Description Usage Arguments Value References Examples
Function to calculate the total losses via the Panjer recursion.
1 |
ELT |
Data frame containing two numeric columns. The column |
s |
Scalar or numeric vector containing the total losses of interest. |
t |
Scalar representing the time period of interest. The default value is |
theta |
Scalar containing information about the variance of the Gamma distribution: sd[X] = x * |
cap |
Scalar representing the financial cap on losses for a single event, i.e. the maximum possible loss caused by a single event. The default value is |
nq |
Scalar, number of quantiles added when |
verbose |
A logical, if |
A numeric matrix containing the pre-specified losses s
in the first column and the exceedance probabilities in the second column.
Panjer, H.H. (1980), ‘The aggregate claims distribution and stop-loss reinsurance,’ Transactions of the Society of Actuaries, 32, 523-545.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | data(UShurricane)
# Compress the table to millions of dollars
USh.m <- compressELT(ELT(UShurricane), digits = -6)
EPC.Panjer <- fPanjer(USh.m, s = 1:40, verbose = TRUE)
EPC.Panjer
plot(EPC.Panjer, type = "l", ylim = c(0,1))
# Assuming the losses follow a Gamma with E[X] = x, and Var[X] = 2 * x and cap = 5m
EPC.Panjer.Gamma <- fPanjer(USh.m, s = 1:40, theta = 2, cap = 5, verbose = TRUE)
EPC.Panjer.Gamma
plot(EPC.Panjer.Gamma, type = "l", ylim = c(0,1))
# Compare the two results:
plot(EPC.Panjer, type = "l", main = 'Exceedance Probability Curve',
ylim = c(0, 1))
lines(EPC.Panjer.Gamma, col = 2, lty = 2)
legend("topright", c("Dirac Delta", expression(paste("Gamma(",
alpha[i] == 1 / theta^2, ", ", beta[i] ==1 / (x[i] * theta^2), ")", " cap =", 5))),
lwd = 2, lty = 1:2, col = 1:2)
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