Loss rate for a general Lévy process with downward periodic barrier

Details Loss rate for a general Lévy process with downward periodic barrier Loss rate for a general Lévy process with downward periodic barrier

2011-10-17

arxiv.org/abs/1110.3827v1

Mathematics

Probability

Scientific paper

In this paper we consider a general L\'{e}vy process $X$ reflected at
downward periodic barrier $A_t$ and constant upper barrier $K$ giving a process
$V^K_t=X_t+L^A_t-L^K_t$. We find the expression for a loss rate defined by
$l^K=\mathbb{E} L^K_1$ and identify its asymptotics as $K\to\infty$ when $X$
has light-tailed jumps and $\mathbb{E}X_1<0$.

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