caa a22 4500 605462216 CHVBK 20210128100247.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s10114-015-4228-2 doi (NATIONALLICENCE)springer-10.1007/s10114-015-4228-2 A periodic dividend problem with inconstant barrier in Markovian environment [Elektronische Daten] [Fang Jin, Hui Ou, Xiang Yang] 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. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 Periodic dividend nationallicence Markovian environment nationallicence inconstant barrier nationallicence ruin time nationallicence discounted dividends nationallicence contraction mapping principle nationallicence Jin Fang College of Mathematics and Computer Sciences, Hu'nan Normal University, 410081, Changsha, P. R. China aut Ou Hui College of Mathematics and Computer Sciences, Hu'nan Normal University, 410081, Changsha, P. R. China aut Yang Xiang College of Mathematics and Computer Sciences, Hu'nan Normal University, 410081, Changsha, P. R. China aut Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/2(2015-02-01), 281-294 1439-8516 31:2<281 2015 31 10114 https://doi.org/10.1007/s10114-015-4228-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10114-015-4228-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Jin Fang College of Mathematics and Computer Sciences, Hu'nan Normal University, 410081, Changsha, P. R. China aut NATIONALLICENCE 700 1- Ou Hui College of Mathematics and Computer Sciences, Hu'nan Normal University, 410081, Changsha, P. R. China aut NATIONALLICENCE 700 1- Yang Xiang College of Mathematics and Computer Sciences, Hu'nan Normal University, 410081, Changsha, P. R. China aut NATIONALLICENCE 773 0- Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/2(2015-02-01), 281-294 1439-8516 31:2<281 2015 31 10114