ReIns (version 1.0.7)

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)

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.

Value

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

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

# NOT RUN {
# 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]))
# }