Transcription of Actuarial Mathematics and Life-Table Statistics
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ActuarialMathematicsand life -TableStatisticsEricV. SludMathematicsDepartmentUniversity of Maryland,CollegeParkc 2001c 2001 EricV. SludStatisticsProgramMathematicsDepartme ntUniversity of MarylandCollegePark, .. vi1 Basicsof Probability & .. Interest.. Streams.. Set 1.. Examples.. 212 Interest& Forceof Theoryof Interest.. ActuarialNotation.. MortgageRe nancing.. MortgageRe nancing.. & Zero-coupon Bonds.. Mortality & AnalyticalModels.. Forcesof Mortality .. Set 2.. Examples.. 583 Probability & life Mortality .. IntegerAges.. of LargeNumbers .. ,Bounds& Approximations.. life TableData.. DiscreteRandomVariables.. ManipulatingExpectations.. Set 3.. Examples.. 934 ExpectedPresent Valuesof Values.. of Insurance& life Annuity Contracts.. SinglePremiums.. Net SinglePremiums.. Valuesform= 1 .. ResidualLife.. life Expectancies.. Set 4.. Examples.. 1215 Net SinglePremiums.
are just the relative frequency in the life table with which those payments are received. More generally, if the restriction that g(t) depends only on theintegerpart [t] of t weredropped, thentheexpectationof Y =g(T) wouldbegivenbythesameformula E(Y)=E(g(T))= Z1 0 f(t)g(t)dt The last displayed integral, like all expectation formulas, can be under-1
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