THE BI-ATOMIC UNIFORM MINIMAL SOLUTION OF SCHMITTERS PROBLEM

Authors
DEVYLDER F GOOVAERTS M MARCEAU E
Citation
F. Devylder et al., THE BI-ATOMIC UNIFORM MINIMAL SOLUTION OF SCHMITTERS PROBLEM, Insurance. Mathematics & economics, 20(1), 1997, pp. 59-78
Citations number
5
Categorie Soggetti
Social Sciences, Mathematical Methods",Economics,"Mathematical, Methods, Social Sciences","Mathematics, Miscellaneous","Statistic & Probability
Journal title
Insurance. Mathematics & economics → ACNP
ISSN journal
01676687
Volume
20
Issue
1
Year of publication
1997
Pages
59 - 78
Database
ISI
SICI code
0167-6687(1997)20:1<59:TBUMSO>2.0.ZU;2-L
Abstract
The problem posed by Schmitter was to maximize the ruin probability wh en mean and variance of the claim size distribution are given. In this note we prove that the minimal ruin probability is given by the bi-at omic distribution with the maximal possible claim size as one of its m ass points. A by-product is a lower bound c e(-rho u) for the ruin pro bability psi (u), where rho is the adjustment coefficient, and c a con stant not depending on the allowed claim size distributions.