Abstract
Let X be a real valued random variable with an unbounded distribution F and let Y be a nonnegative valued random variable with a distribution G. Suppose that X and Y satisfy that holds uniformly for
as
, where
is a positive measurable function. Under the condition that
holds for all constant b > 0, this paper proved that
for some
implied
and that
for some
implied
, where H is the distribution of the product XY, and
is the right endpoint of G, that is,
and when
is understood as 0. Furthermore, in a discrete-time risk model in which the net insurance loss and the stochastic discount factor are equipped with a dependence structure, a general asymptotic formula for the finite-time ruin probability is obtained when the net insurance losses follow a common subexponential distribution.
MATHEMATICS SUBJECT CLASSIFICATION:
Acknowledgements
The authors would like to express their deep gratitude to the two referees for their valuable comments and suggestions which help a lot in the improvement of the paper.