Joint Distribution for the Risk Process with Premiums Depending on the Current Reserve

With the ever-evolving of modern risk theory,more and more attention should be paid to the modification of the classical risk theory. In this paper a risk process with premiums dependent on the current reserve is considered. An explicit expression for the joint distribution of the time of ruin,the s...

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Published in东华大学学报（英文版） Vol. 34; no. 4; pp. 540 - 544
Main Author 何敬民 张炜 李曼曼 方鑫
Format Journal Article
LanguageEnglish
Published School of Science, Tianjin University of Technology, Tianjin 300384, China%School of Mathematics and Statistics, Central South University, Changsha 410083, China%College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China 31.08.2017
Subjects
deficit at ruin
surplus immediately before ruin
time of ruin
strong Markov property
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ISSN1672-5220
DOI10.3969/j.issn.1672-5220.2017.04.011

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Summary:With the ever-evolving of modern risk theory,more and more attention should be paid to the modification of the classical risk theory. In this paper a risk process with premiums dependent on the current reserve is considered. An explicit expression for the joint distribution of the time of ruin,the surplus immediately before ruin and the deficit at ruin is derived. Finally,some important actuarial diagnostics including the ultimate ruin probability is investigated.
Bibliography:With the ever-evolving of modern risk theory,more and more attention should be paid to the modification of the classical risk theory. In this paper a risk process with premiums dependent on the current reserve is considered. An explicit expression for the joint distribution of the time of ruin,the surplus immediately before ruin and the deficit at ruin is derived. Finally,some important actuarial diagnostics including the ultimate ruin probability is investigated.
31-1920/N
time of ruin; surplus immediately before ruin; deficit at ruin; strong Markov property
HE Jingmin1, ZHANG Wei2, LI Man-man3, FANG Xin 2 （1 School of Science, Tianjin University of Technology, Tianjin 300384, China; 2 School of Mathematics and Statistics, Central South University, Changsha 410083, China; 3 College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China）
ISSN:1672-5220
DOI:10.3969/j.issn.1672-5220.2017.04.011