The first exit time and ruin time for a risk process with reserve-dependent income

Sung Nok Chiu; Chuan Cun Yin

doi:10.1016/S0167-7152(02)00311-5

The first exit time and ruin time for a risk process with reserve-dependent income

Sung Nok Chiu^*
, Chuan Cun Yin

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

5 Citations (Scopus)

27 Downloads (Pure)

Abstract

This paper investigates the first exit time and the ruin time of a risk reserve process with reserve-dependent income under the assumption that the claims arrive as a Poisson process. We show that the Laplace transform of the distribution of the first exit time from an interval satisfies an integro-differential equation. The exact solution for the classical model and for the Embrechts-Schmidli model are derived.

Original language	English
Pages (from-to)	417-424
Number of pages	8
Journal	Statistics and Probability Letters
Volume	60
Issue number	4
Early online date	17 Oct 2002
DOIs	https://doi.org/10.1016/S0167-7152(02)00311-5
Publication status	Published - Dec 2002

User-Defined Keywords

First exit time
Ruin time
Ruin probability
Risk reserve process
Embrechts–Schmidli model

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10.1016/S0167-7152(02)00311-5

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title = "The first exit time and ruin time for a risk process with reserve-dependent income",

abstract = "This paper investigates the first exit time and the ruin time of a risk reserve process with reserve-dependent income under the assumption that the claims arrive as a Poisson process. We show that the Laplace transform of the distribution of the first exit time from an interval satisfies an integro-differential equation. The exact solution for the classical model and for the Embrechts-Schmidli model are derived.",

keywords = "First exit time, Ruin time, Ruin probability, Risk reserve process, Embrechts–Schmidli model",

author = "Chiu, \{Sung Nok\} and Yin, \{Chuan Cun\}",

note = "Funding Information: Research supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKBU/2075/98P) and also by the National Natural Science Foundation of China (Project No. 19801020). ",

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T1 - The first exit time and ruin time for a risk process with reserve-dependent income

AU - Chiu, Sung Nok

AU - Yin, Chuan Cun

N1 - Funding Information: Research supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKBU/2075/98P) and also by the National Natural Science Foundation of China (Project No. 19801020).

PY - 2002/12

Y1 - 2002/12

N2 - This paper investigates the first exit time and the ruin time of a risk reserve process with reserve-dependent income under the assumption that the claims arrive as a Poisson process. We show that the Laplace transform of the distribution of the first exit time from an interval satisfies an integro-differential equation. The exact solution for the classical model and for the Embrechts-Schmidli model are derived.

AB - This paper investigates the first exit time and the ruin time of a risk reserve process with reserve-dependent income under the assumption that the claims arrive as a Poisson process. We show that the Laplace transform of the distribution of the first exit time from an interval satisfies an integro-differential equation. The exact solution for the classical model and for the Embrechts-Schmidli model are derived.

KW - First exit time

KW - Ruin time

KW - Ruin probability

KW - Risk reserve process

KW - Embrechts–Schmidli model

UR - https://www.scopus.com/pages/publications/0037114402

U2 - 10.1016/S0167-7152(02)00311-5

DO - 10.1016/S0167-7152(02)00311-5

M3 - Journal article

AN - SCOPUS:0037114402

SN - 0167-7152

VL - 60

SP - 417

EP - 424

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 4

ER -

The first exit time and ruin time for a risk process with reserve-dependent income

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