Significance and possibilities of major accident insurance

121 4, XVIII, 2015 Finance DOI: 10.15240/ ul/001/2015-4-009 In oduc ion The de elopmen o human socie y places con inuously inc easing demands on i s p oduc ion. This b ings o he socie y no only posi i e bu also nega i e e ec s. Along wi h he de elopmen o indus ial p oduc ion, people ha e o ace associa ed isks. Indus ial acciden s, which ha e occu ed ecen ly, s ill ha e a nega i e impac on human li e, heal h, he en i onmen and he economy. Majo acciden s a e de i ned as e en s esul ing om uncon olled de elopmen s du ing an indus ial ac i i y, such as a se ious leakage, i e o explosion, which may immedia ely o subsequen ly lead o se ious h ea o indi iduals in o ou side he p emises, o o he en i onmen , in which one o mo e haza dous subs ances a e in ol ed. This a icle deals wi h di e en aspec s and issues o majo acciden s wi h ocus on he p e en ion o hei occu ence and possible consequences. Since he isks o majo acciden s ake ca as ophic p opo ions, he quali y legisla ion on his issue is needed. O e iew o legisla i e ac ions is in he sepa a e chap e o a icle. This legisla ion imposes o indus ial companies wi h he isk o majo acciden he obliga ion o liabili y insu ance o damages caused by he ealiza ion o hese isks. The main objec i e o he a icle is o p esen he possibili y o loss dis ibu ion o majo acciden s and simula ion o po en ial ex eme losses which a e necessa y o de e mining he p emiums. Fo he sake o illus a ion ha e been selec ed he majo acciden s and hei consequences since he ea ly wen ie h cen u y. The expe ience gained om hese and o he disas e s ha e played a signi i can ole in he de elopmen o legisla ion in ela ion o he p e en ion and liquida ion o consequences o majo acciden s. Minama a, Japan (1932–1968): The Company p oducing e ilize s eleased a o al o 27 ons o me cu y compounds in o he sea. The esul was a mass poisoning o local esiden s called Minama a disease. In he wake o his e en , 2,000 o 3,000 people died. [6] Se eso, I aly (1976): An explosion o a chemical eac o in he chemical plan o Gi audan company. The company’s managemen announced ha i had been a common acciden and hey ailed o p o ide in o ma ion abou he leakage o oxic subs ances. I was as la e as se en een days a e he acciden ha he ac o y managemen admi ed ha abou wo kilog ams o dioxin leaked in he ai , an amoun o poison capable o killing 19,000 people. [5] Bhopal, India (1984): Bhopal disas e is conside ed o be he wo s indus ial acciden in he wo ld. I s a ed in a plan o he U.S. Company Union Ca bide India Limi ed, p oducing pes icides, whe e deadly hyd ogen cyanide gas and me hylisocyana e (MIC) escaped. To his da e, mo e han 20,000 people died and app oxima ely 500,000 we e inju ed as a esul . [1] Cuba ão, B azil (1984): An explosion in a pe ochemical plan o Pe obas esul ed in a i e in local slums. The amoun o demises was due o he comple e bu ning o some si es ne e p ecisely de e mined; i is es ima ed o be app oxima ely 500. San Juan Ixhua epec, Mexico (1984): A se ies o explosions in he la ge wa ehouse LPG Company Pe oleos Mexicanos des oyed pa o he ci y. Abou 500 people died. Sandoz, Swi ze land (1986): A i e in he ag o-chemical company Sandoz wa ehouse caused he elease o oxic ag ochemicals in o he ai , bu also abou 30–40 ons o hese chemicals escaped in o he Rhine Ri e . Mix u e o subs ances in he i e con ained pes icides, dioxins, me cu y, chlo ine compounds, l uo escen dyes, o ganophospha es and o he s. Ciba-Geib, chemical company ound SIGNIFICANCE AND POSSIBILITIES OF MAJOR ACCIDENT INSURANCE Pa la Jind o á, Radim Jakubínský EM_4_2015.indd 121EM_4_2015.indd 121 1.12.2015 8:44:491.12.2015 8:44:49 122 2015, XVIII, 4 Finance close o his si e, a emp ed o make use o his si ua ion eleasing 400 li es o a azine in o he i e , belie ing his will no be e ealed. Chemicals immedia ely caused he dea h o aqua ic animals in he i e . 100 ons o i sh we e killed and pollu ion o he Rhine eached as a as he Ne he lands. [3] Baia Ma e, Romania (2000): Many expe s belie e ha i is Eu ope’s wo s en i onmen al disas e since he Che nobyl explosion. A dam holding back 100,000 cubic me e s o con amina ed wa e bu s con amina ing d inking-wa e supplies o mo e han 2.5 million Hunga ians. Due o he oxici y o cyanide in wa e , especially a ound he basin o he Tisza, i ually all li ing o ganisms pe ished along he i e . Fu he sou hwa ds, in he Se bian pa , app oxima ely 80% o aqua ic li e was killed. Two yea s a e , he ecosys em began o e u n o i s o iginal s a e, al hough s ill a om he le el be o e he disas e . [5] Enschede, The Ne he lands (2000): Fi e a S.E. Fi ewo ks caused a subsequen explosion o i ewo ks ha he company had p oduced. Nume ous explosions ensued wi hin he ollowing 30 minu es, de as a ing an a ea o 5 km2. The i e sp ead o a neighbou ing b ewe y. The esul ing cloud o smoke om he wo companies was seen a a dis ance o 60 km. In his disas e , 22 people los hei li e, including ou i e- i gh e s, and o e 940 people we e inju ed. I des oyed app oxima ely 500 apa men s, 1,500 homes, 60 businesses. [5] Toulouse, F ance (2001): Explosion in he AZF chemical ac o y. I was equi alen o 20– 40 ons o TNT, i caused a emo o 3.4 on Rich e scale and was hea d up o a dis ance o 80 km. The explosion caused a o al o 29 dea hs, 2,500 se ious inju ies and 8,000 mino inju ies. Damages paid ou o insu ance claims exceeded € 1.5 billion. [5] Wes , Texas (2013): Ammonium ni a e exploded in a e ilize ac o y. As a esul 15 people died, nea ly 200 people we e wounded and 150 buildings we e des oyed o damaged. The essen ial in o ma ion, howe e , is he ac ha he company had liabili y insu ance o damages only in he amoun o one million dolla s, bu he o al damage exceeded one hund ed million U.S. dolla s. Wi h espec o he o al damage, i may sound inadequa e ha he company was i ned $ 118,300 agg ega ely. In many s a es, including Texas, he e is no legal obliga ion o he company o conclude liabili y insu ance o he damage wi h he insu ed sum co esponding wi h he ange o possible damages. 1. De elopmen o he Numbe o Acciden s Human socie y is also exposed o he ac ion o na u al causes, o en in he o m o na u al disas e s. The numbe and consequences o man-made disas e s is inc easing wi h he de elopmen o human socie y. De elopmen o indus ial p oduc ion also b ings abou he isk o majo acciden s. Figu e 1 shows he de elopmen o he numbe o disas e s caused by human in l uence, compa ed o na u al disas e s be ween 1970 and 2012. This da a shows a long- e m g ow h o bo h ypes o ca as ophic e en s. The cha shows ha om 1970 onwa ds, he yea 2010 is he i s yea whe e a highe occu ence o na u al disas e s appea ed mo e han man- made disas e s. This is also one o he ala ming signals o he socie y o p o ec hemsel es and hei en i onmen om he e ec s o man- made disas e s. The p ima y challenge o he company is o ake such measu es so ha no majo acciden s occu . Howe e , people mus be adequa ely p epa ed o possible explosions, i es, spills, and o he se ious aul s. Fo his eason i is ad isable o use eme gency scena ios. Damages a ising om indus ial disas e s can each ex eme alues o billions o Eu os. I a company should be able o bea he i nancial consequences o majo acciden s, i is necessa y o ha e insu ance ha co e s possible damages in an adequa e amoun . A his poin i should be no ed ha he insu ance company i sel , howe e , canno bea he isks in such olumes ha a e ypical o hese isks. I is he e o e necessa y o nego ia e ensu ing o each insu ance con ac . 2. Legisla ion a Issue P e en ion o Majo Acciden s The need o legisla ion o ope a o s o indus ial acili ies and o ganisa ions, which a e h ea ened by majo acciden s, was es ablished immedia ely a e he i s occu ence o se ious e en s. U gen alks on a new EU di ec i e on whole egula o y amewo k in ensu ing he sa e y o haza dous ins alla ions s a ed a e EM_4_2015.indd 122EM_4_2015.indd 122 1.12.2015 8:44:491.12.2015 8:44:49 123 4, XVIII, 2015 Finance he explosion o cyclohexane in he ac o y NYPRO L d. in Flixbo ough (UK, 1974). O e he nex wo yea s in he Eu opean Communi y amewo k occu ed h ee addi ional se ious chemical acciden s: Beek (Ne he lands, 1975), Man edonia (I aly, 1976) and Se eso (I aly, 1976). [5] In he ligh o hese ca as ophic acciden s, i was clea ha new legisla ion o imp o e he sa e y o indus ial si es, planning o eme gencies o -si e acciden s and dealing wi h he aspec s o b oade egional and c oss- bo de indus ial sa e y is needed. Di ec i e Se eso, p epa ed in Feb ua y 1977, which was adop ed by he Council o Minis e s o he Eu opean Communi y on 24 6 h, 1982, is he esul o hose e o s. The ollowing measu es ha e o be adop ed by indi idual Membe S a es no la e han Janua y 8 h, 1984. [18] The Di ec i e applies o he p e en ion o majo acciden s which may be caused by ce ain indus ial ac i i ies, and o limi hei consequences o a man and he en i onmen . I ocuses on he con e gence o he measu es aken by he Membe S a es in his a ea. A icle 1 de i nes e ms such as indus ial ac i i y, ope a o , majo acciden s and haza dous subs ances. The Di ec i e was modi i ed wice, in 1987 Di ec i e 87/216/EEC o 19 Ma ch 1987 (O i cial Jou nal No L 85 o 28 Ma ch 1987) and he 1988 Di ec i e 88/610/EEC o 24 No embe 1988 (OJ L 336 o 7 Decembe 1988). Bo h amendmen s aimed o ex end he scope o his Di ec i e, la gely in o de o include he s o age o haza dous subs ances. [18] Changes occu ed in esponse o a majo acciden in he Union Ca bide ac o y in Bhopal, India in 1984 and acciden s in he Sandoz wa ehouse in Basel, Swi ze land in 1986. Se eso I does no apply o nuclea acili ies and plan s p ocessing adioac i e subs ances and ma e ials, mili a y equipmen , p oduc ion and sepa a e s o age o explosi es, gunpowde and ammuni ion, mining and o he mining ope a ions, equipmen used o he disposal o oxic and haza dous was e, which a e subjec o Communi y law, i hei aim is o p e en majo acciden s. As he Council o Eu ope and ep esen a i es o he Go e nmen s o he Membe S a es si ing in he Council s essed he need o a mo e e ec i e implemen a ion o Di ec i e 82/501/EEC and called o a e iew o he di ec i e which, i necessa y, included a possible ex ension o he p o ince scope o Di ec i e and a g ea e exchange o in o ma ion in his i eld be ween Membe S a es. Also he need o imp o ed managemen o isks and acciden s was s essed. In addi ion, he acciden in Bhopal and Mexico highligh ed he dange posed by he p oximi y o esiden ial Fig. 1: De elopmen o he numbe o disas e s 1970–2012 Sou ce: own EM_4_2015.indd 123EM_4_2015.indd 123 1.12.2015 8:44:501.12.2015 8:44:50 124 2015, XVIII, 4 Finance buildings and dange ous a eas. Las bu no leas , om he impo ance and bene i s o in o ming he indi idual Membe S a es was on Decembe 9 h, 1996, a new Di ec i e 96/82/EC accep ed, known as he Se eso II. [6] Due o se e e indus ial acciden s in Toulouse, F ance, in Baia Ma e, Romania and Enschede, in he Ne he lands and conclusions o s udies on ca cinogens and subs ances dange ous o he en i onmen was Se eso II ex ended by Di ec i e 2003/105/EC. The new Di ec i e equi es Membe S a es o ensu e a e y de ailed app aisal o isks by using possible acciden scena ios ha co e isks a ising om s o age and p ocessing ac i i ies in mining, s o age o py o echnics and explosi es s o age o ammonium ni a e based e ilize s [5] The main eason o eplacing he Se eso II Di ec i e is a change in he sys em o classi i ca ion o dange ous subs ances es ablished by he Eu opean Di ec i e No. 1272/2008 o Decembe 16 h 2008, abou classi i ca ion, labelling and packaging o subs ances and mix u es. I was also necessa y o cla i y and upda e ce ain pa s o he di ec i e, o imp o e he implemen a ion and en o cemen o he Di ec i e. In o al, in he Se eso III (2012/18/EU) is lis ed 32 easons. This Di ec i e was adop ed on July 4 h, 2012, published July 24 h, 2012, coming in o o ce on Augus 13 h 2012, o be implemen ed by May 31s , 2015 wi h he excep ion o he implemen a ion o he A icle 30, wi h he la es da e Feb ua y 14 h, 2014. This pa applies o hea y uel oils. Se eso III Di ec i e is ex ended o onsho e unde g ound gas s o age acili ies. The Se eso II di ec i e de i nes 8 concep s: plan , equipmen , ope a o , haza dous subs ances, majo acciden haza ds, isks and wa ehouse. The new Se eso III Di ec i e de i nes 19 concep s, including 7 om he p e ious di ec i e (excluding concep s o e). The Se eso I, II and III, which a e g adually eleased by he Eu opean Economic Communi y, he Eu opean Communi y and he Eu opean Union, a e inco po a ed by indi idual Membe S a es in o hei na ional legisla ion. In he Czech Republic, he law No. 59/2006 Coll is being add essed. The legisla ion also includes access o isk assessmen , eme gency scena ios and plans, he need o insu ance, public access o in o ma ion and many o he se ious measu es. Acco ding o Law No. 59/2006 Coll., abou he p e en ion o majo acciden s, a se e e acciden is de i ned as an abno mal, pa ially o o ally uncon ollable, spa ially and empo ally bounded e en , such as a majo leakage, i e o explosion, which occu ed o he o igin is imminen ly h ea en in he con ex o wi h he use o he building o acili y in which he haza dous subs ance is manu ac u ed, p ocessed, used, anspo ed o s o ed, and leading o se ious dange o se ious impac on he li es and heal h o people, li es ock and he en i onmen o ha m o p ope y. [17] This law pe ained o app oxima ely 150 indus ial companies in he Czech Republic and es ablished basic obliga ions o ope a o s o hese objec s. I can be said ha his law ep esen ed a signi i can con ibu ion o he p e en ion om majo acciden s in he Czech Republic. Howe e , i is clea ha mos companies we e no su i cien ly p epa ed o ul i l obliga ions s emming om his law; he e o e he sa e y documen a ion was in la ge numbe s epea edly e u ned o ep ocessing [1]. Law No. 59/2006 Coll. was pa ially amended se e al imes and by he 1s o Ma ch in 2010 came in o e ec he law No. 488/2009 Coll. ha amends he law No. 59/2006 Coll., abou he p e en ion o majo acciden s caused by dange ous chemicals o chemical p epa a ions and abou amending he law No. 258/2000 Coll., abou he p o ec ion o public heal h and amendmen o some ela ed laws. [17] Legisla ion o liabili y o damages incu ed as a esul o majo acciden is newly ound in § 12. The ope a o is obliged o conclude new insu ance wi hin 100 days om he en y in o o ce o he decision on he app o al o he secu i y so wa e o secu i y epo s. The limi o indemni y mus e l ec he ange o possible impac s o se e e acciden s, which a e cu en ly lis ed in he app o ed secu i y p og am o in an app o ed sa e y epo . [17] In he new legisla ion a e speci i ed indi idual adminis a i e o enses in a sepa a e § 36, which is used in § 37, which deals wi h i nes, while in he p e ious law, he indi idual adminis a i e o enses a e lis ed igh a he indi idual le el o i nes. The legisla ion o majo acciden s in he Czech Republic uses a o al o i e ins umen s o p o ec ion, namely:  Inclusion o an objec o de ice. EM_4_2015.indd 124EM_4_2015.indd 124 1.12.2015 8:44:501.12.2015 8:44:50 125 4, XVIII, 2015 Finance The obliga ion o he ope a o o p epa e a lis o haza dous subs ances; p opose ca ego iza ion o g oup A o B, o handle he p o ocol on non-inclusion.  Risk analysis, secu i y p og am and epo . The obliga ion o he ope a o o pe o m analysis and e alua ion o isk o a majo acciden and on i s basis o p ocess sa e y p og am o p e en ion o majo acciden s o he g oup A, g oup B, hen a sa e y epo .  Plan o he physical p o ec ion o he building o acili y.  In e nal and ex e nal eme gency plan.  Liabili y insu ance. [8] 3. Majo Acciden Insu ance Fo insu ance o majo acciden s in he Czech Republic i is compulso y o conclude con ac ual insu ance, wi h espec o he Law No. 59/2006 Coll. Fo se ious indus ial acciden insu ance, § 12 o Law No 59/2006 Coll. mus be abided by, whe e he limi s o insu ance a e se . The le el o limi o insu ance bene i mus e l ec he ange o possible impac s o se e e acciden s, which a e cu en ly lis ed in he app o ed secu i y p og am o in an app o ed sa e y epo . The le el o limi o insu ance bene i ag eed by he ope a o o he es ing o he ope a ion s age should e l ec he ange o possible impac s o majo acciden based on he esul s o isk analysis and assessmen , submi ed o he Regional O i ce. [17] To al insu ance p emium is de e mined by he ela ion: CP = ZP * KSP * KRM + DN, (1) whe e: CP is he o al insu ance p emium, ZP is he basic insu ance, including pa icipa ion, KSP is he coe i cien o pa icipa ion, KRM is he isk ac o , DN a e addi ional cos s. Fo calcula ion o he isk ac o , a pa ial isk analysis need be ca ied ou , he esul o he e alua ion is h, whe ein: 1 ≤ h ≤ 5, (2) while 1 is he bes a ing and 5 he wo s a ing; co esponding wi h he highes possible isk. Subsequen ly, he o e all coe i cien o he isk ac o KRM is se , whe e: 0.3 ≤ KRM ≤ 6. (3) The o al insu ance p emium inc eases when inc easing he sum and inc easing ela i e pa icipa ion dec eases he o al insu ance p emium. The basic p oblem in de e mining he p emium acco ding o (1) is co ec iden i i ca ion o he basic p emium. Fo his aim, he insu ance company needs o know he ex en o damage p obabili y models including in o ma ion abou possible ex eme losses. In he nex sec ion, he issue o modeling and simula ion o ex eme damages is deal wi h. 3.1 Modelling and Simula ion o he Ex eme Losses Se ious indus ial acciden s a e o en classi i ed as ex eme, ca as ophic damages wi h he insu ance claims amoun ing o billions o eu os. Ex eme alues heo y is used o assess he isks o highly imp obable e en s. To such e en s belong se ious indus ial acciden s and also a ious na u al disas e s (hu icanes, l oods, ea hquakes, i es, e c.) and man-made disas e s, including nuclea acciden s and e o ism. As al eady shown in i gu e 1, he amoun o ca as ophic e en s has a endency o inc ease. The o al insu ance bene i o insu ance companies is made up o 80% paymen o damages om such e en s, while hei sha e in he o al numbe o insu ance bene i is app oxima ely 20%. Insu ance companies a e o ced o inno a e and con inually e alua e hei app oaches o isk assessmen and indi idual insu abili y o isks associa ed wi h he design o insu ance p oduc s. Bo h hese ac s a e o cou se signi i can ly e l ec ed in he p ices o insu ance. To be able o model and simula e he ex eme losses o majo acciden s, he ollowing sec ions p o ide a heo e ical p ocedu e o p ac ical use o quan ile unc ion and o de s a is ics o he simula ion o ex eme losses. Mo e de ails abou ca as ophic isk managemen and abou modeling ca as ophic loses you can i ne in [14] o [16]. EM_4_2015.indd 125EM_4_2015.indd 125 1.12.2015 8:44:501.12.2015 8:44:50 126 2015, XVIII, 4 Finance 3.2 Quan ile Model In he po olios o se ious indus ial acciden s insu ance is he p obabili y o occu ence o he ex eme losses highe in compa ison wi h con en ional insu ance po olio. These claims ha e a la ge i nancial impac on insu ance companies, so i is impo an o he insu e o know he p obabili y model ha adequa ely desc ibes he insu ance losses also in he igh -hand ail. Fo he ex eme losses modelling he long o hea y ailed p obabili y dis ibu ions a e used. The Pa e o dis ibu ion is o en used as a model o claim amoun s needed o ob ain well- i ed ails [12]. Random a iable X has a dis ibu ion wi h he hea y ail, i applicable: limx→∞eλx P(X > x) = limx→∞ eλx F  (x) = ∞, o λ > 0. (4) Quan ile unc ions applica ion is one way o modelling he claim amoun s and subsequen simula ion o ex eme losses. When espec ing speci i c basic ules, ad an ageous ea u es o quan ile unc ions allow o combine and edi unc ions in such a way ha he esul ing shape is non- dec easing, quan ile unc ion again, wi h s a is ically in e p e ed pa ame e s [7], [15]. Quan ile unc ion Q (p) is de i ned o each eal p, 0 ≤ p ≤ 1 by ela ion: Q (p) = xp , o which F(xp) = p. (5) Quan ile unc ion Q (p) is hen de i ned as he in e se o he dis ibu ion unc ion F (x). The alue xp is called p-quan ile. By di e en ia ing he unc ion Q (p) by p we ob ain he quan ile densi y unc ion: q(p) = dQ (p) dp ,0 ≤ p ≤ 1. (6) O de s a is ics play a key ole in modelling using quan ile unc ions. A mo e de ailed explana ion quan ile models can be ound o example in [4], [13] and [15]. 3.3 Simula ion o he Ex eme Values When simula ing ex eme alues, i is p ima ily necessa y o use he p og am o gene a ing pseudo andom numbe s. Basic pseudo andom numbe s a e wi hin he in e al <0, 1> and ep esen a andom obse a ion om a con inuous uni o m dis ibu ion on his in e al. Quan ile unc ion o a uni o m dis ibu ion on his in e al <0, 1> is exp essed as: S(p) = p o 0 ≤ p ≤1. (7) I using a andom numbe gene a o , we can gene a e independen alues om a uni o m dis ibu ion on he in e al <0, 1>. In his way, he gene a ed pseudo- andom numbe s and hei use in he p obabilis ic model o any ype is called simula ion [7]. The basis o such simula ions is Q- ans o ma ion ule. I z = T(x) is a non- dec easing unc ion o x and Q (p) is he quan ile unc ion, hen also T(Q(p)) is a quan ile unc ion [7]. I is a non-dec easing unc ion o T(x) a quan ile unc ion Q (p) o any dis ibu ion, he applica ions o Q- ans o ma ion ule o he case o uni o m dis ibu ion quan ile unc ion S (p) = p we can simula e he alue o x om dis ibu ion wi h quan ile unc ion Q (p) as: xi = Q(ui) o i = 1, 2, …, n, (8) whe e u1, u2,…, un a e simula ed alues om a uni o m p obabili y dis ibu ion on he in e al <0, 1>. Subs i u ing ui o quan ile unc ion xi = Q(ui), we ob ain he a anged alues x(i), ha gua an ee a non-dec easing shape o he unc ion Q(ui). The g ea ad an age o simula ion using he quan ile unc ion is ha i also allows o simula e only he highes alues in uppe ail wi hou necessi y o simula ion he cen al alues o andom a iable. We assume he igh -hand ail o he p obabili y dis ibu ion. By [7] and [13] i is possible o simula e he highes alue as: x(n) = Q(u(n)),whe e u(n) = n 1 n, (9) while n is a andom numbe om he in e al <0, 1>. I he sequence o he ans o med a iables is de i ned in he o m: u(n) = n 1 n u(n–1) = ( n – 1 ) 1 n –1 * u(n) u(n–2) = ( n – 2 ) 1 n –2 * u(n – 1) . . . EM_4_2015.indd 126EM_4_2015.indd 126 1.12.2015 8:44:501.12.2015 8:44:50 127 4, XVIII, 2015 Finance whe e i, o i = n, n-1, n-2,, ..., a e a plu ali y o alues gene a ed as a andom selec ion om a uni o m dis ibu ion, hen by de i ni ion alues ui, o i = n, n-1, n-2..., we ge an inc easing sequence: u(i–1) < ui . (11) Values u(i) o m an o de ed sequence o alues om a uni o m dis ibu ion. I we ge one alue u(n), he ela ion o he simula ion has he o m: u(m) = ( m ) 1 m * u(m+1) , o m = n–1,n–2,… (12) The la ges obse a ions o a iable X a e hen simula ed as: x(n) =Q(u(n) ) , x(n–1) =Q(u(n–1) ) , x(n–2) =Q(u(n–2) ) , (13) ⁞ 3 .4 Simula ion o Ex eme Losses o Majo Acciden s In his pa , heo e ical knowledge abou quan ile unc ion is applied on he da a acqui ed om in o ma ion abou majo acciden s om he p e ious chap e and applied o simula e ex eme losses. In o al, 27 damages calcula ed in eu os ha e been selec ed om he in o ma ion sys ems o majo acciden s (EMARS, ZEMA, ARIA and PZHP). All o hem ook place o e he yea s 2008–2010 and hey a e o de ed in Table 1. Using he s a is ical package STATGRAPHICS Cen u ion XV by he Kolmogo o -Smi no es we ha e ound ou long ailed p obabili y dis ibu ions well i ed o da a in Table 1. Resul s o his es show Table 2. Acco ding o p- alues, he losses a e bes i ed by Pa e o dis ibu ion model in he Eu opean o m [12]: p = F(x) = 1 – ( a x )b (14) By he STATGRAPHICS Cen u ion ou pu , pa ame e s o his p obabili y model a e de e mined as a = 2,000,000; b = 0.774826. The aim is o simula e he highes i e losses, conside ing wen y majo acciden s ha ha e happened. Fo his, he simula ion o ex eme alues h ough quan ile unc ion will be used. Quan ile unc ion o Pa e o dis ibu ion can be de i ned as a unc ion in e ed o he dis ibu ion unc ion (14) in he o m: xp = Q(p) = a (1–p)1 b (15) 2,000,000 2,000,000 2,120,000 2,500,000 2,650,000 3,000,000 3,000,000 3,400,000 3,500,000 4,000,000 4,000,000 4,500,000 5,000,000 5,100,000 6,000,000 7,090,000 8,400,000 10,000,000 12,000,000 12,000,000 14,000,000 14,500,000 15,000,000 21,050,000 32,000,000 36,000,000 435,000,000 Sou ce: he in o ma ion sys ems o majo acciden s Tab. 1: Indi idual i nancial ange o se ious indus ial acciden s (in eu o) Loglogis ic (3-Pa ame e ) Logno mal Logno mal (3-Pa ame e ) Pa e o (2-Pa ame e ) DN s a is ics 0.203818 0.137538 0.110012 0.084416 P-Value 0.212352 0.686701 0.899466 0.990618 Sou ce: own calcula ions Tab. 2: Resul s o he Kolmogo o -Smi no es EM_4_2015.indd 127EM_4_2015.indd 127 1.12.2015 8:44:501.12.2015 8:44:50 128 2015, XVIII, 4 Finance The s a is ical so wa e STATGRAPHICS Cen u ion andomly gene a ed i e numbe s wi hin he in e al <0, 1> om an e en dis ibu ion. The ollowing calcula ions we e done in MS Excels, using he o mulae (10), (12) and (13). The esul o simula ion o he highes i e losses ou o wen y indemni ies gi en, including he p ocedu e, is p o ided in Tables 3 and 4. Figu e 2 shows he simula ed damage x=Q(u), u he jus o each o de s a is ics X(20), X(19), …, X(16) and also hei median alues x0.5 and quan iles x0.005 and x0.995. In [7] and [13] is de i ed he calcula ion o he s a ed quan iles including be a in e sion unc ion, which is why acqui ed ou comes a e p esen ed only. Table 4 makes i clea ha he highes amoun o claim is om he in e al <13,127,418.93 €; 88,829,890,943.26 €> wi h he p obabili y α=0.99, while he median o he highes damage eaches he alue o 156,773,540.72 €. These esul s a e use ul o he pu poses o insu ance and einsu ance. 3.5 Reinsu ance o he La ges Claims Ex eme isks, simula ed in he p e ious chap e , need o be ensu ed h ough a combina ion o nume ous einsu ance ypes. One o he mos used combina ions includes a einsu ance when he applica ion o he insu ance company’s own e en ion is ollowed by quo a einsu ance. A highe ie is ensu ed h ough non-p opo ional WXL/R einsu ance, and also al e na i e o ms o einsu ance can be use. As shows Figu e 1, man-made disas e s ha e been inc easingly ex ensi e la ely. Thei modelling and simula ion is bene i cial o isk- managemen policies o insu ance companies and ackling c ucial issues o hei insu ance and einsu ance. Ex eme- alue simula ion is gene ally used in non-p opo ional la ges claims einsu ance LCR(p) o ECOMOR(p) einsu ance [13]. Conclusion This a icle is de o ed o he analysis o majo indus y acciden s. The isks o majo acciden s and hei consequences each ca as ophic dimensions. Tha is a eason o equi e a quali y legisla i e modi i ca ion ocused on he p e en ion and liquida ion o he consequences. The SEVESO di ec i es No. I, II and III we e sequen ially eleased n 1/n 1/n u(n) Q(u(n)) 0.6489213 20 0.050000 0.978610 0.978610 285,810,153.50 € 0.2682335 19 0.052632 0.933086 0.913127 46,829,591.89 € 0.7592468 18 0.055556 0.984815 0.899261 38,682,768.63 € 0.3568497 17 0.058824 0.941186 0.846373 22,437,953.57 € 0.4219863 16 0.062500 0.947504 0.801942 16,165,793.88 € Sou ce: own calcula ions Tab. 3: Simula ion o op i e damages in wen y insu ance indemni ies Q(BETAINV(0.5; ;n- +1)) = x0.5 Q(BETAINV(0.005; ;n- +1)) = x0.005 Q(BETAINV(0.995; ;n- +1)) = x0.995 156,773,540.72 € 13,127,418.93 € 88,829,890,943.26 € 50,049,792.19 € 8,804,780.17 € 1,732,291,027.22 € 27,432,632.79 € 6,806,971.44 € 366,468,591.03 € 18,216,901.58 € 5,613,897.44 € 147,262,811.20 € 13,353,730.93 € 4,810,419.62 € 78,297,378.84 € Sou ce: own calcula ions Tab. 4: Quan iles o o de ing s a is ics EM_4_2015.indd 128EM_4_2015.indd 128 1.12.2015 8:44:501.12.2015 8:44:50 129 4, XVIII, 2015 Finance by he Eu opean Economic Communi y, he Eu opean Communi y and he Eu opean Union a e implemen ed by indi idual membe s a es in o hei na ional legisla ions. In he Czech Republic hey a e ensh ined in he Ac No. 59/2009 Coll. a his junc u e. Fo he membe s a es o he EU, OECD and UNECE he e is an in o ma ion sys em called EMARS. This sys em collec s da a abou ope a o s subjec o he ele an laws and abou majo acciden s. EMARS p o ides basic in o ma ion abou pas acciden s also o he gene al public. Fo he companies in he EU a ea he e is a legal obliga ion o ake ou liabili y insu ance wi h insu ed sum ha has o co espond o he ex en o he possible damage. In he Czech Republic his obliga ion is es ablished by Ac No. 59/2006 Coll. I is necessa y o secu e e e y insu ance con ac , because he possible damage can each ca as ophic dimensions. Since he e a e big isks in such cases no only he classical p o ec ion bu also a combina ion o he al e na i e isk ans e me hods need o be used. Among he ART me hods ha can be used o hedge he isk o majo acciden s belongs he secu i iza ion o insu ance isks. In he a icle is used da a ela ing o 27 majo acciden s o he applica ion o he ex eme damage simula ion and modelling me hods. Wi h he s a is ic p og amming sys em STATGRAPHICS Cen u ion XV by using Kolmogo o -Smi no es he Pa e o dis ibu ion in Eu opean o m was es ablished as he bes model o goodness o i and also he pa ame e alues o his dis ibu ion we e es ima ed. Knowing he p obabili y dis ibu ion o he amoun o damages will enable he insu ance company o de e mine he basic p emium and o decide o he op imal ensu ing. Owing o ca as ophic damages o majo acciden s, he concluding pa deals wi h modelling and simula ion o possible ex eme damage. In his pa was used quan ile unc ion o Pa e o dis ibu ion in he Eu opean o m. Simula ion using quan ile unc ion enables es ima ion o in e als o he highes damages. This can be used in deciding abou app op ia e ypes o disp opo ional einsu ance and o insu ance company’s ca as ophic isks managemen . This pape was suppo ed in e ms o he p ojec SGS FES 2014 SGSFES_2014003, en i led “Vědecko- ýzkumné ak i i y Sys émo ém inžený s í a in o ma ice”. Fig. 2: G aphic o m o he ex eme losses simula ion Sou ce: Own calcula ions EM_4_2015.indd 129EM_4_2015.indd 129 1.12.2015 8:44:511.12.2015 8:44:51