Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4627146 | Applied Mathematics and Computation | 2015 | 14 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Zhongbao Zhou, Helu Xiao, Yingchun Deng,