ExcessPareto {ReIns} | R Documentation |
Estimates for excess-loss premiums using a Pareto model
Description
Estimate premiums of excess-loss reinsurance with retention and limit
using a (truncated) Pareto model.
Usage
ExcessPareto(data, gamma, R, L = Inf, endpoint = Inf, warnings = TRUE, plot = TRUE,
add = FALSE, main = "Estimates for premium of excess-loss insurance", ...)
ExcessHill(data, gamma, R, L = Inf, endpoint = Inf, warnings = TRUE, plot = TRUE,
add = FALSE, main = "Estimates for premium of excess-loss insurance", ...)
Arguments
data |
Vector of |
gamma |
Vector of |
R |
The retention level of the (re-)insurance. |
L |
The limit of the (re-)insurance, default is |
endpoint |
Endpoint for the truncated Pareto distribution. When |
warnings |
Logical indicating if warnings are displayed, default is |
plot |
Logical indicating if the estimates should be plotted as a function of |
add |
Logical indicating if the estimates should be added to an existing plot, default is |
main |
Title for the plot, default is |
... |
Additional arguments for the |
Details
We need that , the
-th largest observation.
If this is not the case, we return
NA
for the premium. A warning will be issued in
that case if warnings=TRUE
. One should then use global fits: ExcessSplice
.
The premium for the excess-loss insurance with retention and limit
is given by
where is the premium of the excess-loss insurance with retention
. When
, the premium is equal to
.
We estimate (for the untruncated Pareto distribution) by
with the Hill estimator.
The ExcessHill
function is the same function but with a different name for compatibility with old versions of the package.
See Section 4.6 of Albrecher et al. (2017) for more details.
Value
A list with following components:
k |
Vector of the values of the tail parameter |
premium |
The corresponding estimates for the premium. |
R |
The retention level of the (re-)insurance. |
L |
The limit of the (re-)insurance. |
Author(s)
Tom Reynkens
References
Albrecher, H., Beirlant, J. and Teugels, J. (2017). Reinsurance: Actuarial and Statistical Aspects, Wiley, Chichester.
See Also
Hill
, ExcessEPD
, ExcessGPD
, ExcessSplice
Examples
data(secura)
# Hill estimator
H <- Hill(secura$size)
# Premium of excess-loss insurance with retention R
R <- 10^7
ExcessPareto(secura$size, H$gamma, R=R)