We consider the regularity of sample paths of Volterra–Lévy processes. These processes are defined as stochastic integrals M(t)=∫0tF(t,r)dX(r),t∈R+, where X is a Lévy process and F is a deterministic real-valued function. We derive the spectrum of singularities and a result on the...

Consider the problem of approximating the tail probability of randomly weighted sums and their maxima, where {Xi,i=1} is a sequence of identically distributed but not necessarily independent random variables from the extended regular variation class, and {[Theta]i,i=1} is a sequence of...

We propose a stochastic control approach to the dynamic maximization of robust utility functionals that are defined in terms of logarithmic utility and a dynamically consistent convex risk measure. The underlying market is modeled by a diffusion process whose coefficients are driven by an...

A moderate deviation principle and a Strassen-type law of the iterated logarithm for the small-time propagation of super-Brownian motion are derived. Moderate deviation estimates which are uniform with respect to the starting point are developed in order to prove the law of the iterated...