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J. M. Reinhard, “On a Class of Semi-Markov Risk Models Obtained as Classical Risk Models in a Markovian Enviroment,” Astin Bulletin, Vol. 14, 1984, pp. 23-43.

has been cited by the following article:

• TITLE: Dividend Payments and Related Problems in a Markov-Dependent Insurance Risk Model under Absolute Ruin

  AUTHORS: Wenguang Yu, Yujuan Huang

  KEYWORDS: Absolute Ruin, Markov-Dependent Insurance Risk Model, Debit Interest, Moment-Generating Function

  JOURNAL NAME: American Journal of Industrial and Business Management, Vol.1 No.1, October 20, 2011

  ABSTRACT: In this paper, we study the dividend payments prior to absolute ruin in a Markov-dependent risk process in which the claim occurrence and the claim amount are regulated by an external discrete time Markov chain. A system of integro-differential equations with boundary conditions satisfied by the moment-generating function, the nth moment of the discounted dividend payments prior to absolute ruin and the discounted penalty function, given the initial environment state, are derived. In the two-state risk model, explicit solutions to the integro-differential equations satisfied by the nth moment of the discounted dividend payments prior to absolute ruin are obtained when the claim size distribution is exponentially distributed. Finally, the matrix form of systems of integro-differential equations satisfied by the discounted penalty function are presented.