caa a22 4500 445830476 CHVBK 20180317145313.0 cr unu---uuuuu 170323e20110101xx s 000 0 eng 10.1007/s10255-011-0040-7 doi (NATIONALLICENCE)springer-10.1007/s10255-011-0040-7 Ruin probability and joint distributions of some actuarial random vectors in the compound pascal model [Elektronische Daten] [Xian-min Geng, Shu-chen Wan] The compound negative binomial model, introduced in this paper, is a discrete time version. We discuss the Markov properties of the surplus process, and study the ruin probability and the joint distributions of actuarial random vectors in this model. By the strong Markov property and the mass function of a defective renewal sequence, we obtain the explicit expressions of the ruin probability, the finite-horizon ruin probability, the joint distributions of T, U(T − 1), |U(T)| and $$ \mathop {\inf }\limits_{0 \leqslant n < \tau _1 } $$ U(n) (i.e., the time of ruin, the surplus immediately before ruin, the deficit at ruin and maximal deficit from ruin to recovery) and the distributions of some actuarial random vectors. Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg, 2011 Compound negative binomial model nationallicence Ruin probability nationallicence Sequence of up-crossing zero points nationallicence Ultimately leaving deficit time nationallicence Joint distributions nationallicence Geng Xian-min College of Science, Nanjing University of Aeronautics & Astronautics, 210016, Nanjing, China aut Wan Shu-chen College of Science, Nanjing University of Aeronautics & Astronautics, 210016, Nanjing, China aut Acta Mathematicae Applicatae Sinica, English Series Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 27/1(2011-01-01), 63-74 0168-9673 27:1<63 2011 27 10255 https://doi.org/10.1007/s10255-011-0040-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10255-011-0040-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Geng Xian-min College of Science, Nanjing University of Aeronautics & Astronautics, 210016, Nanjing, China aut NATIONALLICENCE 700 1- Wan Shu-chen College of Science, Nanjing University of Aeronautics & Astronautics, 210016, Nanjing, China aut NATIONALLICENCE 773 0- Acta Mathematicae Applicatae Sinica, English Series Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 27/1(2011-01-01), 63-74 0168-9673 27:1<63 2011 27 10255 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer