12. In a Poisson surplus process for aggregate claims, initial reserves are U = 500, the annual claim rate is λ = 40 and the typical claim X is exponential with mean 100. A premium loading of 0 = 0.3 is used on policyholders. (a) Determine the mean and variance of U(2), the net value of the process after two years. (b) What is the adjustment coefficient for the process described above, and what is the probability of ruin for this process? How does this compare with the Lundberg bound for the probability of ruin? (c) Proportional reinsurance is available whereby a proportion a of each claim is retained by the insurer (and the reinsurer handles the remaining proportion 1 - a). The reinsurance loading is = 0.4. Show that the adjustment coefficient for the process with this type of reinsurance as a function of a is given by R(a) = 1 [ 4a - 1 100 a(14a 1). - What is the maximum value of R(a), and for what values of a is R(a) ≥ R(1)?
12. In a Poisson surplus process for aggregate claims, initial reserves are U = 500, the annual claim rate is λ = 40 and the typical claim X is exponential with mean 100. A premium loading of 0 = 0.3 is used on policyholders. (a) Determine the mean and variance of U(2), the net value of the process after two years. (b) What is the adjustment coefficient for the process described above, and what is the probability of ruin for this process? How does this compare with the Lundberg bound for the probability of ruin? (c) Proportional reinsurance is available whereby a proportion a of each claim is retained by the insurer (and the reinsurer handles the remaining proportion 1 - a). The reinsurance loading is = 0.4. Show that the adjustment coefficient for the process with this type of reinsurance as a function of a is given by R(a) = 1 [ 4a - 1 100 a(14a 1). - What is the maximum value of R(a), and for what values of a is R(a) ≥ R(1)?
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Transcribed Image Text:12. In a Poisson surplus process for aggregate claims, initial reserves are
U = 500, the annual claim rate is λ = 40 and the typical claim X is
exponential with mean 100. A premium loading of 0 = 0.3 is used on
policyholders.
(a) Determine the mean and variance of U(2), the net value of the
process after two years.
(b) What is the adjustment coefficient for the process described above,
and what is the probability of ruin for this process? How does this
compare with the Lundberg bound for the probability of ruin?
(c) Proportional reinsurance is available whereby a proportion a of
each claim is retained by the insurer (and the reinsurer handles the
remaining proportion 1 - a). The reinsurance loading is = 0.4.
Show that the adjustment coefficient for the process with this type
of reinsurance as a function of a is given by
R(a)
=
1
[
4a
-
1
100 a(14a 1).
-
What is the maximum value of R(a), and for what values of a is
R(a) ≥ R(1)?
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