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 hypoexponentially distrubuted claim amounts.
1 2 3 4 5  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)

process 
a 
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 
use.splines 
logical; if 
jensen 
logical; if 
normalize 
logical; if 
... 
further arguments that are passed on to 
ruinprob
is a wrapper function for the other ones given here.
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). 
... 
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.
riskproc
, claiminfo
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