Example, Page 11, Chapter 8 - Ruin Theory

Discussion in 'CT6' started by Jooser, Jul 15, 2008.

  1. Jooser

    Jooser Member

    Hi

    I'd like to check my understanding please, with regard to the calculation of var[S(2)] halfway down the solution.

    At first, I was expecting = 60 . exp{6+1.1} . (exp{1.1} - 1)
    i.e. from the variance of the lognormal distribution.

    But is the answer correct because this is a compound Poisson distribution, so that var = lambda.m2 (i.e Poisson parameter multiplied by the second moment of the lognormal distribution (E[X^2], not var[X]))?

    Thanks

    Jooser
     
  2. John Lee

    John Lee ActEd Tutor Staff Member



    Yes.

    If it were not a compound Poisson we would have to use:

    var(S) = E(N)var(X) + E²(X)var(N)
     
  3. Jooser

    Jooser Member

    Thanks John.
     

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