Estimates for excess-loss premiums using splicing
Estimate premiums of excess-loss reinsurance with retention R and limit L using fitted spliced distribution.
ExcessSplice(R, L=Inf, splicefit)
R |
The retention level of the (re-)insurance or a vector of retention levels for the (re-)insurance. |
L |
The limit for the (re-)insurance or a vector of limits for the (re-)insurance, default is |
splicefit |
A |
The premium for the excess-loss insurance with retention R and limit L is given by
E(\min{(X-R)_+, L}) = Π(R) - Π(R+L)
where Π(u)=E((X-u)_+)=\int_u^{∞} (1-F(z)) dz is the premium of the excess-loss insurance with retention u. When L=∞, the premium is equal to Π(R).
See Reynkens et al. (2017) and Section 4.6 of Albrecher et al. (2017) for more details.
An estimate for the premium is returned (for every value of R).
Tom Reynkens with R code from Roel Verbelen for the estimates for the excess-loss premiums using the mixed Erlang distribution.
Albrecher, H., Beirlant, J. and Teugels, J. (2017). Reinsurance: Actuarial and Statistical Aspects, Wiley, Chichester.
Reynkens, T., Verbelen, R., Beirlant, J. and Antonio, K. (2017). "Modelling Censored Losses Using Splicing: a Global Fit Strategy With Mixed Erlang and Extreme Value Distributions". Insurance: Mathematics and Economics, 77, 65–77.
Verbelen, R., Gong, L., Antonio, K., Badescu, A. and Lin, S. (2015). "Fitting Mixtures of Erlangs to Censored and Truncated Data Using the EM Algorithm." Astin Bulletin, 45, 729–758
## Not run: # Pareto random sample X <- rpareto(1000, shape = 2) # Splice ME and Pareto splicefit <- SpliceFitPareto(X, 0.8) # Excess-loss premium ExcessSplice(R=2, splicefit=splicefit) ## End(Not run)
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