Approximations for moments of deficit at ruin with exponential and subexponential claims

Yebin Cheng; Qihe Tang; Hailiang Yang

doi:10.1016/S0167-7152(02)00234-1

Approximations for moments of deficit at ruin with exponential and subexponential claims

Yebin Cheng^*, Qihe Tang, Hailiang Yang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

Consider a renewal insurance risk model with initial surplus u > 0 and let A_u denote the deficit at the time of ruin. This paper investigates the asymptotic behavior of the moments of A_u as u tends to infinity. Under the assumption that the claim size is exponentially or subexponentially distributed, we obtain some asymptotic relationships for the φ-moments of A_u, where φ is a non-negative and non-decreasing function satisfying certain conditions.

Original language	English
Pages (from-to)	367-378
Number of pages	12
Journal	Statistics and Probability Letters
Volume	59
Issue number	4
DOIs	https://doi.org/10.1016/S0167-7152(02)00234-1
Publication status	Published - 15 Oct 2002
Externally published	Yes

Keywords

Ascending ladder
Asymptotics
Renewal risk model
Ruin probabilities
The class L (γ)
φ-moments

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10.1016/S0167-7152(02)00234-1

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AU - Tang, Qihe

AU - Yang, Hailiang

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N2 - Consider a renewal insurance risk model with initial surplus u > 0 and let Au denote the deficit at the time of ruin. This paper investigates the asymptotic behavior of the moments of Au as u tends to infinity. Under the assumption that the claim size is exponentially or subexponentially distributed, we obtain some asymptotic relationships for the φ-moments of Au, where φ is a non-negative and non-decreasing function satisfying certain conditions.

AB - Consider a renewal insurance risk model with initial surplus u > 0 and let Au denote the deficit at the time of ruin. This paper investigates the asymptotic behavior of the moments of Au as u tends to infinity. Under the assumption that the claim size is exponentially or subexponentially distributed, we obtain some asymptotic relationships for the φ-moments of Au, where φ is a non-negative and non-decreasing function satisfying certain conditions.

KW - Ascending ladder

KW - Asymptotics

KW - Renewal risk model

KW - Ruin probabilities

KW - The class L (γ)

KW - φ-moments

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DO - 10.1016/S0167-7152(02)00234-1

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SP - 367

EP - 378

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 4

ER -

Approximations for moments of deficit at ruin with exponential and subexponential claims

Abstract

Keywords

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