破产概率（第2版）

图书标准信息

• 作者 [丹麦]阿斯姆森（Asmussen S.） 著
• 出版社 世界图书出版公司
• 出版时间 2015-01
• 版次 2
• ISBN 9787510084492
• 定价 99.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 602页
• 正文语种 英语

【内容简介】

　　Thisbookisasecondeditionofthebookofthesametitlebythefirstauthorwhichwaspublishedin2000.Thesubjectofruinprobabilitiesandrelatedtop-icshassincethenundergoneaconsiderabledevelopment,nottosayboom.Thismuchexpandedandrevisedsecondeditionaimsatcoveringasubstantialpartofthesedevelopmentsaswellastheclassicaltopics.
　　R,isktheoryingeneralandruinprobabilitiesinparticulararetraditionallyconsideredaspartofinsurancemathematics,andhasbeenanactiveareaofresearchfromthedaysofLundbergallthewayuptotoday.Onereasonforwritingtlusbookisafeelingthattheareahasinrecentyearsachievedacon-siderablemathematicalmaturity,whichhasinparticularremovedoneofthestandardcriticismsofthearea,namelythatitcanonlysaysomethingaboutverysimplemodelsandquestions.Althoughininsurancepractice,usuallysim-pler(andcoarser)riskmeasureslikeValue-at-Riskareused,itiswidelybelievedthatthethinkingadvocatedbyruintheoryisstillimportantformodernriskmanagement.Forinstance,intimesofmarket-consistentvaluationprinciples,theroleofthetimediversificationeffectofinsuranceportfolios,whichisoneofthecoreelementsofruintheory,shouldnotbeforgotten.Inaddition,ruinthe-oryhasfruitfulmethodologicallinksandapplicationstootherfieldsofappliedprobability,likequeueingtheoryandmathematicalfinance(pricingofbarrieroptions,creditproductsetc.).Apartfromtheseremarks,wehavedeliberatelystayedawayfromdiscussingthepracticalrelevanceofthetheory;iftheformu-lationsoccasionallygiveadifferentimpression,itisnotbyintention.Thus,thebookisbasicallymathematicalinitsflavor.

【目录】

Preface
Notationandconventions
ⅠIntroduction
1Theriskprocess
2Claimsizedistributions
3Thearrivalprocess
4Asummaryofmainresultsandmethods

ⅡMartingalesandsimpleruincalculations
1Waldmartingales
2Gambler'sruin.Two-sidedruin.Brownianmotion
3Furthersimplemartingalecalculations
4Moreadvancedmartingales

ⅢFurthergeneraltoolsandresults
1Likelihoodratiosandchangeofmeasure
2Dualitywithotherappliedprobabilitymodels
3Randomwalksindiscreteorcontinuoustime
4Markovadditiveprocesses
5Theladderheightdistribution

ⅣThecompoundPoissonmodel
1Introduction
2ThePollaczeck-Khinchineformula
3SpecialcasesofthePollaczeck-Khinchineformula
4Changeofmeasureviaexponentialfamilies
5Lundbergconjugation
6Furthertopicsrelatedtotheadjustmentcoefficient
7Variousapproximationsfortheruinprobability
8Comparingtherisksofdifferentclaimsizedistributions
9Sensitivityestimates
10Estimationoftheadjustmentcoefficient

ⅤTheprobabilityofruinwithinfinitetime
1Exponentialclaims
2Theruinprobabilitywithnoinitialreserve
3Laplacetransforms
4Whendoesruinoccur？
5Diffusionapproximations
6Correcteddiffusionapproximations
7Howdoesruinoccur？

ⅥRenewalarrivals
1Introduction
2Exponentialclaims.ThecompoundPoissonmodelwithnegativeclaims
3Changeofmeasureviaexponentialfamilies
4Thedualitywithqueueingtheory

ⅦRisktheoryinaMarkovianenvironment
1Modelandexamples
2Theladderheightdistribution
3Changeofmeasureviaexponentialfamilies
4ComparisonswiththecompoundPoissonmodel
5TheMarkovianarrivalprocess
6Risktheoryinaperiodicenvironment
7Dualqueueingmodels

ⅧLevel-dependentriskprocesses
1Introduction
2Themodelwithconstantinterest
3Thelocaladjustmentcoefficient.Logarithmicasymptotics
4Themodelwithtax
5Discrete-timeruinproblemswithstochasticinvestment
6Continuous-timeruinproblemswithstochasticinvestment

ⅨMatrix-analyticmethods
1Definitionandbasicpropertiesofphase-typedistributions
2Renewaltheory
3ThecompoundPoissonmodel
4Therenewalmodel
5Markov-modulatedinput
6Matrix-exponentialdistributions
7Reserve-dependentpremiums
8Erlangizationforthefinitehorizoncase

ⅩRuinprobabilitiesinthepresenceofheavytails
1Subexponentialdistributions
2ThecompoundPoissonmodel
3Therenewalmodel
4Finite-horizonruinprobabilities
5Reserve-dependentpremiums
6Tailestimation

ⅪRuinprobabilitiesforLevyprocesses
1Preliminaries
2One-sidedruintheory
3Thescalefunctionandtwo-sidedruinproblems
4Furthertopics
5Thescalefunctionfortwo-sidedphase-typejumps

ⅫGerber-Shiufunctions
1Introduction
2ThecompoundPoissonmodel
3Therenewalmodel
4Levyriskmodels

ⅩⅢFurthermodelswithdependence
1Largedeviations
2Heavy-tailedriskmodelswithdependentinput
3Linearmodels
4Riskprocesseswithshot-noiseCoxintensities
5Causaldependencymodels
6DependentSparreAndersenmodels
7Gaussianmodels.FractionalBrownianmotion
8Orderingofruinprobabilities
9Multi-dimensionalriskprocesses

ⅩⅣStochasticcontrol
1Introduction
2Stochasticdynamicprogramming
3TheHamilton-Jacobi-Bellmanequation

ⅩⅤSimulationmethodology
1Generalities
2SimulationviathePollaczeck-Khinchineformula
3StaticimportancesamplingviaLundbergconjugation
4Staticimportancesamplingforthefinitehorizoncase
5Dynamicimportancesampling
6Regenerativesimulation
7Sensitivityanalysis

ⅩⅥMiscellaneoustopics
1Moreondiscrete-timeriskmodels
2Thedistributionoftheaggregateclaims
3Principlesforpremiumcalculation
4Reinsurance

Appendix
A1Renewaltheory
A2Wiener-Hopffactorization
A3Matrix-exponentials
A4Somelinearalgebra
A5Complementsonphase-typedistributions
A6Tauberiantheorems
Bibliography
Index