ExcessSplice function

Estimates for excess-loss premiums using splicing

Estimates for excess-loss premiums using splicing

Estimate premiums of excess-loss reinsurance with retention RR and limit LL using fitted spliced distribution.

ExcessSplice(R, L=Inf, splicefit)

Arguments

  • 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 Inf.
  • splicefit: A SpliceFit object, e.g. output from SpliceFitPareto, SpliceFiticPareto or SpliceFitGPD.

Details

The premium for the excess-loss insurance with retention RR and limit LL is given by

E(min(XR)+,L)=Π(R)Π(R+L) E(\min{(X-R)_+, L}) = \Pi(R) - \Pi(R+L)

where Π(u)=E((Xu)+)=u(1F(z))dz\Pi(u)=E((X-u)_+)=\int_u^{\infty} (1-F(z)) dz is the premium of the excess-loss insurance with retention uu. When L=L=\infty, the premium is equal to Π(R)\Pi(R).

See Reynkens et al. (2017) and Section 4.6 of Albrecher et al. (2017) for more details.

Returns

An estimate for the premium is returned (for every value of R).

References

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

Author(s)

Tom Reynkens with R code from Roel Verbelen for the estimates for the excess-loss premiums using the mixed Erlang distribution.

See Also

SpliceFit, SpliceFitPareto, SpliceFiticPareto, SpliceFitGPD

Examples

## 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)
  • Maintainer: Tom Reynkens
  • License: GPL (>= 2)
  • Last published: 2024-12-02