Using the solution of one-sided exit problem, a procedure to price Parisian barrier options in a jump-diffusion model with two-sided exponential jumps is developed. By extending the method developed in Chesney, Jeanblanc-Picqué and Yor (1997; Brownian excursions and Parisian barrier options,...</italic>

We adopt a new approach to find Laplace transforms of joint occupation times over disjoint intervals for spectrally negative Lévy processes. The Laplace transforms are expressed in terms of scale functions.

For spectrally negative Lévy processes, we find expressions of potential measures that are discounted by their joint occupation times over semi-infinite intervals (−∞,0) and (0,∞). These expressions are in terms of the associated scale functions and the inverse functions of Laplace exponents.

Applying excursion theory, we re-express several well studied fluctuation quantities associated to Parisian ruin problem for L´evy risk processes in terms of integrals with respect to excursion measure for spectrally negative L´evy process. We show that these new expressions reconcile with the...

In this paper, we identify Laplace transforms of occupation times of intervals until first passage times for spectrally negative Lévy processes. New analytical identities for scale functions are derived and therefore the results are explicitly stated in terms of the scale functions of the...