First Exit-Time Analysis for an Approximate Barndorff-Nielsen and Shephard Model with Stationary Self-Decomposable Variance Process

@article{Awasthi2021FirstEA,
  title={First Exit-Time Analysis for an Approximate Barndorff-Nielsen and Shephard Model with Stationary Self-Decomposable Variance Process},
  author={Shantanu Awasthi and Indranil Sengupta},
  journal={Journal of Stochastic Analysis},
  year={2021}
}
In this paper, an approximate version of the Barndorff-Nielsen and Shephard model, driven by a Brownian motion and a L\'evy subordinator, is formulated. The first-exit time of the log-return process for this model is analyzed. It is shown that with certain probability, the first-exit time process of the log-return is decomposable into the sum of the first exit time of the Brownian motion with drift, and the first exit time of a L\'evy subordinator with drift. Subsequently, the probability… 
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