Markov-dependent risk model with multi-layer dividend strategy

Zhongbao Zhou, Helu Xiao and Yingchun Deng

Applied Mathematics and Computation, 2015, vol. 252, issue C, 273-286

Abstract: In this paper, we propose a Markov-dependent risk model with multi-layer dividend strategy in which the claim occurrence and the claim amount are regulated by an external discrete time Markov chain. A system of piecewise integro-differential equations with boundary conditions satisfied by the Gerber–Shiu function, with given initial environment state, is derived. The closed form expression of the Gerber–Shiu function is obtained when all the claim amount distributions belong to the rational family. Also, we adopt the Chebyshev polynomial approach to find the approximate solution of the integro-differential equation. The numerical simulation results show the effectiveness of the proposed methods.

Keywords: Markov-dependent risk model; Multi-layer dividend strategy; Integro-differential equation; Gerber–Shiu function; Chebyshev polynomial approximation approach (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:252:y:2015:i:c:p:273-286

DOI: 10.1016/j.amc.2014.12.016

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