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On a Fractional Stochastic Risk Model with a Random Initial Surplus and a Multi-Layer Strategy

Author

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  • Enrica Pirozzi

    (Dipartimento di Matematica e Applicazioni, Università di Napoli “Federico II”, via Cintia, Complesso Monte S. Angelo, I-80126 Napoli, Italy)

Abstract

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 ν -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.

Suggested Citation

  • Enrica Pirozzi, 2022. "On a Fractional Stochastic Risk Model with a Random Initial Surplus and a Multi-Layer Strategy," Mathematics, MDPI, vol. 10(4), pages 1-18, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:570-:d:747692
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    References listed on IDEAS

    as
    1. Giacomo Ascione & Nikolai Leonenko & Enrica Pirozzi, 2018. "Fractional Queues with Catastrophes and Their Transient Behaviour," Mathematics, MDPI, vol. 6(9), pages 1-26, September.
    2. Ascione, Giacomo & Leonenko, Nikolai & Pirozzi, Enrica, 2020. "Fractional Erlang queues," Stochastic Processes and their Applications, Elsevier, vol. 130(6), pages 3249-3276.
    3. Roberto Garrappa & Eva Kaslik & Marina Popolizio, 2019. "Evaluation of Fractional Integrals and Derivatives of Elementary Functions: Overview and Tutorial," Mathematics, MDPI, vol. 7(5), pages 1-21, May.
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    Cited by:

    1. Nikolai Leonenko & Andrey Pepelyshev & Alois Pichler & Enrica Pirozzi & Xiangyun Meng, 2026. "Probability of ruin within finite time and Cramér–Lundberg inequality for fractional risk processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 35(1), pages 23-48, March.

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