# On occupation times in the red of L\'evy risk models

23 Jul 2019  ·  Landriault David, Li Bin, Lkabous Mohamed Amine ·

In this paper, we obtain analytical expression for the distribution of the occupation time in the red (below level $0$) up to an (independent) exponential horizon for spectrally negative L\'{e}vy risk processes and refracted spectrally negative L\'{e}vy risk processes. This result improves the existing literature in which only the Laplace transforms are known. Due to the close connection between occupation time and many other quantities, we provide a few applications of our results including future drawdown, inverse occupation time, Parisian ruin with exponential delay, and the last time at running maximum. By a further Laplace inversion to our results, we obtain the distribution of the occupation time up to a finite time horizon for refracted Brownian motion risk process and refracted Cram\'{e}r-Lundberg risk model with exponential claims.

PDF Abstract

## Code Add Remove Mark official

No code implementations yet. Submit your code now

## Datasets

Add Datasets introduced or used in this paper

## Results from the Paper Add Remove

Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.