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In the present paper we investigate the precise large deviations for heavy-tailed random sums. First, we obtain a result which improves the relative result in Kluppelberg and Mikosch (J. Appl. Probab. 34 (1997) 293). Then we introduce a more realistic risk model than classical ones, named the compound renewal model, and establish the precise large deviations in this model.
The Lab of Financial Engineering Research, Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
Guotai J&A Securities Co. Ltd., Shenzhen, Guangdong 518002, People's Republic of China
The Lab of Financial Engineering Research, Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China