In this paper, we compute the Laplace transform of occupation times (of the negative half-line) of spectrally negative Lévy 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...

Using a Poisson approach, we find Laplace transforms of joint occupation times over n disjoint intervals for spectrally negative Lévy processes. They generalize previous results for dimension two.

This paper revisits the spectrally negative Lévy risk process embedded with the general tax structure introduced in Kyprianou and Zhou (2009). A joint Laplace transform is found concerning the first down-crossing time below level 0. The potential density is also obtained for the taxed Lévy risk...

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.

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...

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>

The (Ξ,A)-Fleming–Viot process with mutation is a probability-measure-valued process whose moment dual is similar to that of the classical Fleming–Viot process except that Kingman’s coalescent is replaced by the Ξ-coalescent, the coalescent with simultaneous multiple collisions. We first...

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.

This paper considers the following generalized almost sure local extinction for the d-dimensional (1+[beta])-super-Brownian motion X starting from Lebesgue measure on . For any t=0 write for a closed ball in with center at 0 and radius g(t), where g is a nonnegative, nondecreasing and right...