ROSESTOLATO M.

We present and apply a theory of one-parameter C0-semigroups of linear operators in locally convex spaces. Replacing the notion of equicontinuity considered by the literature with the weaker notion of sequential equicontinuity, we prove the basic results of the classical theory of C0-equicontinuous semigroups: we show that the semigroup is...

We study value functions which are viscosity solutions of certain Kolmogorov equations. Using PDE techniques we prove that they are C1+α regular on special finite dimensional subspaces. The problem has origins in hedging derivatives of risky assets in mathematical finance.

We introduce a new definition of viscosity solution to path-dependent partial differential equations, which is a slight modification of the definition introduced in [I. Ekren et al., Ann. Probab., 42 (2014), pp. 204-236]. With the new definition, we prove the two important results, until now missing in the literature, namely, a general...

We consider an optimal stochastic impulse control problem over an infinite time horizon motivated by a model of irreversible investment choices with fixed adjustment costs. By employing techniques of viscosity solutions and relying on semiconvexity arguments, we prove that the value function is a classical solution to the associated...

In this paper, we consider a generalisation of the Hobson-Rogers model proposed by Foschi and Pascucci (Decis Eocon Finance 31(1):1-20, 2008) for financial markets where the evolution of the prices of the assets depends not only on the current value but also on past values. Using differentiability of stochastic processes with respect to the...

Path-dependent partial differential equations (PPDEs) are natural objects to study when one deals with non-Markovian models. Recently, after the introduction of the so-called pathwise (or functional or Dupire) calculus [see Dupire (2009)], in the case of finite-dimensional underlying space various papers have been devoted to studying the...