1 results
Large deviations of heavy-tailed random sums with applications in insurance and finance
- Part of
-
- Journal:
- Journal of Applied Probability / Volume 34 / Issue 2 / June 1997
- Published online by Cambridge University Press:
- 14 July 2016, pp. 293-308
- Print publication:
- June 1997
-
- Article
- Export citation
-
We prove large deviation results for the random sum
, 
, where 
are non-negative integer-valued random variables and are 
i.i.d. non-negative random variables with common distribution function F, independent of 
. Special attention is paid to the compound Poisson process and its ramifications. The right tail of the distribution function F is supposed to be of Pareto type (regularly or extended regularly varying). The large deviation results are applied to certain problems in insurance and finance which are related to large claims.
, 
, where 
are non-negative integer-valued random variables and are 
i.i.d. non-negative random variables with common distribution function 
. Special attention is paid to the compound Poisson process and its ramifications. The right tail of the distribution function 