On a Perturbed Risk Model with Time-Dependent Claim Sizes
We consider a risk model perturbed by a Brownian motion, where the individual claim sizes are dependent on the inter-claim times. We study the Gerber–Shiu functions when ruin is due to a claim or the jump-diffusion process. Integro-differential equations and Laplace transforms satisfied by the Gerbe...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/8080309 |
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| _version_ | 1832559645495918592 |
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| author | Longfei Wei Jia Hao Shiyu Song Zhenhua Bao |
| author_facet | Longfei Wei Jia Hao Shiyu Song Zhenhua Bao |
| author_sort | Longfei Wei |
| collection | DOAJ |
| description | We consider a risk model perturbed by a Brownian motion, where the individual claim sizes are dependent on the inter-claim times. We study the Gerber–Shiu functions when ruin is due to a claim or the jump-diffusion process. Integro-differential equations and Laplace transforms satisfied by the Gerber–Shiu functions are obtained. Then, it is shown that the expected discounted penalty functions satisfy defective renewal equations. Explicit expressions can be obtained for exponential claim sizes. Finally, a numerical example is provided to measure the impact of the various dependence parameters in the risk model on the ruin probabilities. |
| format | Article |
| id | doaj-art-af8ff2a8471e41c8ad553392175a9a9c |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-af8ff2a8471e41c8ad553392175a9a9c2025-02-03T01:29:35ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/2024/8080309On a Perturbed Risk Model with Time-Dependent Claim SizesLongfei Wei0Jia Hao1Shiyu Song2Zhenhua Bao3School of ManagementSchool of Investment and Construction ManagementSchool of MathematicsSchool of MathematicsWe consider a risk model perturbed by a Brownian motion, where the individual claim sizes are dependent on the inter-claim times. We study the Gerber–Shiu functions when ruin is due to a claim or the jump-diffusion process. Integro-differential equations and Laplace transforms satisfied by the Gerber–Shiu functions are obtained. Then, it is shown that the expected discounted penalty functions satisfy defective renewal equations. Explicit expressions can be obtained for exponential claim sizes. Finally, a numerical example is provided to measure the impact of the various dependence parameters in the risk model on the ruin probabilities.http://dx.doi.org/10.1155/2024/8080309 |
| spellingShingle | Longfei Wei Jia Hao Shiyu Song Zhenhua Bao On a Perturbed Risk Model with Time-Dependent Claim Sizes Journal of Mathematics |
| title | On a Perturbed Risk Model with Time-Dependent Claim Sizes |
| title_full | On a Perturbed Risk Model with Time-Dependent Claim Sizes |
| title_fullStr | On a Perturbed Risk Model with Time-Dependent Claim Sizes |
| title_full_unstemmed | On a Perturbed Risk Model with Time-Dependent Claim Sizes |
| title_short | On a Perturbed Risk Model with Time-Dependent Claim Sizes |
| title_sort | on a perturbed risk model with time dependent claim sizes |
| url | http://dx.doi.org/10.1155/2024/8080309 |
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