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.

On a Fractional Stochastic Risk Model with a Random Initial Surplus and a Multi-Layer Strategy / Pirozzi, E.. - In: MATHEMATICS. - ISSN 2227-7390. - 10:4(2022), p. 570. [10.3390/math10040570]

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

Pirozzi E.
2022

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.
2022
On a Fractional Stochastic Risk Model with a Random Initial Surplus and a Multi-Layer Strategy / Pirozzi, E.. - In: MATHEMATICS. - ISSN 2227-7390. - 10:4(2022), p. 570. [10.3390/math10040570]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/902042
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