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

Authors: A.S. Dibu; M.J. Jacob

Addresses: Department of Mathematics, National Institute of Technology Calicut, Kozhikode – 673601, Kerala, India ' Department of Mathematics, National Institute of Technology Calicut, Kozhikode – 673601, Kerala, India

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.

DOI: 10.1504/IJMOR.2021.117634

International Journal of Mathematics in Operational Research, 2021 Vol.20 No.1, pp.60 - 84

Received: 12 May 2020
Accepted: 21 Jun 2020
Published online: 17 Sep 2021 *

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