Description Usage Arguments Details Value References See Also

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.

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.

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