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Abstract
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This paper studies the ruin probabilities in a homogeneous continuous compound
Poisson risk model which is adapted for the perturbed insurance risk model with
standard Brownian motion. In such a model, we construct a martingale in terms of
a differentiable exponential function based on the discounted and perturbed surplus
process. We obtain the exponential upper bounds for the ruin probabilities using
Martingale approach and provide a sharper exponential upper bound for the infinite
time ruin probability. Moreover, we derive two asymptotic approximation formulas for
the finite time ruin probability when claim size distribution belongs to some heavy-tailed
families. Finally, several numerical examples are presented to show the effect of
constant force of interest on the ruin probabilities and that our results are excellent and
reliable.
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