OCCUPATION TIMES OF SPECTRALLY NEGATIVE LÉVY PROCESSES WITH APPLICATIONS

By David Landriault, Jean-François Renaud, Xiaowen Zhou. 2010

116 citations recorded by the source corpus.

In this paper, we compute the Laplace transform of occupation times (of the negative half-line) of spectrally negative Levy processes. Our results are extensions of known results for standard Brownian motion and jump-diffusion processes. The results are expressed in terms of the so-called scale functions of the spectrally negative Levy process and its Laplace exponent. Applications to insurance risk models are also presented.

Subfields: Economics and Econometrics, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/95dba376e7c7a02e6226b05e6e3e367a85917ebd

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Citations in the corpus

On magnitude, asymptotics and duration of drawdowns for L\'{e}vy models (2015, background): “[22], Li and Zhou [25], Loeffen et al.”
Ruin Probability with Parisian Delay for a Spectrally Negative Lévy Risk Process (2010, background): “Other relevant papers are [19] and [20], where, loosely speaking, the deterministic and fixed delay ζ is replaced by an independent exponential random variable.”
The Joint Laplace Transforms for Diffusion Occupation Times (2013, methodology): “Since the exit problems for time-homogeneous diffusion processes can also be solved explicitly, in this paper we adopt the strategy of [15] to The results in this paper ﬁnd applications in the study of ruin problems for the so-called diffusion risk process with random observation times and the…”
Exit identities for L\'evy processes observed at Poisson arrival times (2014, background): “Results One of the first general results concerning T− 0 was obtained in [15], where it was shown for q = 0 and EX(1) > 0 that (11) Px(T 0 =∞) = ψ′(0) Φλ λ Z(x,Φλ), x ≥ 0, cf.”
An Insurance Risk Model with Parisian Implementation Delays (2013, unknown): “Also, note that the probability of our stochastic Parisian ruin can be linked to a certain occupation time of the underlying surplus process (see Landriault et al. 2011).”
FROM RUIN TO BANKRUPTCY FOR COMPOUND POISSON SURPLUS PROCESSES (2013, background): “Also, Landriault et al. (2011) generally discuss occupation times for spectrally negative Lévy processes.”
Occupation Times of Refracted Lévy Processes (2012, unknown): “[14] where it is explained how such functionals bear relevance to, so-called, insurance risk models with Parisian implementing delays.”