TY - JOUR
T1 - De Vylder and Goovaerts' conjecture on homogeneous risk models with equalized claim amounts
AU - Kim, Bara
AU - Kim, Jeongsim
AU - Kim, Jerim
N1 - Funding Information:
We are grateful to the reviewers for their valuable comments and suggestions. The first author's research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government ( MSIT ) (No. 2020R1A2B5B01001864 ). The second author's research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government ( MSIT ) (No. 2020R1F1A1A01065568 ). The third author's research was supported by the Basic study and Urban convergence R&D research fund of the University of Seoul ( 2019 ).
Publisher Copyright:
© 2021 Elsevier B.V.
PY - 2021/11
Y1 - 2021/11
N2 - De Vylder and Goovaerts (2000) made a conjecture on the comparison of the finite time ruin probability in a homogeneous risk model and the corresponding ruin probability in an associated model with equalized claim amounts. The conjecture, however, remains an open problem. In this paper, we provide a conjecture that is stronger than De Vylder and Goovaerts' conjecture and also provide sufficient conditions for the conjectures, which are more mathematically tractable than De Vylder and Goovaerts' conjecture and thus easier to work with. By using the sufficient conditions for the conjectures, we solve De Vylder and Goovaerts' conjecture when n=3, where n is the number of claims in the finite time.
AB - De Vylder and Goovaerts (2000) made a conjecture on the comparison of the finite time ruin probability in a homogeneous risk model and the corresponding ruin probability in an associated model with equalized claim amounts. The conjecture, however, remains an open problem. In this paper, we provide a conjecture that is stronger than De Vylder and Goovaerts' conjecture and also provide sufficient conditions for the conjectures, which are more mathematically tractable than De Vylder and Goovaerts' conjecture and thus easier to work with. By using the sufficient conditions for the conjectures, we solve De Vylder and Goovaerts' conjecture when n=3, where n is the number of claims in the finite time.
KW - De Vylder and Goovaerts' conjecture
KW - Homogeneous risk model
KW - Order statistics
KW - Risk reserve process
KW - Ruin probability
UR - http://www.scopus.com/inward/record.url?scp=85113160570&partnerID=8YFLogxK
U2 - 10.1016/j.insmatheco.2021.07.007
DO - 10.1016/j.insmatheco.2021.07.007
M3 - Article
AN - SCOPUS:85113160570
VL - 101
SP - 186
EP - 201
JO - Insurance: Mathematics and Economics
JF - Insurance: Mathematics and Economics
SN - 0167-6687
ER -