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Non-Life Insurance Pricing Using the Generalized Additive Model, Smoothing Splines and L-Curves
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2015 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Prissättning inom sakförsäkring med generaliserade additativa modeller, smoothing splines och L-kurvor (Swedish)
##### Abstract [en]

In non-life insurance, almost every tariff analysis involves continuous rating variables, such as the age of the policyholder or the weight of the insured vehicle. In the generalized linear model, continuous rating variables are categorized into intervals and all values within an interval are treated as identical. By using the generalized additive model, the categorization part of the generalized linear model can be avoided. This thesis will treat different methods for finding the optimal smoothing parameter within the generalized additive model. While the method of cross validation is commonly used for this purpose, a more uncommon method, the L-curve method, is investigated for its performance in comparison to the method of cross validation. Numerical computations on test data show that the L-curve method is significantly faster than the method of cross validation, but suffers from heavy under-smoothing and is thus not a suitable method for estimating the optimal smoothing parameter.

##### Abstract [sv]

Nästan alla tariffanalyser inom sakförsäkring inkluderar kontinuerliga premieargument, såsom försäkringstagarens ålder eller vikten på det försäkrade fordonet. I den generaliserade linjära modellen så grupperas kontinuerliga premiearguments möjliga värden i intervaller och alla värden inom ett intervall behandlas som identiska. Genom att använda den generaliserade additativa modellen så slipper man arbetet med att dela in kontinuerliga premiearguments möjliga värden i intervaller. Detta examensarbete kommer att behandla olika metoder för att uppskatta den optimala smoothing-parametern inom den generaliserade additativa modellen. Metoden för korsvalidering används vanligen för detta ändamål. L-kurve-metoden, som är en mer ovanlig metod, undersöks för dess prestanda i jämförelse med metoden för korsvalidering. Numeriska beräkningar på testdata visar att L-kurve-metoden är betydligt snabbare än metoden för korsvalidering, men att den underutjämnar och därför inte är en lämplig metod för att uppskatta den optimala smoothing-parametern.

2015.
##### Series
TRITA-MAT-E ; 2015:27
##### National Category
Mathematical Analysis
##### Identifiers
OAI: oai:DiVA.org:kth-168389DiVA, id: diva2:818695
##### Subject / course
Mathematical Statistics
##### Educational program
Master of Science in Engineering -Engineering Physics
##### Examiners
Available from: 2015-06-09 Created: 2015-06-02 Last updated: 2015-06-09Bibliographically approved

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File name FULLTEXT01.pdfFile size 807 kBChecksum SHA-512
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##### By organisation
Mathematics (Div.)
##### On the subject
Mathematical Analysis

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Cite
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