The time of ruin, the surplus prior to ruin and the deficit at ruin for the classical risk process perturbed by diffusion

S. N. Chiu; C. C. Yin

doi:10.1016/S0167-6687(03)00143-4

The time of ruin, the surplus prior to ruin and the deficit at ruin for the classical risk process perturbed by diffusion

S. N. Chiu^*, C. C. Yin

^*Corresponding author for this work

Department of Mathematics

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

37 Citations (Scopus)

68 Downloads (Pure)

Abstract

The paper studies the joint distribution of the time of ruin, the surplus prior to ruin and the deficit at ruin for the classical risk process that is perturbed by diffusion. We prove that the expected discounted penalty satisfies an integro-differential equation of renewal type, the solution of which can be expressed as a convolution formula. The asymptotic behaviour of the expected discounted penalty as the initial capital tends to infinity is discussed.

Original language	English
Pages (from-to)	59-66
Number of pages	8
Journal	Insurance: Mathematics and Economics
Volume	33
Issue number	1
DOIs	https://doi.org/10.1016/S0167-6687(03)00143-4
Publication status	Published - 8 Aug 2003

Scopus Subject Areas

Statistics and Probability
Economics and Econometrics
Statistics, Probability and Uncertainty

User-Defined Keywords

Deficit at ruin
Renewal equation
Time of ruin
Ruin probability
Surplus prior to ruin
Surplus process

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10.1016/S0167-6687(03)00143-4

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abstract = "The paper studies the joint distribution of the time of ruin, the surplus prior to ruin and the deficit at ruin for the classical risk process that is perturbed by diffusion. We prove that the expected discounted penalty satisfies an integro-differential equation of renewal type, the solution of which can be expressed as a convolution formula. The asymptotic behaviour of the expected discounted penalty as the initial capital tends to infinity is discussed.",

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AU - Yin, C. C.

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N2 - The paper studies the joint distribution of the time of ruin, the surplus prior to ruin and the deficit at ruin for the classical risk process that is perturbed by diffusion. We prove that the expected discounted penalty satisfies an integro-differential equation of renewal type, the solution of which can be expressed as a convolution formula. The asymptotic behaviour of the expected discounted penalty as the initial capital tends to infinity is discussed.

AB - The paper studies the joint distribution of the time of ruin, the surplus prior to ruin and the deficit at ruin for the classical risk process that is perturbed by diffusion. We prove that the expected discounted penalty satisfies an integro-differential equation of renewal type, the solution of which can be expressed as a convolution formula. The asymptotic behaviour of the expected discounted penalty as the initial capital tends to infinity is discussed.

KW - Deficit at ruin

KW - Renewal equation

KW - Time of ruin

KW - Ruin probability

KW - Surplus prior to ruin

KW - Surplus process

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JO - Insurance: Mathematics and Economics

JF - Insurance: Mathematics and Economics

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The time of ruin, the surplus prior to ruin and the deficit at ruin for the classical risk process perturbed by diffusion

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