The paper improves prior results on Parisian ruin probabilities under hybrid observation and derives additional fluctuation identities expressed via second-generation scale functions.
On the distribution of cumulative Parisian ruin
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abstract
We introduce the concept of cumulative Parisian ruin, which is based on the time spent in the red by the underlying surplus process. Our main result is an explicit representation for the distribution of the occupation time, over a finite-time horizon, for a compound Poisson process with drift and exponential claims. The Brownian ruin model is also studied in details. Finally, we analyze for a general framework the relationships between cumulative Parisian ruin and classical ruin, as well as with Parisian ruin based on exponential implementation delays.
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math.PR 1years
2019 1verdicts
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A note on Parisian ruin under a hybrid observation scheme
The paper improves prior results on Parisian ruin probabilities under hybrid observation and derives additional fluctuation identities expressed via second-generation scale functions.