A note on positive supermartingales in ruin theory

Schmidt, Klaus D.

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URL:	https://madoc.bib.uni-mannheim.de/1982
URN:	urn:nbn:de:bsz:180-madoc-19824
Document Type:	Working paper
Year of publication:	1989
The title of a journal, publication series:	None
Publication language:	English
Institution:	School of Business Informatics and Mathematics > Sonstige - Fakultät für Wirtschaftsinformatik und Wirtschaftsmathematik
MADOC publication series:	Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Mathematik > Mannheimer Manuskripte
Subject:	510 Mathematics
Subject headings (SWD):	Kolmogorov-Ungleichung , Martingal , Ruintheorie
Keywords (English):	Adjustment coefficient , Kolmogorov's inequality , Lundberg's inequality , positive supermartingales , ruin theory
Abstract:	In this note we give an elementary proof of Kolmogorov's inequality for positive supermartingales. As an application we obtain a Lundberg type inequality for a class of surplus processes with i.i.d. increments for which an adjustment coefficient need not exist.