Markov-dependent risk model with multi-layer dividend strategy

作者：Zhou, Zhongbao^*; Xiao, Helu; Deng, Yingchun

来源：Applied Mathematics and Computation, 2015, 252: 273-286.

DOI：10.1016/j.amc.2014.12.016

• Markov-dependent risk model
• Multi-layer dividend strategy
• Integro-differential equation
• Gerber-Shiu function
• Chebyshev polynomial approximation approach

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.

• 出版日期2015-2-1
• 单位湖南师范大学; 湖南大学