쁉꒧꧓꣼ꅁꗑ꧳꣤룻룪ꖻꖫ돵꣣ꟳꑪ꒧궷쁉꓀뒲꿠ꑏꅝꕄ굮결껉뚡룳듁꒧꓀뒲ꅞꅁꝙ꣏꣤궷쁉맯룪ꖻꖫ돵ꚳꑀꥷ땻ꯗꪺ꡴닎꧊ꅁꗑ꧳걆ꦲ쓝꧳꫱륳륈곹궷쁉ꪺꭄ샧ꝑ닕슴ꅁꗧ빁Ꙙ녎꒧뗸결ꭄ꡴닎궷쁉ꅃꕸ왗ꙝꙡꑰꅁꖨꡡ땯ꗍꕩꞹꗾ뗸결뚡쉟낸땯ꗳꅁ걇빁Ꙙꕈ꿂뫩룵아륌땻꣓둹굺ꅇ dL(t)=aL(t)dt+Y(t)dq (6) (6)ꚡ결꿂뫩룵아륌땻ꅝpure jump processꅞꅁ꣤꒤Lꕎꫭ닖군ꖨꡡ띬ꖢꅁa결때룵아ꖨꡡꪺꓑ땍띬ꖢ듁뇦엜냊12ꅁdq결ꑒꗋ꩑륌땻ꅝPoisson processꅞꅃ꣤꒤ꅁꛬ늾뚵aꙢꖨꡡ볆꒤ꕩ뗸결Ꙣ껉뚡뮼늾껉ꅁ띬ꖢ뷟듚ꙝ덱덦뾱뗈ꛓ늣ꗍꪺꓱ꣒꧊뮼뱗ꅃ ꕴꕾY결ꓑ땍ꖨꡡ띬ꖢ덗볒엜볆ꅃꛓ닖군띬ꖢ결 TL(a,T)=∫dL(t) (7) Ꙩꚸ뉺뷟ꖨꡡꙁꭏꮴ곹ꅝmultiple claims catastrophe reinsurance contractꅞ 덜Ꙩꙁꭏ쁉ꮴ곹꒹덜ꭏꙢ곹ꥷ껉뚡ꑗꑕ궭ꅝtrigger and capꅞ꒺ꅁꕩꕈ굮ꡄꙨꚸ뉺뷟ꅝmultiple claimsꅞꅁꝑꗎ뿯뻜앶뗻믹Ꙩꚸ뉺뷟ꭏ쁉ꮴ곹돌ꚭꢣ꧳Shimkoꅝ1992ꅞꅁ꣤꧒ꡄ녯꒧룑곛럭꧳ꑗ론꧒끑뷗ꪺ돦ꑀꡄ쁶볚ꚡ뿯뻜앶꒧껉뚡뽮꓀셠ꥍꅝtime integralꅞꅁꑝ둎걏Ꙣ닖군띬ꖢ뙗륌ꑕ궭ꯡꅁꡃꚸꖨꡡ띬ꖢꞡꕩꙢ룓껉뒣ꭥꡄ쁶ꅁꪽ꣬닖군띬ꖢ뙗륌ꑗ궭13ꅃ낲덝걆ꦲꖨꡡꙁꭏ덝결ꮴ곹Ꙩꚸ뉺뷟ꅁꭨꙢt껉땯ꗍꪺꚳꡄ쁶ꅝcontingent 11??ꢣChangꅝ1995ꅞꅁCummins and Gemanꅝ1995ꅞ떥ꓥ쑭ꅃ?12??ꖨꡡꙁꭏꮴ곹결ꑀ꙾꒺닖뽮ꪺꓑ땍ꖨꡡ띬ꖢꅁꙝꚹ엜냊뉶덝결aꅃ 13 Shimkoꅝ1992ꅞ끑뷗ꪺ걏냲꧳ꡃꚸ땯ꗍꡄ쁶ꮴ곹ꅝper occurrenceꅞꅁꖻꓥ결닖군띬ꖢꮴ곹ꅝaggregated lossesꅞꅃ
242 ꕸ왗ꖨꡡ뙗썂ꙁꭏ쁉ꮴ곹뭐뗻믹 payoffꅞꕩꫭ결 P(t)=Y(t)dqꅁ ꙰ꩇT<L(t)<C P(t)=0ꅁ꙰ꩇT≥L(t)C≤L(t) ꗑ슲돦ꪺ뿯뻜앶귬뉺ꕩꪾꅁꙝ결냵ꛦ껉뚡뒣ꭥꅝearly exerciseꅞꅁ걇껉뚡믹귈ꗧ뱗ꕛꅁꙨꚸ뉺뷟ꮴ곹믹귈ꑝ룻낪ꅃ ꑀ귓귈녯ꩠ띎냝썄걏ꅆꭏ쁉띬ꖢꖻꢭ쓝ꭄ룪꧊ꗦ꧶룪늣ꅝnon-investment assetꅞꅁꛓꕂꮴ곹ꕵ걏Ꙣ걛멣ꑗ쏾뿯뻜앶ꅁ꣤ꣃꭄ구ꗍ꧊뿄냓ꭾꅁBlack & Scholes덳쓲ꗦ꧶ꚡꪺ쇗쁉룪닕Ꙙ때ꩫ륆ꚨꅁ걇뇽ꡄ꣤믹껦믝ꛒ뱻ꕈꑕ놡ꩰꅇ굙ꕸ왗ꙡ냏꙳Ꙣꚳ뭐ꓑ땍ꖨꡡ띬ꖢꅝ볆ꅞ낪ꯗ곛쏶꒧룪꧊룪늣ꅁꭨꕩꡄ꣤듁뇦돸륓뉶ꅃ굙룓룪늣꒣꙳Ꙣꅁꕩ낲덝꣤듁뇦돸륓뉶결때궷쁉ꝑ뉶ꕛꑗ꙰CAPM꒤ꪺꖨꡡ띬ꖢ꡴닎궷쁉뙋ꓴꅝsystematic risk premiumꅞꅁꛓ뉻뉶결때궷쁉ꝑ뉶ꕛꑗꖨꡡ엜냊뉶뭐룓룪늣돸륓뉶꒧깴14ꅃ뒫ꕹ룜뮡ꅁ덳떲꧳ꭄ룪꧊룪늣ꪺ구ꗍ꧊냓ꭾ꒧뗻믹ꅁ꣤꣏ꗎ꒧뉻뉶ꣃ꒣ꑀꥷ결ꖫ돵때궷쁉ꝑ뉶ꅁꛓ걏ꗑ띬ꖢ꒧듁뇦엜냊뉶ꚩ낣ꖫ돵궷쁉뙋ꓴꅁꗧꝙꗑꖫ돵꒧궷쁉믹껦ꅝmarket price of riskꅞ꣓ꡍꥷ15ꅃ걏ꙝ걆ꦲ꒧ꭄ샧ꝑ꽓껭ꢤꛢꅁ걇때뷗ꖨꡡ궷쁉걏ꝟ꣣ꚳ꡴닎꧊ꅁꞡ꒣삳샲녯썂ꕾ궷쁉돸륓ꅁꑝ둎걏ꖫ돵궷쁉믹껦결륳16ꅃꙝꚹꙢꭏ쁉띬ꖢ덱덦뾱몦뉶뭐ꑀ꿫덱덦뾱몦뉶곛Ꙑ놡ꩰꑕ17ꅝCummins, 1988ꅞꅁ귌ꕩ꣏ꗎꖫ돵덱덦뾱몦뉶결뉻뉶18ꅃ Ꙣ뙩ꛦ걆ꦲꙁꭏ쁉ꮴ곹굱믹ꭥꅁ믝굮ꚳ빁럭띬ꖢ꓀끴낲덝ꅁ녠ꢣꪺꖨꡡ띬ꖢ꓀끴롧녠꒣결맯볆녠멁ꅝlognormalꅁꢣRootzen and Tajvidi, 2000ꅞꅃ맯꧳ꭄ맯볆녠멁ꪺ띬ꖢ꓀끴ꅁ쏾Mertonꅝ1976ꅞꭄ덳쓲륌땻룪늣뿯뻜앶뗻믹꒧ꯊ뎬룑때ꩫꡄ녯ꅁ믝ꝑꗎ볆귈ꩫ녎룵아띬ꖢ륌땻녡ꑊꅃ쇶땍Ꙣ과냪ꙝꙡ뉺냏ꑪꅁꙢꖨꡡꙁꭏ맪뗽곣ꡳ꒤ꅝCummins, 2000ꅞ꣤왛듺귈룻Ꙩꅁ녠ꢣ띬ꖢ꓀끴ꥼꚳ꒣뿹ꪺ끴빁19ꅁꑀ꿫ꛓꢥꖨꡡ결땽ꚳꗳꅁ맪믚왛듺귈볆낾ꝃꅁꕈ녠ꢣ띬ꖢ꓀끴끴빁ꅁꚳꕩ꿠늣ꗍ쑙궫꛴군낾뭾ꅃ꣤ 14 낲덝룓쏒꣩듁뇦돸륓뉶결rh=r+bꅁb결꡴닎궷쁉뙋ꓴꅝꙢꚹ결륳ꅞꅁꭨ뿯뻜앶꒧뉻뉶결r+(a−r)ꅁꢣFischerꅝ1978ꅞꅃꕩ뱧결a−(rh−r)ꅁ꣤꒤rh−r곛럭꧳ꖫ돵궷쁉뙋ꓴꅁ룔ꢣhHull (2000), 19뎹ꅃ 15 룔닓ꕩ냑빜Shimkoꅝ1992ꅞ맯꧳ꭏ쁉ꮴ곹ꖫ돵궷쁉믹껦ꪺ뮡ꧺ 16 ꕈ꽕ꑰꪺꕸ왗ꛓꢥꅁꓑ땍ꖨꡡ맯룪ꖻꖫ돵ꕩ꿠ꚳꑀꥷ땻ꯗꪺ꡴닎꧊ꅁꙝ결걆ꦲꢤꛢꪺ꽓껭꧊ꅁꑝ둎걏꣤ꚳ꿠ꑏꕈ껉뚡꣓꓀뒲궷쁉ꅁ뭐ꑀ꿫ꖫ돵Ꙩꢤ꓆꓀뒲꒣Ꙑꅁ걇걆ꦲ꣣룻ꖫ돵결ꝃꪺ궷쁉뷕뻣뉻뉶ꅃ뒫ꕹ룜뮡ꅁꭄ걆ꦲꮴ곹꒧꣤ꖦꖨꡡ구ꗍ꧊냓ꭾ삳ꛒ뱻꡴닎궷쁉ꖫ돵믹껦ꅁꛓꓑ땍ꖨꡡ맯꧳걆ꦲꮴ곹ꛓꢥ쏾ꭄ꡴닎궷쁉ꅃ 17 ꚹ결Ꙙ뉺낲덝ꅃ 18 ꭏ쁉ꪫ믹뾱몦뉶ꕈꩁ냈띾ꪫ믹볆뾱몦뉶꣓군뫢믹ꅁ륌ꕨꑇꑑ꙾ꖭꞡ곹결α=ꅁ룪껆꣓랽걏뭏왗ꙡ냏ꪫ믹닎군ꓫ돸ꅃ 19 낣맯볆녠멁ꕾꅁꥼꚳParetoꅂ BurrꅂGeneralized Beta떥ꅁꖼꖲ빁Ꙙꕸ왗ꅃ
궷쁉뫞뉺뻇돸 닄꒭ꣷ 닄ꑇ듁 2003꙾7ꓫ243 ꖦ맪뗽떲ꩇꅝRootzen and Tajvidi, 2000ꅞꗧꕘ덜Ꙩꖨꡡ띬ꖢ꓀끴롧녠꣣ꚳꭰꟀꅝlong and heavy tailꅞꅁ굙꣏ꗎꑀ꿫꓀끴꛴군ꅁ녠꣏녯랥뫝귈ꅝextreme valueꅞ땯ꗍ뻷뉶덑ꝃ꛴ꅁ뙩ꛓꕩ꿠꣏ꮴ곹믹귈쑙궫ꝃ꛴ꅃ 랥귈뉺뷗ꅝextreme value theoryꅞ 덜Ꙩꓥ쑭ꅝ꣒꙰Jung, 1964; Teugels, 1987; Kremer, 1994; Ramlau-Hansen, 1998 a,bꅞ뒣귒랥귈뉺뷗곛럭빁Ꙙ삳ꗎ꧳꛴군꣣ꚳꭰꟀꪺ룪껆ꅃ랥귈뉺뷗뗛궫꓀끴Ꟁ뎡ꪺ둹굺ꅁ꒣꛴군뻣귓꓀끴ꅁꙝꚹ곛룻맯뫙ꪺ녠멁꓀끴Student’s t꓀끴ꅁꕩ떽ꭄ맯뫙ꪺꭰꟀꅁ뻚뉺뷗ꑀ꿫ꛓꢥꅁ굙뛈둎Ꟁ뎡꓀끴ꅁ랥귈꓀끴삳쁵꧳꣤ꖦ꓀끴ꅃ꽓ꝏꕸ왗Ꙣ룻ꓖ왛듺귈ꕂ꣣ꕩ꿠낪띬ꖢ놡ꩰꑕꅁ낪쉥ꪺ랥귈꓀끴삳결룻ꕩꛦꪺ볒ꮬꅃ랥귈뉺뷗Ꙣ꿊ꕆ랥뫝룪껆ꪺ놡ꑕꅁꕩꝑꗎꕾ뒡ꩫ꣓꛴군랥뫝ꗳꅁ꣣ꚳ룻낪ꭈ뿠ꓴ럇꒧꛴군ꅃ쇶땍랥귈뉺뷗ꯜꚭ둎덑삳ꗎ꣓꛴군ꭏ쁉띬ꖢ꓀끴ꅝ꙰Jung, 1964ꅞꅁ꣤꣏ꗎꪺꕴꑀ뉺ꗑ걏ꅁꙁꭏ쁉곛럭꧳룻낪뱨ꪺ띬ꖢꅁꑝ둎걏ꕵ뗛궫Ꙣ꓀끴Ꟁ뎡ꅁꙝꚹꗎ꣓꛴군띬ꖢ귈뙗륌ꗁ뚡냪믚ꙁꭏꪺ돌ꑪꭏ쁉띬ꖢ꧓ꭏ볆뙱ꅁꝙ뙗썂띬ꖢꅝexcess of lossꅞꪺ꓀끴둎곛럭Ꙙ빁ꅃꖻ곣ꡳ꣏ꗎ랥귈뉺뷗ꪺPOT볒ꮬ냑볆꛴군꓀ꝏ뇄ꗎHillꅂGPD꛴군ꓨꩫꅃ랥귈뉺뷗뮡ꧺꢣ뿽1ꅁ뙩ꑀꡂ귬뉺ꭨꕩ냑빜Reiss and Thomaꅝs2000ꅞ Rootzen and Tajvidiꅝ2000ꅞ떥ꅃ 걆ꦲꙁꭏ쁉ꮴ곹뚷ꛒ뙱ꗁ뚡꧓ꭏ꿠뙱ꅁ꣓꣺Ꙙ빁ꪺꑗꑕ궭ꅝtrigger/capꅞꅁꑀ꿫ꛓꢥꅁꚹꑗꑕ궭뎣곛럭낪ꅁꙝꚹꕵ굮GPDꪺ쉥귈ꑰ꧳ꮴ곹ꑗꑕ궭ꅁꕈGPD꛴군냑볆ꯡꙁꗎ꣓군뫢ꙁꭏ쁉ꮴ곹믹귈ꭋ결ꑀꙘ빁ꪺꝀꩫꅁ뒫ꕹ룜뮡ꅁꙁꭏ쁉ꮴ곹낾궫ꕫꟀ랥뫝꓀끴ꅁ뭐ꖪꟀ룻때쏶ꭙꅁꙢꖻꓥ꒤뇄ꗎ뉖Ꙙ꓀끴꣓둹굺ꖨꡡ띬ꖢꑪꑰ꓀끴ꅁꝙ녎꓀끴냏꓀결꣢뎡꓀ꅁ쉥귈ꕈꑗ결GPD꓀끴ꅁꛓ쉥귈ꕈꑕꭨꙝ왛듺귈룻Ꙩꛓꪽ놵꣏ꗎ롧엧룪껆ꚨꪺ꓀끴ꅝempirical distributionꅞꅃꙘ빁ꪺ쉥귈ꪺ뿯꣺쇶결ꕄ왛ꅁ굮꒴ꛒ뱻빬썂왛듺귓볆꒣ꥹꓓꓖꑪ꧳ꙁꭏꑕ궭ꅁꖻ곣ꡳ꒤Ꙁ뇄ꑔ뫘꒣Ꙑ쉥귈ꅃ결ꭋ꧳ꓱ룻ꅁ꓀ꝏ꧳꒣Ꙑ쉥귈꒧ꑗꅁꚹꕾꅁ귌ꑝ끴빁결ꑪ깡보노ꪺ맯볆녠멁ꅝlognormalꅞ꓀끴20낵결맯럓ꅃ 뭘ꙡꕤ쎹볒샀 Ꙣ뗻믹ꑗꅁ귌ꕈ뭘ꙡꕤ쎹볒샀ꅝMonte Carlo simulationꅞ군뫢ꙁꭏ쁉ꮴ곹믹귈ꅃ볒샀ꚸ볆결10000ꚸꅃ껉뚡꓁돎ꚨ365껦ꅁ곛럭꧳ꑀ꙾ꅃꚹ 20ms21ln(L−m)−m ꝙf(L;,,m=−2)exp[()]ꅁL>m,꣤꒤m,s,m꓀ꝏ결꣤ꛬ(L−m)s2ps롭ꅂ덗볒냑볆쉥귈ꅃ
244 ꕸ왗ꖨꡡ뙗썂ꙁꭏ쁉ꮴ곹뭐뗻믹 ꕾꅁ귌낲덝띬ꖢ귈땯ꗍ쁗뉶ꩁ녱ꑒꗋ꩑륌땻ꅝPoisson processꅞꅃ볒샀ꑪ교ꡂ왊결ꅇ(a) ꓀ꝏ꛴군GPDꅂ볆꓀끴ꅂ맯볆녠멁꓀끴Ꙣꑪ꧳쉥귈꓀ꝏ결5ꅂ10ꅂ20믵꒸꒧ꙕꑰ냏뚡뻷뉶귈ꅁ뭐볒샀ꚸ볆곛궼ꕈ늣ꗍꑪ꧳쉥귈꒧ꑰ냏뚡꒧듁뇦ꚸ볆ꅁ(b) ꕈ맪믚룪껆ꅁꡄ뫢ꑰ꧳쉥귈뎡ꗷ곛맯땯ꗍꪺꚸ볆ꅃ(c) 녎닄ꑀꅂꑇ뚥걱ꪺ꧒늣ꗍ띬ꖢ귈Ꙙ꣖ꅁ샲녯ꖨꡡ띬ꖢ쁈뻷볆귈ꅃ(d) ꕈꑒꗋ꩑륌땻볒샀땯ꗍꚸ볆21ꅃ(e) 돌ꯡ(6)(7)ꚡꕈ늣ꗍꪺ띬ꖢ볆귈볒샀룵아띬ꖢ륌땻ꅁꙢ꒣Ꙑ쉥ꑗꑕ궭뇸ꗳꑕ꓀ꝏ군뫢곛럭꧳돦ꑀ뉺뷟뭐Ꙩꚸ뉺뷟뿯뻜앶ꪺ걆ꦲꙁꭏꮴ곹믹귈ꅃ 4. 떲ꩇ ꕸ왗ꓑ땍ꖨꡡ꒧뇔굺꧊닎군 ꗑ꧳륌ꕨꕸ왗ꙡ냏쏶꧳ꖨꡡ띬ꖢꪺ닎군룪껆ꓨ궱쑙궫꒣ꢬꅁꙢ곛쏶곣ꡳꓨ궱ꅁꙨꗎ듀ꕎ볒샀룪껆ꅝ뎯녠ꡞꅁ녩롧뉺ꅁ1997ꅆ뎢ꓥ쁒ꅁ2000ꅆꭊꑂꓫꅁ2001떥ꅞꅁ곒ꭄꕈ맪믚띬ꖢ룪껆뙩ꛦ꓀꩒ꅃ꣒꙰Ꙣꓵ쁉ꪺ띬ꖢ룪껆꒤ꅁ쏶꧳믤궷ꅂ걸ꓴꅂꙡ빟떥ꓑ땍ꖨꡡ곒걏ꕈꕛ쁉ꪺꚡ꙳Ꙣ꧳ꭏ돦꒤ꅁꙢ덯ꖨꡡ띬ꖢꣃꭄꕄ쁉ꪺ궷쁉볐ꪺꑕꅁꙨꚳ낾뭾ꅃꖻ곣ꡳꪺꖨꡡ룪껆꣓랽결걆ꦲꓑ땍ꡡ깠닎군22ꅁ곣ꡳ듁뚡결ꗁ냪ꕼꑑꑃ꙾ꛜꑅꑑ꙾ꅁꕝꝴ믤궷ꅂꙡ빟떥ꓑ땍ꡡ깠꧒덹ꚨ꒧꧐ꯎꗾ귋ꅂꕢ귋ꅁꑈ귻뮴ꅂ궫뛋ꅂꚺꑠ륁Ꝁꪫ떥띬ꖢ룪껆ꅁꗑ꧳덜Ꙩ닎군룪껆ꣃꭄꕈ썂군뫢ꅁ걇뛈꿠녎꒧신뒫결꫱뉻귈23ꕈ꒧뙩ꛦ꓀꩒ꅃ ????????????????????????????????????????????????????????㐷㐹㔱㔳㔵㔷㔹㘱㘳㘵㘷㘹㜱㜳㜵㜷㜹㠱㠳㠵㠷㠹??????????????????????????????????????????????????????????????????????????????????꙾ꯗꅝꗁ냪ꅞ꙾ꯗꅝꗁ냪ꅞ맏1?ꕸ왗뻺꙾ꓑ땍ꡡ깠띬ꖢ썂꛴군?맏2?ꕸ왗뻺꙾믤궷ꡡ깠띬ꖢ썂꛴군 ꖻ곣ꡳ뻣엩ꓑ땍ꡡ깠띬ꖢꪺ볋ꖻ귓볆Ꙁ208귓ꅃꫭ1결ꕸ왗뻺ꚸꓑ땍ꡡ깠띬ꖢ귈꒧뇔굺꧊닎군ꅁꙢ뻣엩볋ꖻꑕꅁꡃꚸꖭꞡ띬ꖢ귈결믵꒸ꅁ돌ꑪ귈결ꗁ냪88꙾921ꑪꙡ빟ꪺ믵꒸ꅁ돌ꑰ귈결믵꒸ꅁ 21 ꣤꒤냑볆ꍦ결ꖭꞡꚸ볆ꅁ꣒꙰ꗾ엩볋ꖻꑕꡃ꙾ꖭꞡ결208/44=ꚸꅃ 22 ꕝꝴ쒵걆롰ꅂ껸ꢾ롰륁ꥥ라떥ꡡ깠꒧닎군ꅃ 23 ꕈ꧐ꯎꗾ귋결뉻귈ꑔꛊ롕꒸ꅁꕢ귋결ꑀꛊ롕꒸결꫱꛴군ꅃꚹ꛴군쇶ꕩ꿠ꚳ뭾깴ꅁ맯꓀끴ꮬꚡ뱶암ꚳ궭ꅃ 띬ꖢ썂ꅝ믵꒸ꅞ띬ꖢ썂ꅝ믵꒸ꅞ
궷쁉뫞뉺뻇돸 닄꒭ꣷ 닄ꑇ듁 2003꙾7ꓫ245 엣ꗜꕘꕸ왗ꓑ땍ꡡ깠띬ꖢ귈깴늧믡ꑪꅁꕎꫭ꙳ꚳ랥ꑪꪺ엜늧ꅃꫭ1-B엣ꗜ뙗륌5ꅂ10ꅂ20믵꒸ꪺ룪껆떧볆꓀ꝏ결88ꅂ72ꅂ54떧ꅁ꣤띬ꖢꖭꞡ귈꒶꧳143ꛜ227믵꒸ꅁ엣ꗜꕸ왗ꓑ땍ꡡ깠ꑪ뎡꓀띬ꖢ귈ꑰ꧳5믵꒸ꅃ둎ꫭ1-Cꛓꢥꅁꕸ왗ꙡ냏돌녠땯ꗍꓑ땍ꡡ깠결믤궷ꅁꙀ142ꚸꅁꙡ빟땯ꗍ28ꚸꅁ꣤꧒덹ꚨꪺꖭꞡ띬ꖢ썂결돌낪ꅝ믵꒸ꅞꅃ돌ꯡ둎낾멁ꅂ깰ꯗ엣ꗜꓑ땍ꡡ깠띬ꖢ썂ꪺ꓀끴결ꝥ뉻ꕫ낾ꕂ결낪깰뉻뙈ꅃ ꫭ1?ꕸ왗뻺꙾ꓑ땍ꡡ깠꛴군띬ꖢ썂꒧뇔굺꧊닎군떲ꩇ 돦ꛬꅇ믵꒸* 볋ꖻ볆 ꖭꞡ볆 볐럇깴 돌ꑪ귈 돌ꑰ귈 낾 멁 깰 ꯗ Panel A 뻣엩볋ꖻ 208 Panel B 뻣엩볋ꖻꑕꅁ쉥귈냏꓀ > 5믵 88 >10믵 72 >20믵 54 Panel C ꡡ깠쏾ꮬ 믤궷 142 ꙡ빟 28 ꣤ꕌ 38 Panel D Ꙣ믤궷ꡡ깠볋ꖻꑕꅁ쉥귈냏꓀ > 5믵 76 >10믵 62 >20믵 49 * ꛴군띬ꖢ썂껉ꅁꛒ뱻ꑈ귻ꚺꑠꅂ궫뛋ꅂ뮴뛋ꅂ꧐ꯎꗾ귋ꅂꕢ귋륁Ꝁꪫ띬ꖢ썂ꅁ꣤꒤륁Ꝁꪫ띬ꖢ썂꣓ꛛ륁띾닎군꙾돸꒧껰뙈뭐ꡡ깠닎군ꫭꅁꛓꑈ귻ꚺꑠꅂ궫뛋ꅂ뮴뛋ꅂ꧐ꯎꗾ귋ꅂꕢ귋ꅁ꓀ꝏ떹꒩300롕ꅂ100롕ꅂ50롕ꅂ10롕ꅂ300롕ꅂ150롕떥앶볆ꅁꕈ꛴군ꙕ뚵띬ꖢ썂ꅃ ꪬ냑볆샋ꥷ뭐돌빁볒ꮬ뿯꣺ ꙢGPDꪺ쉥ꅝthresholdꅞ꓀ꝏ덝결띳ꕸ맴5믵꒸ꅂ10믵꒸뭐20믵꒸ꑕꅁ룵아꧊ꖨꡡ띬ꖢꅝseverityꅞꪺꙕ꓀끴냑볆꛴군뭐ꪬ냑볆샋ꥷ떲ꩇꙃ꧳ꫭ2ꅂ3ꅃꫭ2ꅂ3꒤ꝑꗎ랧ꓱꅝlikelihood ratio testꅞ샋ꥷꪬ냑볆ꅁ떲ꩇꞡ엣뗛늧꧳0ꅁ엣ꗜꪬ냑볆결궫굮냑볆ꅁꗧꝙGPD쁵꧳볆꓀끴ꅃꚹ떲ꩇꙢꗴ꛳뫘쉥귈꛴군ꩫꑕꅝ돌ꑪ랧ꅂ냊깴ꅂHillꅞꅁꪬ냑볆ꞡ늧꧳륳ꅁ엣ꗜꕸ왗ꓑ땍ꖨꡡꪺ꓀끴뵔결ꕫ뫝ꭰꟀ꓀끴ꅃ
246 ꕸ왗ꖨꡡ뙗썂ꙁꭏ쁉ꮴ곹뭐뗻믹 ꫭ2 뻣엩볋ꖻꑕ꒧꒣ꙐGPD꛴군냑볆뭐ꪬ냑볆꒧샋ꥷ* ꛬ롭냑볆(ꍧ) 덗볒냑볆(ꍭ) ꪬ냑볆(ꍞ) 랧ꓱ샋ꥷp귈 쉥귈결5믵 GPD돌ꑪ랧꛴군ꩫ *** GPD냊깴꛴군ꩫ GPD볆꓀끴 0 Hill ꛴군ꩫ 쉥귈결10믵 GPD돌ꑪ랧꛴군ꩫ *** GPD냊깴꛴군ꩫ GPD볆꓀끴 0 Hill ꛴군ꩫ 쉥귈결20믵 GPD돌ꑪ랧꛴군ꩫ *** GPD냊깴꛴군ꩫ GPD볆꓀끴 Hill ꛴군ꩫ * ꣏ꗎPOTꅝpeak over thresholdꅞꪺ볒ꮬ뙩ꛦ랥귈꓀끴냑볆꛴군ꅁPOT볒ꮬ뇔굺볋ꖻ꒤뙗륌걙꽓ꥷ쉥귈ꪺꟀ뎡꓀끴ꅁ꣏ꗎGPDꅝgeneralized pareto distributionꅞ꣓둹굺Ꟁ뎡꓀끴ꪬꩰꅃ꓀ꝏ꣏ꗎ쉥귈결5믵ꅂ10믵ꅂ20믵ꅃ꣤꒤궫굮냑볆결ꪬ냑볆?ꅁ꣤ꕎꫭꟀ뎡ꪺ끉끨덴ꯗꅃ랧ꓱꅝlikelihood ratio, LRꅞꡄ뫢ꓨꚡ결GPꅝ0ꅞ/GPꅁ꣤꒤GPꅝ0ꅞ결ꪬ냑볆결0ꅁꕎꫭꟀ뎡라ꕈ볆ꚡ끉끨ꅁGPꫭꪬ냑볆꒣결0ꅁꟀ뎡라ꕈꭰꟀ꓀끴끉끨ꅃ꣤꒤뙗륌쉥귈5믵ꅂ10믵ꅂ20믵꒧볋ꖻ볆꓀ꝏ결88ꅂ72ꅂ54ꅃ 맏3ꛜ5뮡ꧺꙢ뻣엩볋ꖻꑕꅁꙕ뫘ꖨꡡ띬ꖢꙕ뫘끴빁ꓨꩫ꒧Ꟁ뎡꓀끴뭐맪믚꓀끴ꓱ룻ꅁꕈꙕ뫘뉖Ꙙ꓀끴ꪺ닖군뻷뉶ꅝCDFꅞ꣓ꫭꗜꅁ귌녎꓀끴냏꓀ꚨ꣢뫘뎡ꗷꅁ뙗륌쉥귈뎡꓀결GPD꓀끴ꅂ맯볆녠멁꓀끴ꅁꛓꖼ뙗륌쉥귈ꪺ뎡꓀ꅁ꣏ꗎ롧엧룪껆ꅝempirical dataꅞ결꣤꓀끴ꅃ맏꒤꓀ꝏ멉꣺ꑪ꧳5ꅂ10ꅂ20믵꒸ꕈꑗꪺꟀ뎡룪껆ꅁ결ꓨꭋꓱ룻ꅁ녎띬ꖢ귈꣺맯볆ꅃꗑ맏꒤ꕩ곝ꕘꅁ맯볆녠멁Ꙣ뙗륌775믵꒸ꅝ띬ꖢ귈꣺ꛛ땍맯볆ꯡ결ꅞꕈꯡꪺ랥뫝Ꟁ뎡뎡꓀ꚳ꒣뿹ꪺ끴빁ꅁꙢ775믵꒸꒧ꭥꭨꚳ곛럭ꪺ낾싷뉻뙈ꅃꕴꕾꅁ볆꓀끴ꅝ때ꪬ냑볆ꅞꙢ뙗륌390믵꒸ꅝ꣺ꛛ땍맯볆ꯡ결ꅞꕈꯡ뎡꓀ꅁꗧ결ꑀ꒣뿹ꪺ끴빁볒ꮬꅁꙢ390믵꒸꒧ꭥꭨꚳ낾싷뉻뙈ꅃ뉖Ꙙ꓀끴ꕈꪬ냑볆꒣결륳ꪺGPDꯘ멣Ꟁ뎡꓀끴돌꣎ꅁꙌ뗽ꑆGPD빁Ꙙ끴빁낪쉥ꪺꟀ뎡꓀끴ꅃ믤궷볋ꖻꑕꪺ떲ꩇ쏾ꅁꗧ엣ꗜꪬ냑볆꒣결륳ꪺGPDꟀ뎡꓀끴ꅁ돌놵꫱왛맮귈ꅝꢣ뿽맏ꅞꅃ
궷쁉뫞뉺뻇돸 닄꒭ꣷ 닄ꑇ듁 2003꙾7ꓫ247 ꫭ3?믤궷ꡡ깠볋ꖻꑕ꒧꒣ꙐGPD꛴군냑볆뭐ꪬ냑볆꒧샋ꥷ* ꛬ롭냑볆(ꍧ) 덗볒냑볆(ꍭ) ꪬ냑볆(ꍞ) 랧ꓱ샋ꥷp귈 쉥귈결5믵 GPD돌ꑪ랧꛴군ꩫ *** GPD냊깴꛴군ꩫ GPD볆꓀끴 Hill ꛴군ꩫ 쉥귈결10믵 GPD돌ꑪ랧꛴군ꩫ *** GPD냊깴꛴군ꩫ GPD볆꓀끴 Hill꛴군ꩫ 쉥귈결20믵 GPD돌ꑪ랧꛴군ꩫ *** GPD냊깴꛴군ꩫ GPD볆꓀끴 Hill ꛴군ꩫ * Ꙑꫭꑇ뗹ꅁ뙗륌쉥귈5믵ꅂ10믵ꅂ20믵꒧볋ꖻ볆꓀ꝏ결76ꅂ62ꅂ49ꅃ ??????????????????????????????????????????????????????????????????ㄮ?㌮?㌮?㐮?㐮?㐮?㐮?㔮?㔮?㔮?㔮?㔮?㔮?㔮?㔮?㔮?㔮?㔮?㔮?㘮????? 맏3 ꗾ엩볋ꖻꑕ뇄쉥귈ꑪ꧳5믵꒧ꙕ뫘끴빁꓀끴CDFꓱ룻 䍄?
248 ꕸ왗ꖨꡡ뙗썂ꙁꭏ쁉ꮴ곹뭐뗻믹 ??????????????????????????????????????????????????????????????????㈮?㌮?㌮?㐮?㐮?㐮?㐮?㔮?㔮?㔮?㔮?㔮?㔮?㔮?㔮?㔮?㔮?㔮?㔮?㘮?????맏 4?ꗾ엩볋ꖻꑕ뇄쉥귈ꑪ꧳10믵꒧ꙕ뫘끴빁꓀끴CDFꓱ룻 ??????????????????????????????????????????????????????????????????????㌮?㌮?㐮?㐮?㐮?㐮?㐮?㔮?㔮?㔮?㔮?㔮?㔮?㔮?㔮?㔮?㔮?㔮?㔮?㘮?????맏 5?ꗾ엩볋ꖻꑕ뇄쉥귈ꑪ꧳20믵꒧ꙕ뫘끴빁꓀끴CDFꓱ룻 ꗑ꧳맏뛈꿠ꑪ늤왛맮ꙕ꓀끴ꪺ끴빁ꪬꩰꅁꑕ궱꣏ꗎKolmogrow-SmirnowꅝK-Sꅞ샋ꥷꩫ꣓샋엧Ꟁ뎡꓀끴빁Ꙙꯗꅝgoodness of fitꅞꅃK-S빁Ꙙꯗ샋ꥷ24꒣꣼궭꧳믝뉺뷗ꚸ볆Ꙙ꣖ꛓ돠ꖢ룪끔ꅁ걇ꓱꕤꓨ꓀끴샋ꥷꟳ꣣샋ꥷꑏꅁꙢ꙰ꖻ곣ꡳꙝ뗛궫ꕫꟀ궫ꑪ띬ꖢ꓀끴덹ꚨꪺꑰ볋ꖻꑕ곛럭Ꙙ빁ꅃꗑꫭ4멉꣺Ꟁ뎡ꪺK-S귈엣ꗜꅁꙢ뻣엩볋ꖻꗴ꛳쉥귈ꑕꅁꕵ굮ꪬ냑볆꒣결륳ꪺGPDꅝ돌ꑪ랧ꅂ냊깴ꅂHill꛴군ꅞ꣤K-S귈ꞡꑰ꧳셻곉귈ꅝꅞꅁ걇뎣결빁Ꙙ꒧볒ꮬꅃ맯볆녠멁꓀끴ꅂ볆꓀끴Ꙣ 24 빁Ꙙꯗ샋ꥷ띎ꚮ놵꣼떴ꗀ엩꧒낲덝ꪺ뻷뉶꓀끴꒧닎군샋ꥷꅁ뗪때낲덝결ꗀ엩결F(L)ꅆ맯ꗟ낲덝결ꗀ엩꒣결F(L)ꅃ 䍄?䍄?
궷쁉뫞뉺뻇돸 닄꒭ꣷ 닄ꑇ듁 2003꙾7ꓫ249 쉥귈결5믵껉ꅁK-S귈ꑪ꧳셻곉귈ꅁ걇꒣결ꯘ멣Ꟁ뎡ꪺ빁Ꙙ꓀끴ꅁ땍ꛓ럭쉥귈결꓀ꝏ10ꅂ20믵껉ꅁ맯볆녠멁꓀끴ꪺK-S귈ꑰ꧳셻곉귈ꅁꗧ결빁Ꙙ꒧꓀끴ꅁꙐ볋볆꓀끴Ꙣꑪ꧳쉥귈20믵ꕈꑗꗧ빁ꙘꅃꙢ믤궷볋ꖻꑕꅁ맯볆녠멁꓀끴Ꙣꑪ꧳쉥귈5ꅂ10ꅂ20믵ꕈꑗꪺK-S귈곒ꑪ꧳셻곉귈ꅁ걇꒣결빁Ꙙꪺ꓀끴ꅃꛓ볆꓀끴ꑪ꧳쉥귈5ꅂ10믵ꕈꑗꪺK-S귈ꗧꑪ꧳셻곉귈걇ꗧ꒣결빁Ꙙꪺ꓀끴ꅁ볆꓀끴Ꙣꑪ꧳쉥귈20믵ꕈꑗ결빁Ꙙ꓀끴ꅃ돌ꯡꅁꙢ믤궷볋ꖻꑕꅁꪬ냑볆꒣결륳ꪺGPD꒧K-S귈곒ꑰ꧳셻곉귈ꅁ걇GPD결ꯘ멣Ꟁ뎡ꪺ빁Ꙙ꓀끴ꅃ뫮ꢥ꒧ꅁꪬ냑볆꒣결륳ꪺꑀ꿫걦꧔맏꓀끴ꅝGPDꅞꅁ꒣뫞Ꙣ뻣엩믤궷볋ꖻꑕꅁꞡ곛럭빁Ꙙꗎ꣓ꯘ멣ꕸ왗ꓑ땍ꖨꡡ띬ꖢꟀ뎡꓀끴ꅃ꒧ꅁ맯볆녠멁꓀끴ꅂ볆꓀끴ꭨ꒣ꑀꥷ빁Ꙙꅁ믝뗸뿯뻜ꪺ쉥ꛓꥷꅃ ꫭ4?ꙕ꓀끴Ꟁ뎡꒧K-S닎군뙱* GPD GPD Exponential GPD Lognormal 돌ꑪ랧꛴군 냊깴꛴군 볆꓀끴 Hill꛴군 맯볆녠멁 뻣엩볋ꖻ ꑪ꧳쉥귈5 ꑪ꧳쉥귈10 ꑪ꧳쉥귈20 믤궷볋ꖻ ꑪ꧳쉥귈5 ꑪ꧳쉥귈10 ꑪ꧳쉥귈20 α= 셻곉귈C= * ꪬ냑볆꒣결륳ꪺ볒ꮬ결ꅇꕈ돌ꑪ랧ꅂ냊깴ꅂHill떥ꓨꩫ꛴군냑볆ꪺGPDꅁ볆꓀끴결GPDꪺꪬ냑볆결륳ꪺ꽓껭꓀끴ꅃ ꖨꡡ뙗썂ꙁꭏꮴ곹믹귈 ꫭ5걏Ꙣ꒣Ꙑ뙗썂ꑗꑕ궭ꅁ뿯뻜앶뙒앶믹깴ꓨꚡ꧒군뫢녯ꪺꓑ땍ꖨꡡꙁꭏꮴ곹믹귈ꅃꗑꫭꕩꪾꅁ꒣뫞Ꙣ뻣엩볋ꖻꑕ믤궷ꡡ깠볋ꖻꑕꅁꕈ맯볆녠멁꓀끴ꯘ멣Ꟁ뎡꓀끴ꪺ걆ꦲꙁꭏ쁉ꮴ곹믹귈뎣ꝃ꧳ꕈGPDꅂ볆꓀끴ꯘ멣Ꟁ뎡꓀끴ꪺ걆ꦲꙁꭏꮴ곹믹귈ꅁꙝ결맯볆녠멁꓀끴ꝃ꛴ꑆ랥ꑪ낾싷귈ꪺ땯ꗍ뻷뉶ꅁ꣒꙰Ꙣ쉥귈10믵ꑕꅁ땯ꗍ띬ꖢ귈결100믵ꛜ110믵뚡ꅁGPD꛴군땯ꗍ뻷뉶결ꅁꛓ맯볆녠멁꓀끴꛴군땯ꗍ뻷뉶ꭨ뛈결ꅁꙢ쏾921ꑪꙡ빟띬ꖢ귈ꅝ2540믵ꛜ2550믵ꅞꪺ땯ꗍ뻷뉶ꅁGPD꛴군꣤땯ꗍ뻷뉶결ꅁ맯볆녠멁꓀끴꛴군땯ꗍ뻷뉶ꟳꕵꚳꅁ뛈곹
250 ꕸ왗ꖨꡡ뙗썂ꙁꭏ쁉ꮴ곹뭐뗻믹 GPD꧒꛴군ꪺ1/10ꅁꕩꪾ맯볆녠멁꓀끴맯낪뱨ꪺ듁뇦띬ꖢꚳ곛럭땻ꯗꪺꝃ꛴ꅃꕴꕾꅁꗑ닖뽮뻷뉶꓀끴맏4ꛜ6엣ꗜꕘ맯볆녠멁꓀끴닖뽮꓀끴Ꙣ룻ꑰ띬ꖢ귈뵤돲꒺ꪺ닖뽮뻷뉶귈ꑪ꧳꣤ꕌ꓀끴ꅁ엣ꗜ곛맯Ꙣ룻ꑪ띬ꖢ귈꛴군ꪺ땯ꗍ뻷뉶라낾ꝃꅁꑝ꧶덹ꚨ낪뱨ꅝhigher layerꅞꪺ걆ꦲꙁꭏꮴ곹ꭏ뙏ꪺꝃ꛴ꅃ굙ꭏ뙏륌ꝃꅁ걆ꦲꙢ듁뚡ꯡꕩ꿠때ꩫ륆꣬띬꽱꣢ꖭꅁ굴뛅닗ꡳ믝ꗑ꣤ꖦ끝랽룉뙋ꅁꚳ륈ꛛ떹ꛛꢬ뫫꾫ꅃꕴꕾꅁꕈ볆꓀끴ꯘ멣Ꟁ뎡꓀끴ꪺꮴ곹믹귈낪꧳ꪬ냑볆꒣결륳ꪺGPDꅃꕈ볆꓀끴ꯘ멣Ꟁ뎡꓀끴ꕩ꿠낪꛴걆ꦲꙁꭏ쁉ꮴ곹믹귈ꅁꭏ뙏낪꛴라꣏ꗁ뚡냓띾ꭏ쁉꒽ꕱꕩ꿠때ꩫ쇊뙒ꢬ냷ꙁꭏ쁉ꅁꑀꖹ땯ꗍ궫ꑪꖨꡡ띬ꖢꅁꗁ뚡ꭏ쁉띾싂궱셻귋뎬궷쁉ꅁ때ꩫ쎭ꥷꭏ쁉ꖫ돵ꅃ ꗑGPDꯘ멣ꪺꟀ뎡꓀끴Ꙣ뇄ꛦ꒣Ꙑ냑볆꛴군ꓨꩫꅝ꙰돌ꑪ랧ꅂ냊깴ꅂHill꛴군ꩫꅞ꧒ꯘ멣걆ꦲꙁꭏ쁉ꮴ곹믹귈ꞡ곛럭놵꫱ꅃꕴꕾꅁꓱ룻싹궫냵ꛦ믹껦ꪺ걆ꦲꙁꭏ쁉ꮴ곹믹귈ꅁ꣒꙰200-400믵뭐400-600믵ꓱ룻ꅁ200-400믵ꪺ싹궫냵ꛦ믹ꪺ걆ꦲꙁꭏ쁉ꮴ곹믹귈곹결400-600믵ꪺꮴ곹ꪺ궿ꅁꑝ둎걏럭띬ꖢ썂뙗륌400600믵껉ꅁꙁꭏꑈꅝreinsuredꅞ뎣걏뛈샲녯200믵뉺뷟ꅁ꛳ꮴ곹룻Ꙙꕇ믝굮ꅁ삳뗸뻣귓ꭏ쁉띾룪ꖻ뙱ꅁ꽽늣ꚨꖻꛓꥷꅃ굙ꓱ룻200-400ꅂ200-600믵ꪺ싹궫냵ꛦ믹ꮴ곹믹귈ꅁ200-600믵ꪺꮴ곹믹귈곹결200-400믵ꪺ궿ꅝꑰ꧳꣢궿ꅞꅁ 200-600믵ꮴ곹듁뇦뉺뷟썂룻낪ꅁꗑ믹깴귬ꭨꅁ걇꒣결뵵꧊ꓱ꣒ꅃ굙걆ꦲꙁꭏ쁉ꮴ곹ꪺꑗꑕ깴뙚ꓓꑪꅁꭏ뙏녎낾낪뻉교ꙁꭏꑈ때ꩫ쇊ꑊꢬ냷ꪺ걆ꦲꙁꭏ쁉ꅁꙘ빁ꪺ걆ꦲꙁꭏ쁉ꮴ곹ꑗꑕ궭꣮ꅁ결ꕴꑀ귓궫굮걆떦뷒썄ꅁ꣒꙰Cummins et al.ꅝ2002ꅞꕘꅁꖨꡡꭏ쁉ꪺꑗꑕ궭덝ꥷꖲ뚷ꛒ뱻ꗁ뚡냓띾ꭏ쁉돌ꑪ룪ꖻ깥뙱ꅁ꙰ꚹ걆ꦲꙁꭏ쁉ꮴ곹ꑾ꿠땯뒧꣤ꭄ샧ꝑꙐ껉뱗ꕛ꧓ꭏ꿠뙱ꪺ뫫꾫ꅃꚹꕾꅁ귌ꑝꩠ띎꣬꛴군꓀끴꒤ꪺ꒣Ꙑ쉥귈덝ꥷꗧ뱶암꣬걆ꦲꙁꭏ쁉ꮴ곹ꪺ믹귈ꅁ꣒꙰Ꙣ뻣엩볋ꖻꑕꅁꕈ돌ꑪ랧ꩫ꛴군GPD냑볆ꅁꙢ200-400싹궫냵ꛦ믹ꮴ곹ꑕꅁ쉥귈5믵ꪺ걆ꦲꙁꭏꮴ곹믹귈ꑰ꧳쉥귈10믵ꅁꛓ쉥귈10믵ꑓꑰ꧳쉥귈20믵ꅁ엣ꗜ쁈뗛쉥귈뱗ꕛꅁ걆ꦲꙁꭏꮴ곹믹귈뮼뱗ꅃ ꫭ6결Ꙩꚸ뉺뷟꣮ꯗꪺ꒣Ꙑ뱨꿅ꓑ땍ꖨꡡꙁꭏꮴ곹꒧믹귈ꅁ꣤뭐ꫭ5ꪺ떲ꩇ곛ꅃꙢꙨꚸ뉺뷟꣮ꯗꑕꅁ럭닖뽮띬ꖢ썂ꯗ뙗륌ꮴ곹ꑕ궭ꅝ꙰100ꅂ200ꅂ400믵ꅞꅁꭨꗟ꣨뙩ꛦ뷟쁶ꅁ걇Ꙩꚸ뉺뷟ꮴ곹ꑕꅁꙕ쏾ꮬ꒧ꮴ곹믹귈ꑪ뎡꓀곒ꑪ꧳ꫭ5ꅁꕄ굮걏ꙝ결꣤ꝴꚳ룻낪ꪺ덦맴껉뚡믹귈ꅃ
궷쁉뫞뉺뻇돸 닄꒭ꣷ 닄ꑇ듁 2003꙾7ꓫ251 ꫭ5?꒣Ꙑ뱨꿅ꑕꓑ땍ꖨꡡꙁꭏꮴ곹꒧믹귈* 닖군 냵ꛦ믹껦 냵ꛦ믹껦 싹궫냵ꛦ믹껦 싹궫냵ꛦ믹껦 싹궫냵ꛦ믹껦 띬ꖢ썂뉻귈 100믵 200믵 200-400믵 200-600믵 400-600믵 뻣엩볋ꖻꅇ쉥귈5믵 GPD-MLE GPD-MME 볆꓀끴 GPD-Hill 맯볆녠멁꓀끴 뻣엩볋ꖻꅇ쉥귈10믵 GPD-MLE GPD-MME 볆꓀끴 GPD-Hill 맯볆녠멁꓀끴 뻣엩볋ꖻꅇ쉥귈20믵 GPD-MLE GPD-MME 볆꓀끴 GPD-Hill 맯볆녠멁꓀끴 믤궷ꡡ깠볋ꖻꅇ쉥귈5믵 GPD-MLE GPD-MME 볆꓀끴 GPD-Hill 맯볆녠멁꓀끴 믤궷ꡡ깠볋ꖻꅇ쉥귈10믵 GPD-MLE GPD-MME 볆꓀끴 GPD-Hill 맯볆녠멁꓀끴 믤궷ꡡ깠볋ꖻꅇ쉥귈20믵 GPD-MLE GPD-MME 볆꓀끴 GPD-Hill 맯볆녠멁꓀끴 * 냵ꛦ믹껦꓀ꝏ결100믵ꅂ200믵ꅁꕎꫭꙢ맰곹ꓩꅁ닖뽮띬ꖢ썂뙗륌냵ꛦ믹껦껉ꅁ룓ꮴ곹믹귈결닖뽮띬ꖢ썂ꚩ낣냵ꛦ믹껦ꅁ꙰닖뽮띬ꖢ썂Ꙣ맰곹ꓩ결110믵ꅁꭨꮴ곹믹귈결10믵ꅃ꒧ꅁ닖뽮띬ꖢ썂ꖼ뙗륌냵ꛦ믹껦ꅁ꣤ꮴ곹믹귈결0ꅁꛓ맰곹믹껦결200-400믵ꅂ200-600믵ꅂ400-600믵ꅁꕎꫭꙢ맰곹ꓩꅁ닖뽮띬ꖢ썂ꑪ꧳ꑕ궭ꕂꖼ뙗륌ꑗ궭ꅁꭨꮴ곹믹귈결닖뽮띬ꖢ썂ꚩ낣ꑕ궭ꅁ꙰닖뽮썂결230믵ꅁꙢ200-400믵싹궫냵ꛦ믹껦꒧뇸ꗳꑕꅁ룓ꮴ곹믹귈결30믵ꅁ굙뙗륌싹궫냵ꛦ믹껦ꑗ궭ꅁꭨꮴ곹믹귈결냵ꛦ믹껦ꑗ궭듮냵ꛦ믹껦ꪺꑕ궭ꅁ굙ꖼ뙗륌싹궫냵ꛦ믹껦ꪺꑕ궭ꅁꭨꮴ곹믹귈결0ꅃ닖뽮띬ꖢ썂ꕈ덱덦뾱뗈뉶뙩ꛦ뷆ꝑꚨꅁꗑꗁ냪47꙾끟ꛜꗁ냪90꙾ꪫ믹덱덦뾱뗈뉶꒧ꖭꞡ결ꅃꮴ곹믹귈ꕈ걆ꦲ듁뛅꣩ꝑ뉶뙩ꛦ뉻ꕈꡄ뫢뉻귈ꅃ
252 ꕸ왗ꖨꡡ뙗썂ꙁꭏ쁉ꮴ곹뭐뗻믹 ꫭ6?꒣Ꙑ뱨꿅ꓑ땍ꖨꡡꙁꭏꮴ곹꒧Ꙩꚸ뉺뷟ꙁꭏꮴ곹믹귈* 냵ꛦ믹껦 냵ꛦ믹껦 싹궫냵ꛦ믹껦 싹궫냵ꛦ믹껦 싹궫냵ꛦ믹껦 100믵 200믵 200-400믵 200-600믵 400-600믵 뻣엩볋ꖻꅇ쉥귈5믵 GPD-MLE GPD-MME 볆꓀끴 GPD-Hill 맯볆녠멁꓀끴 뻣엩볋ꖻꅇ쉥귈10믵 GPD-MLE GPD-MME 볆꓀끴 GPD-Hill 맯볆녠멁꓀끴 뻣엩볋ꖻꅇ쉥귈20믵 GPD-MLE GPD-MME 볆꓀끴 GPD-Hill 맯볆녠멁꓀끴 믤궷ꡡ깠볋ꖻꅇ쉥귈5믵 GPD-MLE GPD-MME 볆꓀끴 GPD-Hill 맯볆녠멁꓀끴 믤궷ꡡ깠볋ꖻꅇ쉥귈10믵 GPD-MLE GPD-MME 볆꓀끴 GPD-Hill 맯볆녠멁꓀끴 믤궷ꡡ깠볋ꖻꅇ쉥귈20믵 GPD-MLE GPD-MME 볆꓀끴 GPD-Hill 맯볆녠멁꓀끴 * Ꙑꫭ꒭뗹ꅁ결Ꙩꚸ뉺뷟꣮ꅃ
궷쁉뫞뉺뻇돸 닄꒭ꣷ 닄ꑇ듁 2003꙾7ꓫ253 5. 떲뷗뭐ꯘ쒳 쇶땍ꖨꡡ궷쁉뗽꣩꓆Ꙣꕸ왗ꑷ덑뱳꩸끑뷗ꅁꙢꖫ돵ꥼꖼꚨ보ꭥꅁꗁ뚡끴Ꙙ걆ꦲꪺꙁꭏ쁉꒴결늣쁉꒽ꕱꕄ굮ꕩꛦꪺ늾신궷쁉ꓨꚡꅃꖻꓥ궺ꗽ뷗굺빁Ꙙꕸ왗ꪺ걆ꦲꖨꡡ뙗썂ꙁꭏꪺꮴ곹꒧뉺뷗뻚걛멣ꅁꙁ껚뻚ꕸ왗ꙡ냏ꓑ땍ꖨꡡ맪믚띬깠닎군룪껆ꕈ랥귈꓀끴끴빁ꅁꣃ끷맯ꖨꡡ띬ꖢꪺ꽓꧊ꅁꕈ귗ꖿ꒧꿂룵아륌땻결껚뻚꒧끝냈뿯뻜앶꣓뗻믹ꅁ곣ꡳ떲ꩇꕩꝀ결걆ꦲꖨꡡ뙗썂ꙁꭏꮴ곹덝군굱ꥷ꦳믹ꪺ냑ꛒꅃ 륌ꕨ끑뷗꣣룵아꧊룪늣ꪺꓥ쑭Ꙩꗎ꧳ꑀ꿫ꪺ쏒꣩ꅝ꙰믹볆ꅞꅁꛓ삳ꗎ꧳ꭏ쁉ꑗꪺꖨꡡ궷쁉꒧뗻믹ꕴ삳ꛒ뱻ꙝ꿀ꅁꕝ걁엜냊뉶ꅂ룵아ꪺ띬ꖢ꓀끴ꮬꚡꕈ룪늣ꕩꗦ꧶꧊떥냝썄ꅁ꣏꒧꓁Ꙙꖨꡡꪺ꽓꧊ꅃꖻꓥ덂뉺ꑆ룵아띬ꖢ꓀끴결맯볆녠멁ꕈꕈꭄ맯볆녠멁ꪺ놡ꩰꅃ녱뗻믹ꪺ떲ꩇ꣓곝ꅁꕸ왗땯ꛦꪺꚹ뫘뙗썂ꙁꭏꮴ곹ꅁꗑ꒣Ꙑ곉궭꣣ꚳ꒧띬ꖢ꓀끴ꅁꕩ꿠쇴ꝴꪺꑀ꽓꧊걏귈녯ꩠ띎ꪺꅃꚹꕾꅁ곣ꡳꪺ떲ꩇꕩ꣑Ꙙ빁ꪺ쉥뭐ꑗ궭꒧ꡍꥷꅁꕈ늣쁉꒽ꕱ돌빁쇗쁉ꪺ떦늤떥냑ꛒꅃ ꖻ곣ꡳ꒧돌ꑪ궭꣮ꣃꭄ볋ꖻ왛듺볆꒣ꢬꅁꛓ걏ꕩ꿠ꪺ룪껆듺뙱뭾깴ꅝmeasurement errorꅞꅁꕸ왗ꙡ냏ꪺꓑ땍ꡡ깠띬ꖢ꣬ꑅꑇꑀꑪꙡ빟ꅁꓨꚳ룻ꞹ뻣뫫뵔ꪺ닎군룪껆ꅁ꣏녯끴빁떲ꩇ쇴ꝴ곛럭땻ꯗꪺ냑볆꛴군궷쁉ꅃꛓ뿯뻜앶ꪺ믹귈ꅁ꙰ꑪ깡꧒ꪾꅁ맯냑볆ꑑ꓀뇓띐ꅁ꣏녯군뫢ꕘꪺ뙗썂ꙁꭏꮴ곹ꪺ믹귈ꅁꕩ꿠뛈룻꣣ꚳ믹껦ꛦ결왛맮ꪺ띎롱ꅁ냑볆ꪺ꒣뵔ꥷ꧊ꅝparameters’ uncertaintyꅞ꣼궭꧳룪껆ꕩ빡꧊ꥼ쏸놱꣮ꅁꖻ곣ꡳꕄ굮ꗘꪺꙢ꧳뒣꣑꓁Ꙙ뗻믹뉺뷗뭐맪믚ꪺ군뫢ꓨꚡꅁꕂꛜ돌꫱듁ꅝꑅꑑ꙾ꅞ결ꓮꑷ걏돌ꞹ뻣룪껆ꅁ듁뇦ꖼ꣓걆ꦲ곛쏶뎡늣띾곉ꖻꢭ맯꧳ꚹ쏾룪껆ꪺ뭠뚰몥쇍ꖿ뵔ꞹ돆ꅁꝙꕩ덶몥ꕘ귗ꖿꮴ곹ꪺꖿ뵔믹귈ꅃ ꣤ꚸꅁꖻ곣ꡳ둍ꡄꖨꡡ쁗뉶ꪺ꓀끴껉ꅁ뇄ꛦ뉖Ꙙꚡ꓀끴ꅁꝙ걏ꑪ꧳쉥귈뎡꓀ꅝꟀ뎡꓀끴ꅞꕈGPD꓀끴ꅂ맯볆녠멁꓀끴꣓ꯘ멣ꅁꑰ꧳쉥귈뎡꓀ꕈ롧엧룪껆ꯘ멣꓀끴ꅁ귌땯뉻ꮴ곹쁈뗛꒣Ꙑ꛴군ꩫꅂꑗꑕ궭ꅂ쉥귈ꞡꚳ꧒꒣Ꙑꅃ땍ꛓ귌ꑝꑆ룑꣣빁럭ꪺꑗꑕ궭ꪺꙁꭏꮴ곹ꅁꑾ꿠꽵ꖿ땯뒧걆ꦲꭏ쁉ꪺꢤꛢꕜ꿠ꅆꚹꕾꅁꙘ빁쉥귈ꪺ뿯꣺ꗧꚳꝕ꛴군꒧ꖿ뵔꧊ꅁ꣒꙰럭쉥귈ꪺ덝ꥷ륌낪ꅁ깥꧶꣏녯룪껆땽ꓖꅁ뙩ꛓ꣏녯냑볆꛴군ꪺ궷쁉낪ꅁ굙덝ꥷ륌ꝃ끴빁ꯗ꧶꒣ꅁꙢ덯ꓨ궱ꅁꕩꗑꖻ곣ꡳ뒣꣑꒧ꓨꩫ뙩ꛦꕈꖼ꣓룪껆뙩ꛦꙁ듺룕ꅝparameter stability testꅞꅁꕈ룉꒣ꢬꅃ
254 ꕸ왗ꖨꡡ뙗썂ꙁꭏ쁉ꮴ곹뭐뗻믹 냑ꛒꓥ쑭 1. ꩌ뇓뗘ꅁꓑ땍ꖨꡡ뙗썂뷟듚ꙁꭏ쁉꒧곣ꡳꅁ덻ꗒꑪ뻇ꭏ쁉뻇곣ꡳ꧒뫓ꑨ뷗ꓥꅁ1994꙾ꅃ 2. ꭊꑂꓫꅁꖨꡡ궷쁉쏒꣩꓆꒧꓀꩒ꅁ 냪ꗟ걆ꩶꑪ뻇궷쁉뫞뉺뭐ꭏ쁉뻇꡴뫓ꑨ뷗ꓥꅁ2001꙾ꅃ 3. 뎢ꓥ쁒ꅁꭏ쁉띬ꖢꪺ뉖Ꙙ냑볆볒ꮬꅁ덻ꗒꑪ뻇ꭏ쁉뻇곣ꡳ꧒뫓ꑨ뷗ꓥꅁ2000꙾ꅃ 4. 뎯녠ꡞꅁ녩롧뉺ꅁꖨꡡꭏ쁉듁덦쇗쁉꒧곣ꡳꅁꭏ쁉녍ꕚꅁ닄47ꣷꅁ1997꙾ꅁ74-94ꅃ 5. 뎯뷷럗ꅁꖨꡡ궷쁉쏒꣩꓆ꇐꕈHull and Whiteꑔ꒸뻰볒ꮬ놴끑ꕸ왗ꖨꡡ볆뿯뻜앶믹귈ꅁ맪뷮ꑪ뻇ꗸ띾뫞뉺곣ꡳ꧒뫓ꑨ뷗ꓥꅁ2001꙾ꅃ 6. 뱂ꣴ꽅ꅁꖨꡡꭏ쁉뿯뻜앶뗻믹볒ꚡ꒧곣ꡳꅁ냪ꗟ걆ꩶꑪ뻇ꭏ쁉뻇곣ꡳ꧒뫓ꑨ뷗ꓥꅁ 1997꙾ꅃ 7. Chang, C., 1995, A No Arbitrage Martingale Analysis for Jump Diffusion Valuation, Journal of Financial Research, 18, 3, 351-81. 8. Cummins, D., 1988, Risk-Based Premium for Insurance Guaranty Funds, Journal of Finance, 43, 4, 823-839. 9. Cummins, D., G. Dioone and M. Pritcett, 1990, Application of GB2 Family of Distribution in Modeling Insurance Losses Processes, Insurance, Mathematics & Economics, 9, 4, 257-272. 10. Cummins, D., 1992, Financial Pricing of Property and Liability Insurance. in Contribution to Insurance Economics, G.. Dionne ed., Boston: Massachsett , Kluwer Academic Publisher, 139-168. 11. Cummins, D. and H. Geman, 1995, Pricing Catastrophe Insurance Futures and Call Spread: An Arbitrage Application Approach, Journal of Fixed Income, 4, 4, 46-57. 12. Cummins, D., C. Lewis and R. Phillips, 1999, Pricing Excess of Losses Reinsurance Contract against Catastrophe Loss, in The Financing of Catastrophe Risk, K. Froot ed., Chicago: Illinois, Chicago Press. 13. Cummins, D., N. Doherty and A. Lo, 2002, Can Insurers Pay for the Big One? Measuring the Capacity of the Insurance Market to Respond to Catastrophic Losses, Journal of Banking & Finance, 26, 2, 557-583. 14. Danielsson, J. and C. de Vries, 1997, Tail Index and Quantile Estimation with Vary High Frequency Data, Journal of Empirical Finance, 4, 241-257. 15. Doherty, N. and J. Garven, 1986, Price Regulation in Property-Liability Insurance: A Contingent Claim Approach, Journal of Finance, 41, 5,
궷쁉뫞뉺뻇돸 닄꒭ꣷ 닄ꑇ듁 2003꙾7ꓫ255 1031-1050. 16. Dong, W., H. Shah and F. Wong, 1996, A Rational Approach to Pricing of Catastrophe Insurance, Journal of Risk and Uncertainty, 12, 201-218. 17. Fischer, S., 1978, Call Option Pricing when Exercise Price is Uncertain, and The Valuation of Index Bonds, Journal of Finance, 33, 169-176. 18. Froot, K., 1999a, The Envolving Market for Catastrophe Risk, Risk Management and Insurance Review, 2, 1-28. 19. Froot, K., 1999b, The Financing of Catastrophe Risk, Chicago: Illinois, Chicago Press. 20. Froot, K. and P. O’Connell, 1999, The Pricing of . Catastrophe Reinsurance, in The Financing of Catastrophe Risk, K. Froot ed., Chicago: Illinois, Chicago Press. 21. Geman, H., 2000, Insurance Risk Securitisation and CAT Insurance Derivatives, in Insurance and Weather Derivatives, H. Geman ed., London: Risk Books. 22. Harrington, S. and G. Nihau’s, 1999, Basis Risk with PCS Catastrophe Insurance Derivative Contracts, The Journal of Risk and Insurance, 66, 1, 49-82. 23. Hull, J., 2000, Options, futures, and other derivatives, 3ed. London: Prentice Hall. 24. Jung, J., 1964, On the Use of Extreme Values to Estimate the Premium for an Excess of Loss Reinsurance, ASTIN, Bulletin, 178-84. 25. Kremer, E., 1994, On the Probable Maximum Loss, Blatter der Deutschen Gesellschaft fur Versicherungs-mathmematik, 3, 201-205. 26. Lamm R., 1999. The Catastrophe Reinsurance Market: Economic Gyrations and Innovations Amid Major Structural Transformation. in Insurance and Weather Derivatives, H. Geman ed., London: Risk Book. 27. Lewis, C. and K. Murdock, 1996, The Role of Government Contract in Discretionary Reinsurance Market for Natural Disaster, Journal of Risk and Insurance, 63, 4, 567-597. 28. Lewis, C. and K. Murdock, 1999, Alternative Means of Redistributing Catastrophic Risk in a National Risk Management System, in The Financing of Catastrophe Risk, K. Froot ed., Chicago: Illinois, Chicago Press. 29. Litzenberger, R., D. Beaglehole and C. Reynolds, 1996, Assessing Catastrophe Reinsurance Linked Securities as a New Asset Class, in Insurance and Weather Derivatives. H. Geman ed., London: Risk Book. 30. McNeil, A. and R. Frey, 2000, Estimation of Tail-Related Risk Measures for Heteroscedastic Financial Time Series: An Extreme Value Approach, Journal of Empirical Finance, 7, 271-300. 31. Merton, R., 1976, Option Pricing when Underlying Stock Returns are
256 ꕸ왗ꖨꡡ뙗썂ꙁꭏ쁉ꮴ곹뭐뗻믹 Discontinues, Journal of Financial Economics, 3, 125-144. 32. Niehaus, G.., 2002, The Allocation of Catastrophe Risk, Journal of Banking & Finance, 26, 2, 585-596. 33. Pickands, J., 1975, Statistical Inference Using Extreme Order Statistics, The Annals of Statistics, 3, 119-131. 34. Priest, G.., 1996, The Government, the Market, and the Problem of Catastrophic Loss, Journal of Risk and Uncertainty, 12, 219-237. 35. Ramlau-Hansen, H., 1988a, A Solvency Study in Non-Life Insurance Part 1: Analysis of Fire, Windstorm, and Glass claims, Scandinavian Actuarial Journal, 3-34. 36. Ramlau-Hansen, H., 1988b, A Solvency Study in Non-Life Insurance Part 2: Solvency Margin Requirements, Scandinavian Actuarial Journal, 3-34. 37. Reiss, R. D. and M. Thomas, 2000, Statistical Analysis of Extreme Value, Basel: Birkhauser Verlag. 38. Rootzen, H. and N. Tajvidi, 2000, Extreme Value Statistics and Wind Storm Losses: A Case Study, in Extremes and Integrated risk management, London: Risk Books. 39. Shimko, D., 1992, The Valuation of Multiple Claim Insurance Contract, Journal of Financial and Quantitative Analysis, 27, 2, 229-246 40. Taylor, G., 1997, Reserving Consecutive Layers of Inwards Excess of Loss Reinsurance, Insurance: Mathematics & Economics, 20, 3, 225-242. 41. Teugels, J. L., 1987, On Pareto Type Distributions, Probability Theory and Mathematical Statistics, 2, 649-51.
궷쁉뫞뉺뻇돸 닄꒭ꣷ 닄ꑇ듁 2003꙾7ꓫ257 뿽 1 랥귈뉺뷗ꕄ굮ꚳ꣢뫘볒ꮬꅁ꓀ꝏ결Block MaximaPOT ꅝpeak over thresholdꅞ볒ꮬꅃ꣤꒤Block Maximaꕄ굮ꯘꗟꙢꑀ귓ꪺ쁈뻷볋ꖻ꒤ꅁꑀ걱듁뚡ꅝ꣒꙰ꡃ꙾ꅞ꒺ꪺ돌ꑪ귈ꅁꑝ둎걏꧒뿗ꪺꑀ꿫랥귈꓀끴ꅝgeneralized extreme value distribution, GEVꅞꅁ꣤빁Ꙙꗎ꣓둹굺덯냏뚡랥ꑪ귈ꪺꛦ결ꅃBlock Maxima볒ꮬ삳ꗎ꧳땽ꚳꗳꅝ꙰ꓑ땍ꖨꡡꅞ녎라꣏녯GEV꓀끴ꪺ냑볆꛴군꧶ꚳ낾뭾ꅁꙝ결꣤꧒ꚨꪺ돌ꑪ귈뚰Ꙙꪺ왛듺귈귓볆낾ꝃꅁ꣒꙰ꖻ곣ꡳꙀꚳ44꙾ꅁꡃ꙾ꕘꑀ귓돌ꑪ귈ꅁ꣓ꚨ돌ꑪ귈뚰Ꙙꅁ걇돌ꑪ귈뚰Ꙙ꒤ꕵꚳ44귓왛듺귈ꅃ곛맯ꪺꅁPOTꓱBlock Maxima볒ꮬꟳ꿠ꚳ껄ꙡ삳ꗎ꧳ꚳ궭룪껆ꅁꗑ꧳ꖻ곣ꡳ맯뙈쓝꧳땽ꓖꚳ궭룪껆ꅁ걇뇄POTꅃꚳ쏶꧳랥귈뉺뷗볒ꮬ냑볆ꪺ꛴군ꓨꩫꕄ굮ꚳ꣢뫘ꅁꑀ결ꕢ냑볆볒ꮬꅝsemi-parametric modelsꅞꅁ돌ꚭꕈHill뒣ꕘꪺ꛴군귈결ꕎꫭꅁꛓDainjelsson and De Variesꅝ1997ꅞꭨ뙩ꑀꡂ뒣ꕘ귗ꖿ꛴군Ꟁ뎡ꪺꓨꩫꅆꕴꑀ뫘결ꗾ냑볆볒ꮬꅝfully parametric modelsꅞꅁꕈPickandsꅝ1975ꅞ꧒땯깩ꪺGPD결ꕄꅃ쇶땍꣢뫘ꓨꩫ뎣녠덑꣏ꗎꅁMcNeil and Freyꅝ2000ꅞꕘGPDꪺ꛴군귈ꓱHill꛴군귈결슲돦ꅂ쎭ꥷꅁꣃꙐ껉빁ꗎ꧳땵ꟀꅂꭰꟀꪺ꓀끴ꅁꕌ귌ꑝꕘHill꛴군ꩫ뛈빁ꗎ꧳ꭰꟀꪺ꓀끴ꅃꕈꑕ뮡ꧺPOT볒ꮬ꛴군ꓨꩫꅃ POT볒ꮬꪺ껖ꓟꙢ둹굺볋ꖻ뙗륌걙꽓ꥷ쉥귈ꅝthresholdꅞ꒧빬썂ꪺꟀ뎡꓀끴ꅁꕩꕈꗎꑀ꿫걦꧔맏꓀끴ꅝGeneralized Pareto distribution, GPDꅞ꣓ꕎꫭꅁꯜ빁ꙘꗎꙢꯘ멣ꭏ쁉ꪺ뙗썂띬ꖢ꓀끴ꑗꅃGPD덱녠꣣꣢귓냑볆ꅁ꣤꒤ꍭ결덗볒냑볆ꅝscale parameterꅞꅁꕴꕾꍞ결ꪬ냑볆ꅝshape parameterꅞꅁꕄ굮ꗎ꣓둹굺Ꟁ뎡ꪺ끉끨덴ꯗꅃ굙뱗ꕛꛬ롭냑볆mꅝ곛럭꧳쉥ꅞꅁꝙGgms(L)→G(L−m),,g,sꅁꕩ꓀끴뱧결 1g−1−(1+(L−mg))g≠0,L≥0sGms(L)= g,,−(L−m)1−esg=0,L≥0굙떹꒩ꑀ낪쉥귈ꅝmꅞꅁꕏ뙗륌ꚹꑀ쉥귈빬썂ꪺ뇸ꗳ꓀끴결Fm(L)ꅃ덳쓲꓀끴F꒤ꅁ럭뿯꣺ꪺ쉥귈m덶몥뱗ꕛꅁꭨ빬썂꣧볆Fm()라ꙖGPDꚬ샄ꅃꕏL0결꓀끴꒧ꚳ궭때궭ꪺꕫ쉉ꅁꝙ L0=sup{L∈R:F(L)<1}
258 ꕸ왗ꖨꡡ뙗썂ꙁꭏ쁉ꮴ곹뭐뗻믹 굙ꕈ볆뻇ꚡꫭꗜꅁ낲덝쁈뗛ꑀ쁈뻷엜볆Lꪺ꓀끴꣧볆FꅁꛓL뙗륌ꑀ꽓ꥷ쉥귈mꪺ뇸ꗳ꓀끴꣧볆Fm()ꑓ뫙결빬썂꣧볆ꅝexcess distributionꅞꅁꕏL*=L−mꅁ꣤ꥷ롱꙰ꑕꅇ F**m(L−m)=Fm(L)=P{L−m≤LL≥m} PL≤m+L*,L≥m)F(m+L*()−F(m) == P(L≥m)1−F(m)꣤꒤0≤L*≤L0−mꕂL0≤∞ꅃꑝ둎걏뮡ꅁ맯꧳빬썂꓀끴Fm(L)ꅁ럭꣤쉥귈ꍧ쇍꧳ꚹ꓀끴ꪺꕫ쉉L0껉ꅁꕩ꣬ꑀꖿꪺꕩ뿅뙱꣧볆꣏녯 F*lim*supm(L)−Ggs(L)=0→, mL00≤y≤L0−mꑗꚡꪺꝴ띎결ꅇꝙ꣏궱맯꒣ꪾꙗꪺ덳쓲꓀끴ꅁꕵ굮꣤쉥귈m꣺녯냷낪ꅁꭨ뙗륌쉥귈mꪺ빬썂뇸ꗳ꓀끴Fm(L)둎걏GPDꅁ걇ꕵ굮Ꙣ맪믚룪껆꒤뿯꣺빁럭ꪺ쉥귈ꅁ꣒꙰McNeil and Freyꅝ2000ꅞꙢ곣ꡳ꒤꣏ꗎ꓀끴ꪺ닄90ꉈꛊ꓀ꛬ볆결쉥귈ꅁꝙꕩꕈGPD꓀끴꣓끴빁ꅁꖨꡡ룪껆ꗧꙐꅃꚹꕾꅁ럭m→∞ꕂL*=L−m≥0ꅁꭨFm(L*)≅Ggs(L*)=Ggms(L)ꅁ꣤뻷뉶녋ꯗ,,,꣧볆결ꅇ 11g−−1+*g(1L)g≠0 ssgL*()=ꅀꅀꅀg,s 1−L*esg=0 s굙ꍞ>0ꅁ귬ꖻꪺ꓀끴쓝꧳ꭰꟀ꓀끴ꅁ꙰paretoꅂloggammaꅂcauchystudent’s t떥꓀끴ꅃ럭ꍞ<0ꅁꭨ결ꮬꊺ pareto꓀끴ꅁ귬꣓ꪺ꓀끴쓝꧳땵Ꟁꅁ꙰uniformbeta떥ꅃ굙ꍞꇗ0ꅁꭨ결끨꓆결볆꓀끴ꅝexponential distributionꅞꅁꛓ귬ꖻ쓝꧳꒤Ꟁ뎡ꪺ꓀끴ꅁꕂ꣤Ꟁ뎡라ꕈ볆ꪺꮬ멁끉끨ꅁ꙰녠멁ꅂ볆ꅂgammaꅂlognormal떥꒤Ꟁ뎡꓀끴ꅃ뒫ꢥ꒧ꅁ둎Ꟁ뎡꓀끴ꛓꢥꅁGPDꕩ뗸결ꑀ귓곛럭ꑀ꿫꓆ꪺ꓀끴ꅃ ꙝꚹGPD꓀끴ꕩꕈꝑꗎ꣓ꯘ멣뙗륌mꪺ띬ꖢ꓀끴ꅃ껚뻚ꑗꚡꕩ녯FL=FL*()(+m)=[1−F(m)]×Fm(L−m)+F(m)ꅁ꣤꒤F(m)=P(L≤m)ꕩꕈꗑ롧엧룪껆ꅝempirical dataꅞꡄꕘFN(m)=1−nm/Nꅁ꣤꒤nm결뙗륌mꪺ볋ꖻ볆ꗘꅁN결뻣엩볋ꖻ볆ꅁꙝꚹ럭L≥m껉ꅁꟀ뎡ꪺ꓀끴결ꅇFˆL=FL*()(+m)=[1−FN(m)]×Fm(L−m)+FN(m)
궷쁉뫞뉺뻇돸 닄꒭ꣷ 닄ꑇ듁 2003꙾7ꓫ259 Fˆ(L)결ꑀꪬ냑볆ꍞꅁ덗볒냑볆s~=s(1−Fn(mg))ꅁꛬ롭냑볆결m~=m−s~Fm−g[(1−N())−1}/gꪺGPD꓀끴ꅁ뱧결 )×L−~1g−(m)Fg(L)=1−[1+ s~]GPDꪺ덗볒ꅂꪬ냑볆꛴군ꚳ꒣Ꙑꓨꩫꅁ녠ꢣꕝ걁돌ꑪ랧ꅝmaximum likelihoodꅞꅂ냊깴ꅝmomentꅞꅂHillꕢ냑볆떥ꅝ룔ꢣReiss and Thomas, 2000ꅞ떥ꅃ
260 ꕸ왗ꖨꡡ뙗썂ꙁꭏ쁉ꮴ곹뭐뗻믹 뿽 2 ???????????????????????????????????????????????????????????????????????ㄮ㘱㌮㈲㌮㠱㐮ㄷ㐮㐴㐮㘵㐮㠳㐮㤸㔮ㄱ㔮㈲㔮㌲㔮㐲㔮㔰㔮㔸㔮㘵㔮㜲㔮㜸㔮㠴㔮㤰㔮㤵?????맏 1?믤궷볋ꖻꑕ쉥귈ꑪ꧳5믵ꙕ뫘끴빁꓀끴ꪺCDFꓱ룻 䍄맏2?믤궷볋ꖻꑕ쉥귈ꑪ꧳10믵ꙕ뫘끴빁꓀끴ꪺCDFꓱ룻 ???????????????????????????????????????????????????????????????????????㌮〰㌮㘹㐮〹㐮㌸㐮㘱㐮㜹㐮㤴㔮〸㔮ㄹ㔮㌰㔮㌹㔮㐸㔮㔶㔮㘳㔮㜰㔮㜷㔮㠳㔮㠹㔮㤴㔮㤹????맏 3?믤궷볋ꖻꑕ쉥 귈ꑪ꧳20믵ꙕ뫘끴빁꓀끴ꪺCDFꓱ룻 䍄?䍄?
