On the Gerber-Shiu function of a MAP risk model with possible delayed phase-type by-claims

A.S. Dibu and M.J. Jacob

International Journal of Mathematics in Operational Research, 2021, vol. 20, issue 1, 60-84

Abstract: This paper introduces the delayed claim settlement feature in a MAP risk model. Surplus process of the model incorporates two kinds of phase-type claims, the main claim and the by-claim. The delay feature is defined in such a way that every main claim may induce a by-claim with probability 'θ' and payment of the by-claim is delayed until the next claim arrival. An appropriate Gerber-Shiu function under an auxiliary (delayed) timeline is assumed to analyse the Gerber-Shiu function under the primary (original) timeline. Transient analysis of the Markovian fluid flow models is tailored to develop defective renewal equations satisfying Gerber-Shiu functions. An explicit solution for renewal equations is derived in terms of the Lundberg roots. Further, a Neumann series solution is also provided. A numerical example on the moment of surplus before ruin in a two-state model.

Keywords: Gerber-Shiu; function?; MAP; risk; model?; PH; claims?; delayed; by-claims?; system; of; Volterra; integro-differential; equation?; matrix; Lundberg; equation. (search for similar items in EconPapers)
Date: 2021
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