morden actuarial risk theory

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1、ContentsForewordvPrefacevii1Utilitytheoryandinsurance11.1Introduction11.2Theexpectedutilitymodel21.3Classesofutilityfunctions71.4Optimalityofstop-lossreinsurance101.5Exercises152Theindividualriskmodel192.1Introduction192.2Mixeddistributionsandrisks202

2、.3Convolution282.4Transformations312.5Approximations34xvxviCONTENTS2.6Application:optimalreinsurance392.7Exercises403Collectiveriskmodels453.1Introduction453.2Compounddistributions463.3Distributionsforthenumberofclaims503.4CompoundPoissondistributions

3、523.5Panjer’srecursion543.6Approximationsforcompounddistributions593.7Individualandcollectiveriskmodel603.8Someparametricclaimsizedistributions633.9Stop-lossinsuranceandapproximations673.10Stop-losspremiumsincaseofunequalvariances713.11Exercises754Rui

4、ntheory814.1Introduction814.2Theriskprocess834.3Exponentialupperbound854.4Ruinprobabilityandexponentialclaims884.5Discretetimemodel914.6Reinsuranceandruinprobabilities924.7Beekman’sconvolutionformula954.8Explicitexpressionsforruinprobabilities1004.9Ap

5、proximationofruinprobabilities1034.10Exercises1065Premiumprinciples1115.1Introduction1115.2Premiumcalculationfromtop-down1125.3Variouspremiumprinciples1155.4Propertiesofpremiumprinciples117CONTENTSxvii5.5Characterizationsofpremiumprinciples1205.6Premi

6、umreductionbycoinsurance1235.7Exercises1256Bonus-malussystems1276.1Introduction1276.2Anexampleofabonus-malussystem1286.3Markovanalysis1316.4Exercises1377Credibilitytheory1397.1Introduction1397.2ThebalancedBühlmannmodel1417.3Moregeneralcredibilitymodel

7、s1497.4TheBühlmann-Straubmodel1537.5Negativebinomialmodelforthenumberofcarinsuranceclaims1607.6Exercises1668Generalizedlinearmodels1698.1Introduction1698.2GeneralizedLinearModels1718.3SometraditionalestimationproceduresandGLM’s1748.4Devianceandscaledd

8、eviance1828.5Example:analysisofacontingencytable1868.6ThestochasticcomponentofGLM’s1908.7Exercises2009IBNRtechniques2039.1Introduction2039.2AGLMthatencompassesvariousIBNRmethods2079.3IllustrationofsomeIBNRmethods2139.4Exercises220xviiiCONTENTS