On the Gerber–Shiu discounted penalty function in a risk model with two types of delayed-claims and random income
This paper considers a risk model with random premium income and two types of by-claims, which is an extension to the general delayed claims process where there is only one type of by-claim and the premium income is a constant. Assume that each main claim induces one of the two by-claims, the by-cla...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Gao, Jianwei [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2014transfer abstract |
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| Schlagwörter: |
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| Umfang: |
11 |
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| Übergeordnetes Werk: |
Enthalten in: Dielectric relaxation and microwave dielectric properties of low temperature sintering LiMnPO4 ceramics - Hu, Xing ELSEVIER, 2015transfer abstract, Amsterdam [u.a.] |
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| Übergeordnetes Werk: |
volume:269 ; year:2014 ; day:15 ; month:10 ; pages:42-52 ; extent:11 |
| Links: |
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| DOI / URN: |
10.1016/j.cam.2014.03.011 |
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ELV028139631 |
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| 245 | 1 | 0 | |a On the Gerber–Shiu discounted penalty function in a risk model with two types of delayed-claims and random income |
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| 520 | |a This paper considers a risk model with random premium income and two types of by-claims, which is an extension to the general delayed claims process where there is only one type of by-claim and the premium income is a constant. Assume that each main claim induces one of the two by-claims, the by-claim and its associated main claim occur at the same time when the main claim amount is less than a threshold variable; otherwise, the occurrence of the by-claim will be delayed. An integral equations system for the Gerber–Shiu discounted penalty functions is presented by using auxiliary risk models. Given that the premium size is exponentially distributed, the explicit expression for the Laplace transform of the Gerber–Shiu penalty function is derived. By applying Rouché theorem, the Gerber–Shiu discounted penalty functions with reciprocal of the mean of premium surplus are obtained. According to Lagrange interpolation theorem, we prove that the Gerber–Shiu discounted penalty function satisfies a defective renewal equation. Finally, under the assumption of the claim sizes satisfying exponential distribution, the explicit formula of the ruin probability is derived when the discounted factor equals zero and the penalty function equals one. | ||
| 520 | |a This paper considers a risk model with random premium income and two types of by-claims, which is an extension to the general delayed claims process where there is only one type of by-claim and the premium income is a constant. Assume that each main claim induces one of the two by-claims, the by-claim and its associated main claim occur at the same time when the main claim amount is less than a threshold variable; otherwise, the occurrence of the by-claim will be delayed. An integral equations system for the Gerber–Shiu discounted penalty functions is presented by using auxiliary risk models. Given that the premium size is exponentially distributed, the explicit expression for the Laplace transform of the Gerber–Shiu penalty function is derived. By applying Rouché theorem, the Gerber–Shiu discounted penalty functions with reciprocal of the mean of premium surplus are obtained. According to Lagrange interpolation theorem, we prove that the Gerber–Shiu discounted penalty function satisfies a defective renewal equation. Finally, under the assumption of the claim sizes satisfying exponential distribution, the explicit formula of the ruin probability is derived when the discounted factor equals zero and the penalty function equals one. | ||
| 650 | 7 | |a Auxiliary model |2 Elsevier | |
| 650 | 7 | |a Rouché theorem |2 Elsevier | |
| 650 | 7 | |a By-claim |2 Elsevier | |
| 650 | 7 | |a Laplace transform |2 Elsevier | |
| 650 | 7 | |a Lagrange interpolation theorem |2 Elsevier | |
| 700 | 1 | |a Wu, Liyuan |4 oth | |
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10.1016/j.cam.2014.03.011 doi GBVA2014012000018.pica (DE-627)ELV028139631 (ELSEVIER)S0377-0427(14)00151-4 DE-627 ger DE-627 rakwb eng 510 510 DE-600 670 VZ 540 VZ 630 VZ Gao, Jianwei verfasserin aut On the Gerber–Shiu discounted penalty function in a risk model with two types of delayed-claims and random income 2014transfer abstract 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier This paper considers a risk model with random premium income and two types of by-claims, which is an extension to the general delayed claims process where there is only one type of by-claim and the premium income is a constant. Assume that each main claim induces one of the two by-claims, the by-claim and its associated main claim occur at the same time when the main claim amount is less than a threshold variable; otherwise, the occurrence of the by-claim will be delayed. An integral equations system for the Gerber–Shiu discounted penalty functions is presented by using auxiliary risk models. Given that the premium size is exponentially distributed, the explicit expression for the Laplace transform of the Gerber–Shiu penalty function is derived. By applying Rouché theorem, the Gerber–Shiu discounted penalty functions with reciprocal of the mean of premium surplus are obtained. According to Lagrange interpolation theorem, we prove that the Gerber–Shiu discounted penalty function satisfies a defective renewal equation. Finally, under the assumption of the claim sizes satisfying exponential distribution, the explicit formula of the ruin probability is derived when the discounted factor equals zero and the penalty function equals one. This paper considers a risk model with random premium income and two types of by-claims, which is an extension to the general delayed claims process where there is only one type of by-claim and the premium income is a constant. Assume that each main claim induces one of the two by-claims, the by-claim and its associated main claim occur at the same time when the main claim amount is less than a threshold variable; otherwise, the occurrence of the by-claim will be delayed. An integral equations system for the Gerber–Shiu discounted penalty functions is presented by using auxiliary risk models. Given that the premium size is exponentially distributed, the explicit expression for the Laplace transform of the Gerber–Shiu penalty function is derived. By applying Rouché theorem, the Gerber–Shiu discounted penalty functions with reciprocal of the mean of premium surplus are obtained. According to Lagrange interpolation theorem, we prove that the Gerber–Shiu discounted penalty function satisfies a defective renewal equation. Finally, under the assumption of the claim sizes satisfying exponential distribution, the explicit formula of the ruin probability is derived when the discounted factor equals zero and the penalty function equals one. Auxiliary model Elsevier Rouché theorem Elsevier By-claim Elsevier Laplace transform Elsevier Lagrange interpolation theorem Elsevier Wu, Liyuan oth Enthalten in North-Holland Hu, Xing ELSEVIER Dielectric relaxation and microwave dielectric properties of low temperature sintering LiMnPO4 ceramics 2015transfer abstract Amsterdam [u.a.] (DE-627)ELV013217658 volume:269 year:2014 day:15 month:10 pages:42-52 extent:11 https://doi.org/10.1016/j.cam.2014.03.011 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA AR 269 2014 15 1015 42-52 11 045F 510 |
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10.1016/j.cam.2014.03.011 doi GBVA2014012000018.pica (DE-627)ELV028139631 (ELSEVIER)S0377-0427(14)00151-4 DE-627 ger DE-627 rakwb eng 510 510 DE-600 670 VZ 540 VZ 630 VZ Gao, Jianwei verfasserin aut On the Gerber–Shiu discounted penalty function in a risk model with two types of delayed-claims and random income 2014transfer abstract 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier This paper considers a risk model with random premium income and two types of by-claims, which is an extension to the general delayed claims process where there is only one type of by-claim and the premium income is a constant. Assume that each main claim induces one of the two by-claims, the by-claim and its associated main claim occur at the same time when the main claim amount is less than a threshold variable; otherwise, the occurrence of the by-claim will be delayed. An integral equations system for the Gerber–Shiu discounted penalty functions is presented by using auxiliary risk models. Given that the premium size is exponentially distributed, the explicit expression for the Laplace transform of the Gerber–Shiu penalty function is derived. By applying Rouché theorem, the Gerber–Shiu discounted penalty functions with reciprocal of the mean of premium surplus are obtained. According to Lagrange interpolation theorem, we prove that the Gerber–Shiu discounted penalty function satisfies a defective renewal equation. Finally, under the assumption of the claim sizes satisfying exponential distribution, the explicit formula of the ruin probability is derived when the discounted factor equals zero and the penalty function equals one. This paper considers a risk model with random premium income and two types of by-claims, which is an extension to the general delayed claims process where there is only one type of by-claim and the premium income is a constant. Assume that each main claim induces one of the two by-claims, the by-claim and its associated main claim occur at the same time when the main claim amount is less than a threshold variable; otherwise, the occurrence of the by-claim will be delayed. An integral equations system for the Gerber–Shiu discounted penalty functions is presented by using auxiliary risk models. Given that the premium size is exponentially distributed, the explicit expression for the Laplace transform of the Gerber–Shiu penalty function is derived. By applying Rouché theorem, the Gerber–Shiu discounted penalty functions with reciprocal of the mean of premium surplus are obtained. According to Lagrange interpolation theorem, we prove that the Gerber–Shiu discounted penalty function satisfies a defective renewal equation. Finally, under the assumption of the claim sizes satisfying exponential distribution, the explicit formula of the ruin probability is derived when the discounted factor equals zero and the penalty function equals one. Auxiliary model Elsevier Rouché theorem Elsevier By-claim Elsevier Laplace transform Elsevier Lagrange interpolation theorem Elsevier Wu, Liyuan oth Enthalten in North-Holland Hu, Xing ELSEVIER Dielectric relaxation and microwave dielectric properties of low temperature sintering LiMnPO4 ceramics 2015transfer abstract Amsterdam [u.a.] (DE-627)ELV013217658 volume:269 year:2014 day:15 month:10 pages:42-52 extent:11 https://doi.org/10.1016/j.cam.2014.03.011 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA AR 269 2014 15 1015 42-52 11 045F 510 |
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10.1016/j.cam.2014.03.011 doi GBVA2014012000018.pica (DE-627)ELV028139631 (ELSEVIER)S0377-0427(14)00151-4 DE-627 ger DE-627 rakwb eng 510 510 DE-600 670 VZ 540 VZ 630 VZ Gao, Jianwei verfasserin aut On the Gerber–Shiu discounted penalty function in a risk model with two types of delayed-claims and random income 2014transfer abstract 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier This paper considers a risk model with random premium income and two types of by-claims, which is an extension to the general delayed claims process where there is only one type of by-claim and the premium income is a constant. Assume that each main claim induces one of the two by-claims, the by-claim and its associated main claim occur at the same time when the main claim amount is less than a threshold variable; otherwise, the occurrence of the by-claim will be delayed. An integral equations system for the Gerber–Shiu discounted penalty functions is presented by using auxiliary risk models. Given that the premium size is exponentially distributed, the explicit expression for the Laplace transform of the Gerber–Shiu penalty function is derived. By applying Rouché theorem, the Gerber–Shiu discounted penalty functions with reciprocal of the mean of premium surplus are obtained. According to Lagrange interpolation theorem, we prove that the Gerber–Shiu discounted penalty function satisfies a defective renewal equation. Finally, under the assumption of the claim sizes satisfying exponential distribution, the explicit formula of the ruin probability is derived when the discounted factor equals zero and the penalty function equals one. This paper considers a risk model with random premium income and two types of by-claims, which is an extension to the general delayed claims process where there is only one type of by-claim and the premium income is a constant. Assume that each main claim induces one of the two by-claims, the by-claim and its associated main claim occur at the same time when the main claim amount is less than a threshold variable; otherwise, the occurrence of the by-claim will be delayed. An integral equations system for the Gerber–Shiu discounted penalty functions is presented by using auxiliary risk models. Given that the premium size is exponentially distributed, the explicit expression for the Laplace transform of the Gerber–Shiu penalty function is derived. By applying Rouché theorem, the Gerber–Shiu discounted penalty functions with reciprocal of the mean of premium surplus are obtained. According to Lagrange interpolation theorem, we prove that the Gerber–Shiu discounted penalty function satisfies a defective renewal equation. Finally, under the assumption of the claim sizes satisfying exponential distribution, the explicit formula of the ruin probability is derived when the discounted factor equals zero and the penalty function equals one. Auxiliary model Elsevier Rouché theorem Elsevier By-claim Elsevier Laplace transform Elsevier Lagrange interpolation theorem Elsevier Wu, Liyuan oth Enthalten in North-Holland Hu, Xing ELSEVIER Dielectric relaxation and microwave dielectric properties of low temperature sintering LiMnPO4 ceramics 2015transfer abstract Amsterdam [u.a.] (DE-627)ELV013217658 volume:269 year:2014 day:15 month:10 pages:42-52 extent:11 https://doi.org/10.1016/j.cam.2014.03.011 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA AR 269 2014 15 1015 42-52 11 045F 510 |
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10.1016/j.cam.2014.03.011 doi GBVA2014012000018.pica (DE-627)ELV028139631 (ELSEVIER)S0377-0427(14)00151-4 DE-627 ger DE-627 rakwb eng 510 510 DE-600 670 VZ 540 VZ 630 VZ Gao, Jianwei verfasserin aut On the Gerber–Shiu discounted penalty function in a risk model with two types of delayed-claims and random income 2014transfer abstract 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier This paper considers a risk model with random premium income and two types of by-claims, which is an extension to the general delayed claims process where there is only one type of by-claim and the premium income is a constant. Assume that each main claim induces one of the two by-claims, the by-claim and its associated main claim occur at the same time when the main claim amount is less than a threshold variable; otherwise, the occurrence of the by-claim will be delayed. An integral equations system for the Gerber–Shiu discounted penalty functions is presented by using auxiliary risk models. Given that the premium size is exponentially distributed, the explicit expression for the Laplace transform of the Gerber–Shiu penalty function is derived. By applying Rouché theorem, the Gerber–Shiu discounted penalty functions with reciprocal of the mean of premium surplus are obtained. According to Lagrange interpolation theorem, we prove that the Gerber–Shiu discounted penalty function satisfies a defective renewal equation. Finally, under the assumption of the claim sizes satisfying exponential distribution, the explicit formula of the ruin probability is derived when the discounted factor equals zero and the penalty function equals one. This paper considers a risk model with random premium income and two types of by-claims, which is an extension to the general delayed claims process where there is only one type of by-claim and the premium income is a constant. Assume that each main claim induces one of the two by-claims, the by-claim and its associated main claim occur at the same time when the main claim amount is less than a threshold variable; otherwise, the occurrence of the by-claim will be delayed. An integral equations system for the Gerber–Shiu discounted penalty functions is presented by using auxiliary risk models. Given that the premium size is exponentially distributed, the explicit expression for the Laplace transform of the Gerber–Shiu penalty function is derived. By applying Rouché theorem, the Gerber–Shiu discounted penalty functions with reciprocal of the mean of premium surplus are obtained. According to Lagrange interpolation theorem, we prove that the Gerber–Shiu discounted penalty function satisfies a defective renewal equation. Finally, under the assumption of the claim sizes satisfying exponential distribution, the explicit formula of the ruin probability is derived when the discounted factor equals zero and the penalty function equals one. Auxiliary model Elsevier Rouché theorem Elsevier By-claim Elsevier Laplace transform Elsevier Lagrange interpolation theorem Elsevier Wu, Liyuan oth Enthalten in North-Holland Hu, Xing ELSEVIER Dielectric relaxation and microwave dielectric properties of low temperature sintering LiMnPO4 ceramics 2015transfer abstract Amsterdam [u.a.] (DE-627)ELV013217658 volume:269 year:2014 day:15 month:10 pages:42-52 extent:11 https://doi.org/10.1016/j.cam.2014.03.011 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA AR 269 2014 15 1015 42-52 11 045F 510 |
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10.1016/j.cam.2014.03.011 doi GBVA2014012000018.pica (DE-627)ELV028139631 (ELSEVIER)S0377-0427(14)00151-4 DE-627 ger DE-627 rakwb eng 510 510 DE-600 670 VZ 540 VZ 630 VZ Gao, Jianwei verfasserin aut On the Gerber–Shiu discounted penalty function in a risk model with two types of delayed-claims and random income 2014transfer abstract 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier This paper considers a risk model with random premium income and two types of by-claims, which is an extension to the general delayed claims process where there is only one type of by-claim and the premium income is a constant. Assume that each main claim induces one of the two by-claims, the by-claim and its associated main claim occur at the same time when the main claim amount is less than a threshold variable; otherwise, the occurrence of the by-claim will be delayed. An integral equations system for the Gerber–Shiu discounted penalty functions is presented by using auxiliary risk models. Given that the premium size is exponentially distributed, the explicit expression for the Laplace transform of the Gerber–Shiu penalty function is derived. By applying Rouché theorem, the Gerber–Shiu discounted penalty functions with reciprocal of the mean of premium surplus are obtained. According to Lagrange interpolation theorem, we prove that the Gerber–Shiu discounted penalty function satisfies a defective renewal equation. Finally, under the assumption of the claim sizes satisfying exponential distribution, the explicit formula of the ruin probability is derived when the discounted factor equals zero and the penalty function equals one. This paper considers a risk model with random premium income and two types of by-claims, which is an extension to the general delayed claims process where there is only one type of by-claim and the premium income is a constant. Assume that each main claim induces one of the two by-claims, the by-claim and its associated main claim occur at the same time when the main claim amount is less than a threshold variable; otherwise, the occurrence of the by-claim will be delayed. An integral equations system for the Gerber–Shiu discounted penalty functions is presented by using auxiliary risk models. Given that the premium size is exponentially distributed, the explicit expression for the Laplace transform of the Gerber–Shiu penalty function is derived. By applying Rouché theorem, the Gerber–Shiu discounted penalty functions with reciprocal of the mean of premium surplus are obtained. According to Lagrange interpolation theorem, we prove that the Gerber–Shiu discounted penalty function satisfies a defective renewal equation. Finally, under the assumption of the claim sizes satisfying exponential distribution, the explicit formula of the ruin probability is derived when the discounted factor equals zero and the penalty function equals one. Auxiliary model Elsevier Rouché theorem Elsevier By-claim Elsevier Laplace transform Elsevier Lagrange interpolation theorem Elsevier Wu, Liyuan oth Enthalten in North-Holland Hu, Xing ELSEVIER Dielectric relaxation and microwave dielectric properties of low temperature sintering LiMnPO4 ceramics 2015transfer abstract Amsterdam [u.a.] (DE-627)ELV013217658 volume:269 year:2014 day:15 month:10 pages:42-52 extent:11 https://doi.org/10.1016/j.cam.2014.03.011 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA AR 269 2014 15 1015 42-52 11 045F 510 |
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Enthalten in Dielectric relaxation and microwave dielectric properties of low temperature sintering LiMnPO4 ceramics Amsterdam [u.a.] volume:269 year:2014 day:15 month:10 pages:42-52 extent:11 |
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Finally, under the assumption of the claim sizes satisfying exponential distribution, the explicit formula of the ruin probability is derived when the discounted factor equals zero and the penalty function equals one.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This paper considers a risk model with random premium income and two types of by-claims, which is an extension to the general delayed claims process where there is only one type of by-claim and the premium income is a constant. Assume that each main claim induces one of the two by-claims, the by-claim and its associated main claim occur at the same time when the main claim amount is less than a threshold variable; otherwise, the occurrence of the by-claim will be delayed. An integral equations system for the Gerber–Shiu discounted penalty functions is presented by using auxiliary risk models. Given that the premium size is exponentially distributed, the explicit expression for the Laplace transform of the Gerber–Shiu penalty function is derived. By applying Rouché theorem, the Gerber–Shiu discounted penalty functions with reciprocal of the mean of premium surplus are obtained. According to Lagrange interpolation theorem, we prove that the Gerber–Shiu discounted penalty function satisfies a defective renewal equation. 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on the gerber–shiu discounted penalty function in a risk model with two types of delayed-claims and random income |
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On the Gerber–Shiu discounted penalty function in a risk model with two types of delayed-claims and random income |
| abstract |
This paper considers a risk model with random premium income and two types of by-claims, which is an extension to the general delayed claims process where there is only one type of by-claim and the premium income is a constant. Assume that each main claim induces one of the two by-claims, the by-claim and its associated main claim occur at the same time when the main claim amount is less than a threshold variable; otherwise, the occurrence of the by-claim will be delayed. An integral equations system for the Gerber–Shiu discounted penalty functions is presented by using auxiliary risk models. Given that the premium size is exponentially distributed, the explicit expression for the Laplace transform of the Gerber–Shiu penalty function is derived. By applying Rouché theorem, the Gerber–Shiu discounted penalty functions with reciprocal of the mean of premium surplus are obtained. According to Lagrange interpolation theorem, we prove that the Gerber–Shiu discounted penalty function satisfies a defective renewal equation. Finally, under the assumption of the claim sizes satisfying exponential distribution, the explicit formula of the ruin probability is derived when the discounted factor equals zero and the penalty function equals one. |
| abstractGer |
This paper considers a risk model with random premium income and two types of by-claims, which is an extension to the general delayed claims process where there is only one type of by-claim and the premium income is a constant. Assume that each main claim induces one of the two by-claims, the by-claim and its associated main claim occur at the same time when the main claim amount is less than a threshold variable; otherwise, the occurrence of the by-claim will be delayed. An integral equations system for the Gerber–Shiu discounted penalty functions is presented by using auxiliary risk models. Given that the premium size is exponentially distributed, the explicit expression for the Laplace transform of the Gerber–Shiu penalty function is derived. By applying Rouché theorem, the Gerber–Shiu discounted penalty functions with reciprocal of the mean of premium surplus are obtained. According to Lagrange interpolation theorem, we prove that the Gerber–Shiu discounted penalty function satisfies a defective renewal equation. Finally, under the assumption of the claim sizes satisfying exponential distribution, the explicit formula of the ruin probability is derived when the discounted factor equals zero and the penalty function equals one. |
| abstract_unstemmed |
This paper considers a risk model with random premium income and two types of by-claims, which is an extension to the general delayed claims process where there is only one type of by-claim and the premium income is a constant. Assume that each main claim induces one of the two by-claims, the by-claim and its associated main claim occur at the same time when the main claim amount is less than a threshold variable; otherwise, the occurrence of the by-claim will be delayed. An integral equations system for the Gerber–Shiu discounted penalty functions is presented by using auxiliary risk models. Given that the premium size is exponentially distributed, the explicit expression for the Laplace transform of the Gerber–Shiu penalty function is derived. By applying Rouché theorem, the Gerber–Shiu discounted penalty functions with reciprocal of the mean of premium surplus are obtained. According to Lagrange interpolation theorem, we prove that the Gerber–Shiu discounted penalty function satisfies a defective renewal equation. Finally, under the assumption of the claim sizes satisfying exponential distribution, the explicit formula of the ruin probability is derived when the discounted factor equals zero and the penalty function equals one. |
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