On a Fractional Stochastic Risk Model with a Random Initial Surplus and a Multi-Layer Strategy
The paper deals with a fractional time-changed stochastic risk model, including stochastic premiums, dividends and also a stochastic initial surplus as a capital derived from a previous investment. The inverse of a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" d...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/4/570 |
| _version_ | 1827654173035855872 |
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| author | Enrica Pirozzi |
| author_facet | Enrica Pirozzi |
| author_sort | Enrica Pirozzi |
| collection | DOAJ |
| description | The paper deals with a fractional time-changed stochastic risk model, including stochastic premiums, dividends and also a stochastic initial surplus as a capital derived from a previous investment. The inverse of a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>-stable subordinator is used for the time-change. The submartingale property is assumed to guarantee the net-profit condition. The long-range dependence behavior is proven. The infinite-horizon ruin probability, a specialized version of the Gerber–Shiu function, is considered and investigated. In particular, we prove that the distribution function of the infinite-horizon ruin time satisfies an integral-differential equation. The case of the dividends paid according to a multi-layer dividend strategy is also considered. |
| first_indexed | 2024-03-09T21:30:45Z |
| format | Article |
| id | doaj.art-addf2d2bd5974a22aac242ff24668bac |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T21:30:45Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-addf2d2bd5974a22aac242ff24668bac2023-11-23T20:56:48ZengMDPI AGMathematics2227-73902022-02-0110457010.3390/math10040570On a Fractional Stochastic Risk Model with a Random Initial Surplus and a Multi-Layer StrategyEnrica Pirozzi0Dipartimento di Matematica e Applicazioni, Università di Napoli “Federico II”, via Cintia, Complesso Monte S. Angelo, I-80126 Napoli, ItalyThe paper deals with a fractional time-changed stochastic risk model, including stochastic premiums, dividends and also a stochastic initial surplus as a capital derived from a previous investment. The inverse of a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>-stable subordinator is used for the time-change. The submartingale property is assumed to guarantee the net-profit condition. The long-range dependence behavior is proven. The infinite-horizon ruin probability, a specialized version of the Gerber–Shiu function, is considered and investigated. In particular, we prove that the distribution function of the infinite-horizon ruin time satisfies an integral-differential equation. The case of the dividends paid according to a multi-layer dividend strategy is also considered.https://www.mdpi.com/2227-7390/10/4/570stochastic premiums and claimsfractional Poisson processmulti–layer dividend strategyruin probabilitypiecewise integro-differential equation |
| spellingShingle | Enrica Pirozzi On a Fractional Stochastic Risk Model with a Random Initial Surplus and a Multi-Layer Strategy Mathematics stochastic premiums and claims fractional Poisson process multi–layer dividend strategy ruin probability piecewise integro-differential equation |
| title | On a Fractional Stochastic Risk Model with a Random Initial Surplus and a Multi-Layer Strategy |
| title_full | On a Fractional Stochastic Risk Model with a Random Initial Surplus and a Multi-Layer Strategy |
| title_fullStr | On a Fractional Stochastic Risk Model with a Random Initial Surplus and a Multi-Layer Strategy |
| title_full_unstemmed | On a Fractional Stochastic Risk Model with a Random Initial Surplus and a Multi-Layer Strategy |
| title_short | On a Fractional Stochastic Risk Model with a Random Initial Surplus and a Multi-Layer Strategy |
| title_sort | on a fractional stochastic risk model with a random initial surplus and a multi layer strategy |
| topic | stochastic premiums and claims fractional Poisson process multi–layer dividend strategy ruin probability piecewise integro-differential equation |
| url | https://www.mdpi.com/2227-7390/10/4/570 |
| work_keys_str_mv | AT enricapirozzi onafractionalstochasticriskmodelwitharandominitialsurplusandamultilayerstrategy |