Let $W_t:0\le t\le 1$ be a linear Brownian motion, starting from 0, defined on the canonical probability space (Ω,ℱ,P). Consider a process $u_t:0\le t\le 1$ belonging to the space ${ℒ}^{2,1}$ (see Definition II.2). The Skorokhod integral $U_t={ʃ}_0^{t}u\delta W$ is then well defined, for every t ∈ [0,1]. In this paper, we study the Besov regularity of the Skorokhod integral process $t\mapsto U_t$. More precisely, we prove the following THEOREM III.1. (1)If 0 < α < 1/2 and $u\in {ℒ}^{p,1}$ with 1/α < p < ∞, then a.s. $t\mapsto U_t\in {ℬ}_{p,q}^{\alpha }$ for all q ∈ [1,∞], and $t\to U_t\in {ℬ}_{p,\infty }^{\alpha ,0}$. (2) For every even integer p ≥...

In this paper we prove that a Gaussian white noise on the d-dimensional torus has paths in the Besov spaces $B_{p,\infty }^{-d/2}{(}^d)$ with p ∈ [1,∞). This result is shown to be optimal in several ways. We also show that Gaussian white noise on the d-dimensional torus has paths in the Fourier-Besov space $b{̂}_{p,\infty }^{-d/p}{(}^d)$. This is shown to be optimal as well.

We describe a new model of multiple reinsurance. The main idea is that the reinsurance premium is paid conditionally. It is motivated by some analysis of the ultimate price of the reinsurance contract. For simplicity we assume that the underlying risk pricing functional is the L₂-norm. An unexpected relation to the general theory of sample regularity of stochastic processes is given.

Brownian motion is the most studied of all stochastic processes; it is also the basis for stochastic analysis developed in the second half of the 20th century. The fine properties of the sample path of a Brownian motion have been carefully studied, starting with the fundamental work of Paul Lévy who also considered more general processes with independent increments and extended the Brownian motion results to this class. Lévy showed that a Brownian path in d (d ≥ 2) dimensions had zero Lebesgue measure;...