### Abstract

In the classic model of collective risk theory, let the function G(u, y) be the probability that ruin occurs from initial reserve level u, and that the deficit at the time of ruin is less than y. In two recent papers [Gerber (1987), Dufresne and Gerber (1988)] explicit solutions for G(u, y) have been found when the claim amount distribution is a combination of exponential or gamma distributions. In this paper we consider an alternative approach to the problem of calculating G(u, y) by deriving an equation which can be used to calculate approximate values of G(u, y) by a recursive method. © 1989.

Original language | English |
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Pages (from-to) | 145-148 |

Number of pages | 4 |

Journal | Insurance: Mathematics and Economics |

Volume | 8 |

Issue number | 2 |

Publication status | Published - Jun 1989 |

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### Keywords

- Probability of ruin
- Severity of ruin

### Cite this

*Insurance: Mathematics and Economics*,

*8*(2), 145-148.

}

*Insurance: Mathematics and Economics*, vol. 8, no. 2, pp. 145-148.

**Recursive calculation of the probability and severity of ruin.** / Dickson, D. C M.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Recursive calculation of the probability and severity of ruin

AU - Dickson, D. C M

PY - 1989/6

Y1 - 1989/6

N2 - In the classic model of collective risk theory, let the function G(u, y) be the probability that ruin occurs from initial reserve level u, and that the deficit at the time of ruin is less than y. In two recent papers [Gerber (1987), Dufresne and Gerber (1988)] explicit solutions for G(u, y) have been found when the claim amount distribution is a combination of exponential or gamma distributions. In this paper we consider an alternative approach to the problem of calculating G(u, y) by deriving an equation which can be used to calculate approximate values of G(u, y) by a recursive method. © 1989.

AB - In the classic model of collective risk theory, let the function G(u, y) be the probability that ruin occurs from initial reserve level u, and that the deficit at the time of ruin is less than y. In two recent papers [Gerber (1987), Dufresne and Gerber (1988)] explicit solutions for G(u, y) have been found when the claim amount distribution is a combination of exponential or gamma distributions. In this paper we consider an alternative approach to the problem of calculating G(u, y) by deriving an equation which can be used to calculate approximate values of G(u, y) by a recursive method. © 1989.

KW - Probability of ruin

KW - Severity of ruin

UR - http://www.scopus.com/inward/record.url?scp=0011473033&partnerID=8YFLogxK

M3 - Article

VL - 8

SP - 145

EP - 148

JO - Insurance: Mathematics and Economics

JF - Insurance: Mathematics and Economics

SN - 0167-6687

IS - 2

ER -