Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/257985 
Year of Publication: 
2020
Citation: 
[Journal:] Risks [ISSN:] 2227-9091 [Volume:] 8 [Issue:] 1 [Article No.:] 30 [Publisher:] MDPI [Place:] Basel [Year:] 2020 [Pages:] 1-25
Publisher: 
MDPI, Basel
Abstract: 
This paper considers the risk model perturbed by a diffusion process with a time delay in the arrival of the first two claims and takes into account dependence between claim amounts and the claim inter-occurrence times. Assuming that the time arrival of the first claim follows a generalized mixed equilibrium distribution, we derive the integro-differential Equations of the Gerber–Shiu function and its defective renewal equations. For the situation where claim amounts follow exponential distribution, we provide an explicit expression of the Gerber–Shiu function. Numerical examples are provided to illustrate the ruin probability.
Subjects: 
ruin theory
delay renewal risk process
renewal equation
convolution formula
diffusionprocess
FGM copula
exponential and equilibrium distribution
Persistent Identifier of the first edition: 
Creative Commons License: 
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Document Type: 
Article
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