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# The generalization of stop loss transforms and its applications in ruin probabilities

 dc.contributor.author Cheng, Yu en_US dc.date.accessioned 2007-05-15T19:04:50Z dc.date.available 2007-05-15T19:04:50Z dc.date.issued 1998-05-01T00:00:00Z en_US dc.identifier.uri http://hdl.handle.net/1993/1181 dc.description.abstract This thesis generalized the concept of stop-loss transforms, an important concept in risk theory (6), to the nth stop-loss transforms. Some useful properties of the nth stop-loss transforms were discovered and a recursion formula for the nth stop-loss transforms was established. Also, the maintenance properties of the nth stop-loss order under convolution, compound and mixture operations were proved. Finally the results mentioned above were applied to the study of losses $L\sb{i}\ (i = 1,2,\cdots),$ maximal aggregate loss L and ruin probability $T\psi(u).$ Some inequalities for the expectation of $L\sb{i}$ and L were given, and a relationship between the claim amount random variable and ruin probability was found. en_US dc.format.extent 2209928 bytes dc.format.extent 184 bytes dc.format.mimetype application/pdf dc.format.mimetype text/plain dc.language en en_US dc.language.iso en_US dc.title The generalization of stop loss transforms and its applications in ruin probabilities en_US dc.degree.discipline Mathematics, Computational & Statistical Science en_US dc.degree.level Master of Science (M.Sc.) en_US
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