An Actuarial Approach for Aggregate Loss Assessment of the Critical Infrastructure Due to Natural Disasters

Transcription

1 0 Intenational Confeence on Education and anagement Innovation IPEDR vol30 (0 (0 IACSIT Pess, Singapoe An Actuaial Appoach fo Aggegate Loss Assessment of the Citical Infastuctue Due to atual Disastes Plamena Zlateva and Dimite Velev + Institute of System Engineeing and Robotics - BAS, Sofia, Bulgaia Univesity of ational and Wold Economy, Sofia, Bulgaia Abstact An actuaial model is poposed that will be used fo aggegate loss assessment of the citical infastuctue elements due to natual disastes fo a given time inteval This actuaial appoach is based on the collective isk model The main components of the collective isk model ae discussed - the numbe of natual disastes (advese events and the negative consequences (seveity of the losses The isk assessment esults can suppot the stakeholdes to take moe infomed decisions egading the efficient allocation of the available funding fo the impovement of the citical infastuctue potection fom natual disastes Guidelines fo implementing the collective isk model as a pat of a Web Integated Infomation System fo isk management of natual disastes using by Cloud Computing technology ae outlined Keywods: collective isk model, aggegate loss, natual disaste, cloud computing, citical infastuctue Intoduction owadays the negative impact of natual disastes on sustainable development of the citical infastuctue inceases In this context it should be noted that the citical infastuctue geneally includes all systems and assets, both physical and vitual, which make vital contibutions to national secuity, economic stability, public health, o safety Scientific eseach and statistic data show a gowth in numbe and seveity of natual disastes compaed to pevious yeas [] Billions of dollas cost annual losses esulting fom floods, huicanes, eathquakes, tonadoes, etc atual disastes ae impossible to avoid, and citical infastuctue elements cannot be made totally invulneable The only viable solution is to pepae cities, towns and communities though a combination of mitigation and adaptation stategies [, 3] Theefoe it is necessay to develop long-tem loss-eduction stategies and disaste pepaedness which could impove the citical infastuctue esilience with espect to of natual disastes, esulting in less popety damage and educed ebuilding costs Hence thee is a need to popose integated appoaches to assess the possible aggegate loss fo each citical element of infastuctue at occuence of advese events The availability of an adequate assessment of the potential total loss would help taking moe infomed decisions fo effective use of limited financial esouces to activities in emegency situations On the othe hand is well known that the so-called collective isk model is a fundamental model fo insuance isk assessment The collective isk model teats the aggegate loss (total claims as a compound distibution with two main components One is the claim fequency, ie the numbe of claims (accidences, advese events that which may be occu ove a cetain peiod This is a discete andom vaiable taking nonnegative intege values The second component descibes the seveity (size, amount of the claim o the loss esulting fom the occuence of an advese event The stochastic natue of both components is a + Coesponding autho Tel: ; fax: addess: dvelev@unweacadbg 34

2 fundamental assumption of a ealistic isk model [4, 5, 6] The collective isk model is often used fo modeling othe noninsuance poduct isks, such as cedit and opeational isk [7] The pupose of the pape is to popose an actuaial appoach to assess the possible aggegate loss due to natual disastes fo each element of citical infastuctue This actuaial appoach is based on the collective isk model In paticula, the main components of the collective isk model ae the numbe of natual disastes (advese events and the negative consequences (seveity of the losses The poposed collective isk model is envisaged to be implemented as a pat of a Web Integated Infomation System fo isk management of natual disastes using the Cloud Computing technology Collective Risk odel Essentials The collective isk model computes the aggegate loss as an independent sum of all losses (negative consequences fom all occued natual disastes incued ove a cetain peiod: S whee S is the aggegate loss; - the numbe ( fequency of losses; i - the seveity of the i-th loss, fo i,, It is assumed that the loss seveities i, i,, ae independently and identically distibuted (iid as the loss seveity andom vaiable The loss-fequency is itself a nonnegative intege-valued andom vaiable distibuted independently of i, i,, The aggegate loss S is assumed to follow a nonnegative compound distibution The loss-fequency andom vaiable epesents the pimay distibution and the loss-seveity andom vaiable is seconday distibution of the compound distibution Futhemoe, and ae assumed to be independent Thee ae some advantages in modeling loss-fequency and loss-seveity sepaately, and then combining them to detemine the aggegate-loss distibution In this study pimay and seconday distibutions ae detemined by non-negative discete andom vaiables In pactice fo the computation of the aggegate-loss distibution ae used both ecusive and appoximate methods The main popeties of compound distibutions ae descibed below [6] The moment geneating function (mgf of the andom vaiable as a function of t is denoted by (t If the expectation exists then it is defined as follow t ( e ( t E If the (t exists fo t in an open inteval aound t 0, then the moments of exist and can be obtained by successively diffeentiating the (t with espect to t and evaluating the esult at t 0 The -th deivative of the (t is descibed by the following dependence: d ( t d t d t t E( e E ( e E( e ( t dt dt dt Theefoe, at the point t 0 fo the -th deivative of the (t is obtained ' E( μ ( 0, whee by definition -th initial moment of the andom vaiable in the geneal case is given by the fomula E ' ( x f ( x μ i i i i, 34

3 The pobability geneating function (pgf of the nonnegative andom vaiable is denoted by P ( t If the expectation exists then it is defined as follow ( t P ( t E It is known that the mgf (t and pgf P ( t ae elated though the following equations t ( e ( t P The moment geneating function (mgf of the aggegate loss S as a function of t is denoted by S (t If the pimay distibution has mgf (t and the seconday distibution has mgf (t, then the mgf of the compound distibution S is deduce as follow ( ( ts t S (t ( ( t t t e e E E E e t + t + + t ( ( t e E E E ( E( e ( ( ln (t E ( (t E e ( log ( t If has pgf P ( t and is nonnegative intege valued with pgf P ( t, then the pgf of S is ( S PS ( t E( t E( t E E( t E ( E( t E( P ( t P ( P ( t Futhemoe, the aggegate loss S is nonnegative and discete, because the loss-seveities take nonnegative discete values The mean of the aggegate loss S is given by ( ( ( E S E( S E E + + E E( E ( E( ( μ μ E( μ μ ( E( E( E( E E E E The vaiance of the andom vaiables S is defined using the condition of independence between andom vaiables and, and the following elations: D ( S E( S ( ES and ( S E( E( S E, ( E E D ( D and, D ( S E( S ( E( S and E( S D( S + E( S Thus the vaiance of the aggegate loss S is is deduce as follow ( ( S D ( S E( S ( ES E E( S E ( ( ( E S E D( S + ( E( S 343

4 ( ( E( D( S + E ( E( S ( E( E S E ( D( S + D( E( S ( D( D( E( + E + ( D( D( E( E + E( σ + D( μ E( μ D( σ + μ σ + σ μ μ D + μ D The collective isk model is descibed only theoetically Futhe eseach is needed paticulaly egading its implementation fo aggegate loss assessment of the citical infastuctue elements due to natual disastes fo a given time inteval 3 Guidelines fo Implementing the Collective Risk odel by Cloud Computing Cloud computing is an on-demand sevice model fo IT povision based on vitualization and distibuted computing technologies Cloud computing is a model fo enabling ubiquitous, convenient, on-demand netwok access to a shaed pool of configuable computing esouces (eg, netwoks, seves, stoage, applications, and sevices that can be apidly povisioned and eleased with minimal management effot o sevice povide inteaction This cloud model is composed of five essential chaacteistics, thee sevice models, and fou deployment models [8] Cloud Computing is implemented though thee sevice models that have matued fom a boade set of elated technologies - Softwae as a sevice (SaaS, Platfom as a sevice (PaaS and Infastuctue as sevice (IaaS SaaS is a softwae application delivey model whee the esponsibility fo softwae delivey and application management lies within a cetain sevice povide In this sevice oiented model a softwae company develops a web-native softwae application fo use by clients which is hosted and opeated independently o though a thid-paty vendo ove Intenet Clients do not own the softwae itself but pay fo it on the basis of its actual usage The sevice is used though an Application Pogamming Inteface (API which is Web accessible and the code is implemented by using Web Sevices The main advantage of the SaaS model is the IT opeational cost eduction, especially small to mediumsized businesses whee high investment costs could be saved in the aeas of IT implementation and infastuctue maintenance A key featue of cloud computing is that infomation of the uses is stoed in multiple, geogaphically dispesed data centes that povide extensive backup, data achive and failove capabilities This includes a multi-level backup stategy of disk-to-disk-to-tape data backups which ensue maximum ecovey speed with minimum potential fo data loss ajo supplies of cloud computing infastuctue such as Salesfocecom povide vey high levels of sevice availability though vitualized seves at multiple data centes Uses of web-based sevices have both thei data and seve availability potected in the event of a natual disaste The data involved in emegency management includes geogaphical data about the infected aea, data about sheltes and available tanspotation means, data about victims and elief pesonnel, available escuing esouces, and measuements fom the field The data may belong to multiple autonomous oganizations, such as govenment oganizations, non-govenmental oganizations, intenational non-govenmental oganizations, individuals, communities, and industies Theefoe, besides integating and manage data fom these diffeent oganizations, thee is a need to coodinate these oganizations by enabling efficient communication and collaboation Risk assessment as a sevice is a new paadigm fo measuing isk as an autonomic method that follows the on-demand, automated, multi-tenant achitectue of the cloud a way to get a continuous isk scoe of the cloud envionment with espect to a given tenant, a specific application o moe geneally, fo use by new tenants and applications Risk assessment povides a significant value in inceasing tust in a commecial 344

5 sevice, and thus appea paticulaly beneficial to the adoption of cloud computing Taditional assessments developed fo conventional IT envionments do not eadily fit the dynamic natue of the cloud [9] The following issues must be esolved in ode to implement the poposed collective isk model as a SaaS application: ulti-tenancy - designing the application in such a way that it suppots a huge numbe of potential uses simultaneously Secuity - custome data must be secue and completely sepaated fom othe use s data Scalability - the application should opeate with many individual uses Availability - the application must be always online Pefomance the application should povide fo smallest pocessing times Customizable GUI the application should allow the customization the GUI Customizable Business Logic the application should povide the addition of the business logic fom diffeent uses Wokflow - customes should be allowed to add thei own wokflows to the application Implementing the poposed collective isk model as a SaaS application is to make what is sometimes a complex pocess simple, changing the dynamics of how softwae is puchased, consumed and maintained, and is quickly becoming an effective IT delivey option 4 Conclusions The collective isk model essentials ae pesented This actuaial model is poposed to be used fo aggegate loss assessment of the citical infastuctue elements due to natual disastes fo a given time inteval Guidelines fo implementing the collective isk model by Cloud Computing technology ae outlined The isk assessment esults can suppot the stakeholdes to take moe infomed decisions egading the efficient allocation of the available funding fo the impovement of the citical infastuctue potection fom natual disastes 5 Acknowledgment The autho expesses his gatitude to the Science Fund of the Univesity of ational and Wold Economy, Sofia, Bulgaia fo financial suppot unde the Gant I -8/0, titled "ethodology fo the Implementation of Web-based Integated Infomation System fo Risk Assessment Due to atual Hazads" 6 Refeences [] J Pollne, J Kyspin-Watson, S ieuwejaa Disaste Risk anagement and Climate Change Adaptation in Euope and Cental Asia Global Facility fo Disaste Reduction and Recovey: The Wold Bank, 00 [] J Padli, Habibullah, A Bahaom Economic impact of natual disastes' fatalities, Intenational Jounal of Social Economics, 00, 37 (6: [3] Pevention Web - Stengthening climate change adaptation though effective disaste isk eduction, [4] R Kaas, Goovaets, J Dhaene, Denuit oden ActuaialRisk Theoy: Using R, Spinge, 008 [5] S Klugman, H Panje, G Willmot Loss odels: Fom Data to Decisions (3d ed, Wiley, ew Yok, 008 [6] Y-K Tse onlife Actuaial odels: Theoy, ethods and Evaluation, Cambidge Univesity Pess, Cambidge, 009 [7] A Chenobai, S Rachev, F Fabozzi Opeational Risk: A Guide to Basel II Capital Requiements, odels, and Analysis, Wiley, ew Yok, 007 [8] The IST Definition of Cloud Computing, [9] B Kaliski, W Pauley Towad Risk Assessment as a Sevice in Cloud Envionments, 00, 345