Abstract
We study the stochastic properties of the area under some function of the difference between (i) a spectrally positive Lévy process W t x that jumps to a level x > 0 whenever it hits zero and (ii) its reflected version W t . Remarkably, even though the analysis of each of these areas is challenging, we succeed in attaining explicit expressions for their difference. The main result concerns the Laplace-Stieltjes transform of the integral A x of (a function of) the distance between W t x and W t until W t x hits zero. This result is extended in a number of directions, including the area between A x and A y and a Gaussian limit theorem. We conclude the article with an inventory problem for which our results are particularly useful.
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