ReIns (version 1.0.10)

VaR: VaR of splicing fit

Description

Compute Value-at-Risk (\(VaR_{1-p}=Q(1-p)\)) of the fitted spliced distribution.

Usage

VaR(p, splicefit)

Value

Vector of quantiles \(VaR_{1-p}=Q(1-p)\).

Arguments

p

The exceedance probability (we estimate \(VaR_{1-p}=Q(1-p)\)).

splicefit

A SpliceFit object, e.g. output from SpliceFitPareto, SpliceFiticPareto or SpliceFitGPD.

Author

Tom Reynkens with R code from Roel Verbelen for the mixed Erlang quantiles.

Details

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

Note that VaR(p, splicefit) corresponds to qSplice(p, splicefit, lower.tail = FALSE).

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

See Also

qSplice, CTE, SpliceFit, SpliceFitPareto, SpliceFiticPareto, SpliceFitGPD

Examples

if (FALSE) {

# Pareto random sample
X <- rpareto(1000, shape = 2)

# Splice ME and Pareto
splicefit <- SpliceFitPareto(X, 0.6)



p <- seq(0,1,0.01)

# Plot of quantiles
plot(p, qSplice(p, splicefit), type="l", xlab="p", ylab="Q(p)")

# Plot of VaR
plot(p, VaR(p, splicefit), type="l", xlab="p", ylab=bquote(VaR[1-p]))
}