Hedging with temporary price impact

We consider the problem of hedging a European contingent claim in a Bachelier model with temporary price impact as proposed by Almgren and Chriss (J Risk 3:5–39, 2001). Following the approach of Rogers and Singh (Math Financ 20:597–615, 2010) and Naujokat and Westray (Math Financ Econ 4(4):299–335, 2011), the hedging problem can be regarded as a cost optimal tracking problem of the frictionless hedging strategy. We solve this problem explicitly for general predictable target hedging strategies. It turns out that, rather than towards the current target position, the optimal policy trades towards a weighted average of expected future target positions. This generalizes an observation of Gârleanu and Pedersen (Dynamic portfolio choice with frictions. Preprint, 2013b) from their homogenous Markovian optimal investment problem to a general hedging problem. Our findings complement a number of previous studies in the literature on optimal strategies in illiquid markets as, e.g., Gârleanu and Pedersen (Dynamic portfolio choice with frictions. Preprint, 2013b), Naujokat and Westray (Math Financ Econ 4(4):299–335, 2011), Rogers and Singh (Math Financ 20:597–615, 2010), Almgren and Li (Option hedging with smooth market impact. Preprint, 2015), Moreau et al. (Math Financ. doi: 10.1111/mafi.12098, 2015), Kallsen and Muhle-Karbe (High-resilience limits of block-shaped order books. Preprint, 2014), Guasoni and Weber (Mathematical Financ. doi: 10.1111/mafi.12099, 2015a; Nonlinear price impact and portfolio choice. Preprint, 2015b), where the frictionless hedging strategy is confined to diffusions. The consideration of general predictable reference strategies is made possible by the use of a convex analysis approach instead of the more common dynamic programming methods.     

Atomic mechanism of the heating-induced phase transitions of the simple monatomic glasses

Atomic mechanism of the heating-induced phase transitions of the monatomic Lennard-Jones (LJ) glass has been studied via molecular dynamics (MD) simulations. Monatomic LJ glass was heated up at two different heating rates, crystallization occurs at the lowest one and further heating leads to the melting of LJ crystal. Thermodynamics of the phase transitions and corresponding evolution of structural properties upon heating have been analyzed in details. Atomic mechanism of a crystallization of the glassy state was monitored via spatio-temporal arrangements of the atoms involved in the 1421 bond-pair of the fcc crystalline structure. The 1421 bond-pair was detected via the Honeycutt-Andersen analysis [J.D. Honeycutt, H.C. Andersen, J. Phys. Chem. 91 (1987) 4950]. We found that crystallization of the monatomic LJ glass occurs via homogeneous local rearrangements of atoms in the glassy matrix and we found an important role of the liquid-like atoms (existed in the glassy state) in crystallization of the system. In addition, spatio-temporal arrangements of the liquid-like atoms in the system upon further heating were shown in order to clarify the atomic mechanism of a melting of the obtained LJ crystal. Liquid-like atoms were defined by the Lindemann melting criterion. Our results provide previously un-reported data and give deeper understanding of the heating-induced phase transitions in the less stable metallic glasses, which have been observed in practice.     

Remote entanglement between a single atom and a Bose-Einstein condensate

Entanglement between stationary systems at remote locations is a key resource for quantum networks. We report on the experimental generation of remote entanglement between a single atom inside an optical cavity and a Bose-Einstein condensate (BEC). To produce this, a single photon is created in the atom-cavity system, thereby generating atom-photon entanglement. The photon is transported to the BEC and converted into a collective excitation in the BEC, thus establishing matter-matter entanglement. After a variable delay, this entanglement is converted into photon-photon entanglement. The matter-matter entanglement lifetime of 100 μs exceeds the photon duration by 2 orders of magnitude. The total fidelity of all concatenated operations is 95%. This hybrid system opens up promising perspectives in the field of quantum information.