In this paper, we study the risk model with Markovian arrivals where we allow the surplus process to continue if the surplus falls below zero. We first derive expressions for the severity of ruin. Then by using the st...In this paper, we study the risk model with Markovian arrivals where we allow the surplus process to continue if the surplus falls below zero. We first derive expressions for the severity of ruin. Then by using the strong Markovian property of a two-dimensional Markov process and the expression for the severity of ruin, we obtain the Laplace transform of the total duration of negative surplus.展开更多
基金Supported by the National Natural Science Foundation of China(11571198)the Tianyuan Fund for Mathematics(11226251)+3 种基金the Natural Science Foundation of Shandong(ZR2014AM021)the Natural Science Foundation of Qufu Normal University(2012ZRB01473)the Research Fund of Qufu Normal University for Doctor(BSQD2012039)the postdoctoral Foundation of Qufu Normal University
文摘In this paper, we study the risk model with Markovian arrivals where we allow the surplus process to continue if the surplus falls below zero. We first derive expressions for the severity of ruin. Then by using the strong Markovian property of a two-dimensional Markov process and the expression for the severity of ruin, we obtain the Laplace transform of the total duration of negative surplus.
