ACTSC232 Lecture Notes - Lecture 4: Life Annuity, Equivalence Principle, Term Life Insurance

• School: University of Waterloo
• Department: Actuarial Science
• Course: ACTSC232
• Professor: Diana K Skrzydlo

Document Summary

Summaryoflecturenotes actsc232,winter2010part4 bene tpremiums thelossrandomvariablelforaninsuranceorannuityisde nedasl=thepvofbene ts thepvofpremiums. theexpectationofthelossrandomvariableise[l]=theapvofbene ts theapvofpremiums. equivalenceprinciple(ep):setpremiumssuchthate[l]=0ortheapvofbene ts=theapvofpremiums. percentileprinciple(pp):setpremiumssuchthatpr{l>0}= . notethatweassumetheequivalenceprinciplethroughoutthiscoursesunlessotherwisestated. 4. 1fullycontinuousbene tpremiums inaninsurance,thebene tsoftheinsuranceformacontinuouslifeinsurancewhilethepremiumsoftheinsuranceformacontinuouslifeannuity. (a)afullycontinuouswholelifeinsuranceof1on(x)withanannualpremiumrateof p:l=vtx p atx, p= ax ax= ax1 ax=1 ax ax,var[l]= 1+ p !2var(vt)= 1+ p !2h2 ax ( ax)2i=2 ax ( ax)2( ax)2. (b)afullycontinuoush-paymentwholelifeinsuranceof1on(x)withanannualpre-miumrateof p:l=vtx p atx h, p= ax ax:h. 1 shared via c ourse h ero. co m. T his study resource w as https://www. coursehero. com/file/6180481/part-4-notes-232-2010w/ (c)afullycontinuousn-yearterminsuranceof1on(x)withanannualpremiumrateof p:l= vtx p atx,tx n0 p an,tx>n p= a1x:n ax:n. (d)afullycontinuousn-yearendowmentinsuranceof1on(x)withanannualpremiumrateof p:l=vtx n p atx n, p= ax:n ax:n= ax:n1 ax:n=1 ax:n ax:n,var[l]= 1+ p !2var(vtx n)= 1+ p !2h2 ax:n ( ax:n)2i=2 ax:n ( ax:n)2( ax:n)2. (e)afullycontinuousn-yearpureendowmentof1on(x)withanannualpremiumrateof p:l= 0 p atx,tx nvn p an,tx>n p=a1x:n ax:n=nex ax:n. (f)afullycontinuousn-yeardeferredwholelifeannuityof1on(x)withanannualpremiumrateof p:l= 0 p atx,tx nvn atx n p an,tx>n p=n| ax ax:n=nex ax+n ax:n= ax ax:n ax:n. (g)afullycontinuoush-payment,n-yearendowmentinsuranceof1on(x)(h