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Application and Bootstrapping of the Munich Chain Ladder Method
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2016 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Om Bootstrapping av Munich Chain Ladde (Swedish)
Abstract [en]

Point estimates of the Standard Chain Ladder method (CLM) and of the more complex Munich Chain Ladder method (MCL) are compared to real data on 38 different datasets in order to evaluate if MCL produces better predictions on average with a dataset from an arbitrary insurance portfolio. MCL is also examined to determine if the future paid and incurred claims converge as time progresses. A bootstrap model based on MCL (BMCL) is examined in order to evaluate its possibility to estimate the probability density function (PDF) of future claims and observable claim development results (OCDR). The results show that the paid and incurred predictions by MCL converge. The results also show that when considering all datasets MCL produce on average better estimations than CLM with paid data but no improvement can be seen with incurred data. Further the results show that by considering a subset of datasets which fulfil certain criteria, or by only considering accident years after 1999 the percentage of datasets in which MCL produce superior estimations increases. When examining BMCL one finds that it can produce estimated PDFs of ultimate reserves and OCDRs, however the mean of estimate of ultimate reserves does not converge to the MCL estimates nor do the mean of the OCDRs converge to zero. In order to get the right convergence the estimated OCDR PDFs are centered and the mean of the BMCL estimated ultimate reserve is set to the MCL estimate by multiplication.

Abstract [sv]

Punktskattningar gjorda med Standard Chain Ladder (CLM) och den mer komplexa Munich Chain Ladder-metoden (MCL) jämförs med verklig data för 38 olika dataset för att evaluera om MCL ger bättre prediktioner i genomsnitt än CLM för en godtycklig försäkringsportfölj. MCLs prediktioner undersöks också för att se om de betalda och de kända skadekostnaderna konvergerar. En bootstrapmodell baserad på MCL (BMCL) undersöks för att utvärdera om möjligheterna att estimera täthetsfunktionen (probability density function, PDF) av framtida skadekostnader och av ”observable claim development results (OCDR)”. Resultaten visar att MCLs estimerade betalda och kända skadekostnader konvergerar. Resultaten visar även att när man evaluerar alla dataseten så ger MCL i genomsnitt bättre prediktioner än CLM med betald data, men ingen förbättring kan ses med CLM med känd skadekostnadsdata. Vidare visar resultaten även att genom att bara titta på dataset som uppfyller vissa krav, eller genom att bara använda olycksår efter 1999, så ökar andelen dataset där MCL ger bättre prediktioner än CLM.Vid evaluering av BMCL ser man att den kan producera estimerade PDF:er för ultimo-reserver och OCDR:er, men att medelvärdet av ultimo-reserv prediktionerna från BMCL inte konvergerar mot MCL-prediktionerna och att medelvärdet av OCDR:erna inte konvergerar mot noll. För att få rätt konvergens så centreras OCDR PDF:erna och ultimo-reservernas medelvärden sätts till motsvarande MCL-prediktionens värde genom multiplikation.

Place, publisher, year, edition, pages
2016.
Series
TRITA-MAT-E, 2016:07
Keyword [en]
Munich Chain Ladder (MCL), Bootstrap
Keyword [sv]
Reservsättning, Munich Chain Ladder (MCL), Bootstrap
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-182136OAI: oai:DiVA.org:kth-182136DiVA: diva2:911535
External cooperation
Trygg-Hansa
Subject / course
Mathematical Statistics
Educational program
Master of Science - Applied and Computational Mathematics
Supervisors
Examiners
Available from: 2016-03-13 Created: 2016-02-16 Last updated: 2016-03-13Bibliographically approved

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