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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4 Citations
Background Citations
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Methods Citations
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4 Citations

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References

SHOWING 1-10 OF 58 REFERENCES
First-exit times of an inverse Gaussian process
Abstract The first-exit time process of an inverse Gaussian Lévy process is considered. The one-dimensional distribution functions of the process are obtained. They are not infinitely divisible and…
Using differential equations to obtain joint moments of first-passage times of increasing Lévy processes
A note on first-passage times of continuously time-changed Brownian motion
Numerical Computation of First-Passage Times of Increasing Lévy Processes
Let {D(s), s ≥ 0} be a non-decreasing Lévy process. The first-hitting time process {E(t), t ≥ 0} (which is sometimes referred to as an inverse subordinator) defined by $E(t) = \inf \{s: D(s) > t \}$…
First and Last Passage Times of Spectrally Positive Lévy Processes with Application to Reliability
We consider a wide class of increasing Lévy processes perturbed by an independent Brownian motion as a degradation model. Such family contains almost all classical degradation models considered in…
The first exit time of Brownian motion from a parabolic domain
Consider a planar Brownian motion starting at an interior point of the parabolic domain D = {(x, y) :y > x2}, and let TrD denote the first time the Brownian motion exits from D. The tail behaviour…
First exit times of SDEs driven by stable Lévy processes
The First Exit Time Stochastic Theory Applied to Estimate the Life-Time of a Complicated System
We develop a first exit time methodology to model the life time process of a complicated system. We assume that the functionality level of a complicated system follows a stochastic process during…
First passage times of diffusion processes and their applications to finance
TLDR
The purpose of this thesis is to provide quantitative tools for investment decision and risk management by combining probability theory with financial practice, and to solve the closed-form asymptotic for the model’s first passage time.
Some remarks on first passage of Levy processes, the American put and pasting principles
The purpose of this article is to provide, with the help of a fluctuation identity, a generic link between a number of known identities for the first passage time and overshoot above/below a fixed…
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