Abstract
It is possible to consider a sequence of wave governed random motions such that their paths converge to the path of a suitable ruin process with exponentially distributed claim sizes (see the proof of Theorem 1 in [Mazza, C., Rulliére, D., 2004. A link between wave governed random motions and ruin processes. Insurance Math. Econom. 35, 205–222]). In this paper we verify that some large deviation rates for these wave governed random motions converge to the analogous rates for the same ruin process.
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