# Calculation or Approximation of the Probability of Ruin

### 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

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)
``` |

### Arguments

`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 |

### 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`