Ruin probability for renewal risk models with neutral net profit condition
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916081180868608 |
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| author | Grigutis, Andrius Karbonskis, Arvydas Šiaulys, Jonas |
| author_facet | Grigutis, Andrius Karbonskis, Arvydas Šiaulys, Jonas |
| contents | In ruin theory, the net profit condition intuitively means that the incurred random claims on average do not occur more often than premiums are gained. The breach of the net profit condition causes guaranteed ruin in few but simple cases when both the claims' inter-occurrence time and random claims are degenerate. In this work, we give a simplified argumentation for the unavoidable ruin when the incurred claims on average occur equally as the premiums are gained. We study the discrete-time risk model with $N\in\mathbb{N}$ periodically occurring independent distributions, the classical risk model, also known as the Cramér-Lundberg risk process, and the more general E. Sparre Andersen model. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2306_01502 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Ruin probability for renewal risk models with neutral net profit condition Grigutis, Andrius Karbonskis, Arvydas Šiaulys, Jonas Probability 60G50, 60J80, 91G05 In ruin theory, the net profit condition intuitively means that the incurred random claims on average do not occur more often than premiums are gained. The breach of the net profit condition causes guaranteed ruin in few but simple cases when both the claims' inter-occurrence time and random claims are degenerate. In this work, we give a simplified argumentation for the unavoidable ruin when the incurred claims on average occur equally as the premiums are gained. We study the discrete-time risk model with $N\in\mathbb{N}$ periodically occurring independent distributions, the classical risk model, also known as the Cramér-Lundberg risk process, and the more general E. Sparre Andersen model. |
| title | Ruin probability for renewal risk models with neutral net profit condition |
| topic | Probability 60G50, 60J80, 91G05 |
| url | https://arxiv.org/abs/2306.01502 |