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...

In a Post Keynesian theoretical framework with sequential financing, two solutions to the problem of the monetary realization of profits are presented. Both of these are consistent with the Kaleckian view, according to which actual profits arise from the present expenditure of their anticipated...

A discretization scheme for nonnegative diffusion processes is proposed and the convergence of the corresponding sequence of approximate processes is proved using the martingale problem framework. Motivations for this scheme come typically from finance, especially for path-dependent option...

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...

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...

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...

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.