Calculation or Approximation of the Probability of Ruin

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Description

This functions provide various approximation methods for the (total) probability of ruin, the probability of ruin due to oscillation and the probability of ruin due to a claim. Exact calculations are possible in the case of hypo-exponentially distrubuted claim amounts.

Usage

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ruinprob(process, method = c("saddlepoint", "fft", "bounds", "hypoexp", "lundberg"), ...)
boundsRuinprob(process, interval, maxreserve, richardson = TRUE, use.splines = FALSE)
fftRuinprob(process, interval, maxreserve, n, use.splines = FALSE)
hypoexpRuinprob(process)
saddlepointRuinprob(process, jensen = FALSE, normalize = TRUE)

Arguments

process

a "riskproc" object.

method

character string indicating the method used for approximation or calculation.

interval

interval width for the discretization of the claim distribution.

maxreserve

maximal value of the initial reserve for which the approximation can be calculated.

n

Length of the probability vectors resulting from the discretization.

richardson

logical; if TRUE, Richardson extrapolation is used for the approximation of the probability of ruin due to oscillation.

use.splines

logical; if TRUE, a cubic spline interpolation is used instead of step functions.

jensen

logical; if TRUE, the formulae of Jensen (1992) are used instead of the ones by Lugannani and Rice (1980) and Daniels (1954) (see references).

normalize

logical; if TRUE, the saddlepoint approximations based on densities are re-normalized such that those densities integrate to 1.

...

further arguments that are passed on to boundsRuinprob, fftRuinprob, hypoexpRuinprob or saddlepointRuinprob, depending on the value of method.

Details

ruinprob is a wrapper function for the other ones given here.

Value

psi

the total probability of ruin (as a function of the initial reserve).

psi.1

the probability of ruin due to oscillation (as a function of the initial reserve).

psi.2

the probability of ruin due to a claim (as a function of the initial reserve).

...

References

Daniels, H. E. (1954) Saddlepoint Approximations in Statistics. Annals of Mathematical Statistics 25(4), pp. 631–650.

Gatto, R. and Mosimann, M. (2012) Four Approaches to Compute the Probability of Ruin in the Compound Poisson Risk Process with Diffusion. Mathematical and Computer Modelling 55(3–4), pp. 1169–1185

Jensen, J. L. (1992) The Modified Signed Likelihood Statistic and Saddlepoint Approximations. Biometrika 79(4), pp. 693–703.

Lugannani, R. and Rice, S. (1980) Saddle Point Approximation for the Distribution of the Sum of Independent Random Variables. Advances in Applied Probability 12(2), pp. 475–490.

See Also

riskproc, claiminfo