Abstract. This paper studies regularity property of the value function for an infinite-horizon discounted cost impulse control problem, where the underlying controlled process is a multidimensional jump diffusion with possibly 'infinite-activity' jumps. Surprisingly, despite these jumps, we obtain the same degree of regularity as for the diffusion case, at least when the jump satisfies certain integrability conditions.

Value functions of impulse control problems are known to satisfy Quasi-Variational Inequalities (QVI) (Bensoussan and Lions (1982)). This paper proves the smooth-fit C 1 property of the value function for multi-dimensional controlled diffusions, using a viscosity solution approach. We show by examples how to exploit this regularity property to derive explicitly optimal policy and value function.

No abstract

This study was carried out on nanocomposites consisting of nanometer silica fillers embedded in thermoset polymers that were prepared via the in situ polymerization of ultraviolet (UV) curable systems containing different contents of nanometer silicas by irradiation of UV light. Because of the introduction of nanosilicas, the curing rates of the UV curing of dispersing systems were played down; that is, the curing times were prolonged, but the mechanical properties of the nanocomposites, such as tensile strength and Young's modulus, increased, and the thermostability of the nanocomposites at temperatures lower than 400 K improved. The dispersing states of nanometer silicas within the polymer matrix were characterized by transmission electron microscopy, and the results show that the nanometer silicas had good homogeneously dispersing states within nanocomposites containing less than 3 wt % nanometer silicas.