Robust mean–variance hedging via G-expectation

In this paper we study mean–variance hedging under the $G$-expectation framework. Our analysis is carried out by exploiting the $G$-martingale representation theorem and the related probabilistic tools, in a continuous financial market with two assets, where the discounted risky one is modeled as a symmetric $G$-martingale. By tackling progressively larger classes of contingent claims, we are able to explicitly compute the optimal strategy under general assumptions on the form of the contingent claim.     

The asymptotic smile of a multiscaling stochastic volatility model

We consider a stochastic volatility model which captures relevant stylized facts of financial series, including the multi-scaling of moments. The volatility evolves according to a generalized Ornstein–Uhlenbeck processes with super-linear mean reversion.Using large deviations techniques, we determine the asymptotic shape of the implied volatility surface in any regime of small maturity $t\to 0$ or extreme log-strike $\left|\kappa \right|\to \infty$ (with bounded maturity). Even if the price has continuous paths, out-of-the-money implied volatility diverges for small maturity, producing a very pronounced smile.     

Orbits of strongly solvable spherical subgroups on the flag variety

Let G be a connected reductive complex algebraic group and B a Borel subgroup of G. We consider a subgroup \(H \subset B\) which acts with finitely many orbits on the flag variety G / B, and we classify the H-orbits in G / B in terms of suitable root systems. As well, we study the Weyl group action defined by Knop on the set of H-orbits in G / B, and we give a combinatorial model for this action in terms of weight polytopes.     

D0–D6 States Counting and GW Invariants

We describe a correspondence between the Donaldson?CThomas invariants enumerating D0?CD6 bound states on a Calabi?CYau 3-fold and certain Gromov?CWitten invariants counting rational curves in a family of blowups of weighted projective planes. This is a variation on a correspondence found by Gross?CPandharipande, with D0?CD6 bound states replacing representations of generalised Kronecker quivers. We build on a small part of the theories developed by Joyce?CSong and Kontsevich?CSoibelman for wall-crossing formulae and by Gross?CPandharipande?CSiebert for factorisations in the tropical vertex group. Along the way we write down an explicit formula for the BPS state counts which arise up to rank 3 and prove their integrality. We also compare with previous ??noncommutative DT invariants?? computations in the physics literature.     

Adaptive Organic Nanoparticles of a Teflon‐Coated Iron (III) Porphyrin Catalytically Activate Dioxygen for Cyclohexene Oxidation

Self‐organized organic nanoparticles (ONP) are adaptive to the environmental reaction conditions. ONP of fluorous alkyl iron(III) porphyrin catalytically oxidize cyclohexene to the allylic oxidation products. In contrast, the solvated metalloporphyrin yields both allylic oxidation and epoxidation products. The ONP system facilitates a greener reaction because about 89% reaction medium is water, molecular oxygen is used in place of synthetic oxidants, and the ambient reaction conditions used require less energy. The enhanced catalytic activity of these ONP is unexpected because the metalloporphyrins in the nanoaggregates are in the close proximity and the TON should diminish by self‐oxidative degradation. The fluorous alkyl chain stabilizes the ONP toward self‐oxidative degradation.     

Dynamics of some piecewise smooth Fermi-Ulam models

We find a normal form which describes the high energy dynamics of a class of piecewise smooth Fermi-Ulam ping pong models. Depending on the value of a single real parameter, the dynamics can be either hyperbolic or elliptic. In the first case, we prove that the set of orbits undergoing Fermi acceleration has zero measure but full Hausdorff dimension. We also show that for almost every orbit, the energy eventually falls below a fixed threshold. In the second case, we prove that, generically, we have stable periodic orbits for arbitrarily high energies and that the set of Fermi accelerating orbits may have infinite measure.     

Dispersion and repulsion contributions to the solvation free energy: comparison of quantum mechanical and classical approaches in the polarizable continuum model

We report a systematic comparison of the dispersion and repulsion contributions to the free energy of solvation determined using quantum mechanical self-consistent reaction field (QM-SCRF) and classical methods. In particular, QM-SCRF computations have been performed using the dispersion and repulsion expressions developed in the framework of the integral equation formalism of the polarizable continuum model, whereas classical methods involve both empirical pairwise potential and surface-dependent approaches. Calculations have been performed for a series of aliphatic and aromatic compounds containing prototypical functional groups in four solvents: water, octanol, chloroform, and carbon tetrachloride. The analysis is focused on the dependence of the dispersion and repulsion components on the level of theory used in QM-SCRF computations, the contribution of those terms in different solvents, and the magnitude of the coupling between electrostatic and dispersion-repulsion components. Finally, comparison is made between the dispersion-repulsion contributions obtained from QM-SCRF calculations and the results determined from classical approaches.     

Confined Polymerization in Highly Ordered Mesoporous Organosilicas

Hybrid mesoporous organosilica exhibiting crystal‐like order in the walls provided an ideal channel reaction vessel for the confined polymerization of acrylonitrile (PAN). The resulting high‐molecular‐mass PAN fills the channels at high yield and forms an ordered nanostructure of polymer nanobundles enclosed into the hybrid matrix. The in situ thermal transformation of PAN into rigid polyconjugated and, eventually, into condensed polyaromatic carbon nanofibers, retains the periodic architecture. Simultaneously, the matrix evolves showing the fusion of the p‐phenylene rings and the cleavage of carbon?silicon bonds: this gives rise to graphitic‐carbon/silica nanocomposites containing hyper‐oxydrylated silica nanophases. Interestingly, the 3D hexagonal mesostructure survives in the carbonaceous material. The exploitation of porous materials of high capacity and a hybrid nature, for polymerization in the confined state, followed by high temperature treatments, allowed us to achieve unique and precisely fabricated nanostructures, thus paving the way for the construction of fine‐tuned electronic and light‐harvesting materials.