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Y. Lu and S. Li, “On the Probability of Ruin in a Markov-modulated Risk Model,” Insurance: Mathemat- ics and Economics, Vol. 37, No. 3, 2005, pp. 522-532. doi:10.1016/j.insmatheco.2005.05.006

has been cited by the following article:

• TITLE: The Markovian Regime-Switching Risk Model with Constant Dividend Barrier under Absolute Ruin

  AUTHORS: Wenguang Yu, Yujuan Huang

  KEYWORDS: Absolute Ruin, Debit Interest, Moment-Generating Function, Markovian Regime-Switching Risk Model, Dividend Barrier, Integro-Differential Equation

  JOURNAL NAME: Journal of Mathematical Finance, Vol.1 No.3, November 8, 2011

  ABSTRACT: In this paper, we consider the dividend payments prior to absolute ruin in a Markovian regime-switching risk process in which the rate for the Poisson claim arrivals and the distribution of the claim amounts are driven by an underlying Markov jump process. A system of integro-differential equations with boundary conditions satisfied by the moment-generating function, the n th moment of the discounted dividend payments prior to absolute ruin and the expected discounted penalty function, given the initial environment state, are derived. Then, the matrix form of systems of integro-differential equations satisfied by the discounted penalty function are presented. Finally, we obtain the integro-differential equations satisfied by the time to reach the dividend barrier.