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

Enrica Pirozzi
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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

Mathematics, 2022, vol. 10, issue 4, 1-18

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.

Keywords: stochastic premiums and claims; fractional Poisson process; multi–layer dividend strategy; ruin probability; piecewise integro-differential equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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