the expected present value

Discussion in 'CT5' started by saksham, Jun 22, 2017.

  1. saksham

    saksham Member

    In the attached photo I am not able to understand how n|qx and p[Kx=k] has those expressions.please help asap.
    P.s I haven't done ct4
     

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  2. shdh

    shdh Ton up Member

    n|qx is the deferred probability that a person now aged x lives for another n years, so npx and then dies within age x+n and x+n+1, so qx+n.

    qx+n can also be written as 1qx+n, that is he who is aged x+n dies between the period n and n+1.

    P(Kx=k) is the probability that a person now aged x will survive for the next k years and die within the next moment or instant.

    So P(Kx=k) is equal to kpx*qx+k, that is the probability that a person now aged x lives for another k years (kpx) and then dies within the next moment (1qx+k or simply qx+k).

    Hope this helps.

    Regards.
    Shyam
     
  3. Actually P(Kx=k) means the probability that the person dies anywhere in the year between time k and time k+1, not at the "moment". Notice that qx+k is also the probability of dying between x+k and x+k+1.

    I think Shyam may be thinking of the PDF of Tx, which would be kpx*mu(x+k). (mu relates to the moment of death, q relates to death over a whole year of age.)
    Best wishes
    Robert
     
    shdh likes this.
  4. saksham

    saksham Member

    Th
    Thankyou :)
     

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