A periodic dividend problem with inconstant barrier in Markovian environment |
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Authors: | Fang Jin Hui Ou Xiang Qun Yang |
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Institution: | College of Mathematics and Computer Sciences, Hu'nan Normal University, Changsha 410081, P. R. China |
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Abstract: | Periodic dividend problem is a meaningful issue. Based on a compound binomial model with periodic dividend, we use a homogeneous, ergodic and irreducible discrete-time Markov chain to express the evolution from one period to the subsequent of the economic or the environmental and climatic conditions. We derive some properties about the model. A system of integral equations for the expectation and the r-th moment of discounted dividends until ruin time are obtained respectively. Moreover, by using of Contraction Mapping Principle, we solve the equation system and obtain the explicit expression. |
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Keywords: | Periodic dividend Markovian environment inconstant barrier ruin time discounted dividends contraction mapping principle |
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