Laplace Transformation of the Ruin Time for a Risk Model with a Parisian Implementation Delay
In this paper, we apply the concept of the Parisian implementation delay to dividend payments and assume that the claim amount paid <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>Z</mi><...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/4/551 |
| _version_ | 1797297517025558528 |
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| author | Tao Sun Xinqiu Zhang |
| author_facet | Tao Sun Xinqiu Zhang |
| author_sort | Tao Sun |
| collection | DOAJ |
| description | In this paper, we apply the concept of the Parisian implementation delay to dividend payments and assume that the claim amount paid <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>Z</mi><mi>i</mi></msub></semantics></math></inline-formula> by the insurance company for the <i>i</i>th time follows an exponential distribution. We give the Laplace transformation of the ruin time for a risk model with a Parisian implementation delay and give display expressions using the scale function. |
| first_indexed | 2024-03-07T22:22:27Z |
| format | Article |
| id | doaj.art-0994e831518846e1815aff7085bf6b91 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-07T22:22:27Z |
| publishDate | 2024-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-0994e831518846e1815aff7085bf6b912024-02-23T15:26:08ZengMDPI AGMathematics2227-73902024-02-0112455110.3390/math12040551Laplace Transformation of the Ruin Time for a Risk Model with a Parisian Implementation DelayTao Sun0Xinqiu Zhang1School of Statistics and Data Science, Qufu Normal University, Qufu 273165, ChinaSchool of Mathematical Sciences, Qufu Normal University, Qufu 273165, ChinaIn this paper, we apply the concept of the Parisian implementation delay to dividend payments and assume that the claim amount paid <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>Z</mi><mi>i</mi></msub></semantics></math></inline-formula> by the insurance company for the <i>i</i>th time follows an exponential distribution. We give the Laplace transformation of the ruin time for a risk model with a Parisian implementation delay and give display expressions using the scale function.https://www.mdpi.com/2227-7390/12/4/551Laplace transformationParisian implementation delayrisk model |
| spellingShingle | Tao Sun Xinqiu Zhang Laplace Transformation of the Ruin Time for a Risk Model with a Parisian Implementation Delay Mathematics Laplace transformation Parisian implementation delay risk model |
| title | Laplace Transformation of the Ruin Time for a Risk Model with a Parisian Implementation Delay |
| title_full | Laplace Transformation of the Ruin Time for a Risk Model with a Parisian Implementation Delay |
| title_fullStr | Laplace Transformation of the Ruin Time for a Risk Model with a Parisian Implementation Delay |
| title_full_unstemmed | Laplace Transformation of the Ruin Time for a Risk Model with a Parisian Implementation Delay |
| title_short | Laplace Transformation of the Ruin Time for a Risk Model with a Parisian Implementation Delay |
| title_sort | laplace transformation of the ruin time for a risk model with a parisian implementation delay |
| topic | Laplace transformation Parisian implementation delay risk model |
| url | https://www.mdpi.com/2227-7390/12/4/551 |
| work_keys_str_mv | AT taosun laplacetransformationoftheruintimeforariskmodelwithaparisianimplementationdelay AT xinqiuzhang laplacetransformationoftheruintimeforariskmodelwithaparisianimplementationdelay |