In a market with one safe and one risky asset, an investor with a long horizon, constant investment opportunities, and constant relative risk aversion trades with small proportional transaction costs. We derive explicit formulas for the optimal investment policy, its implied welfare, liquidity premium, and trading volume. At the first order, the liquidity premium equals the spread, times share turnover, times a universal constant. Results are robust to consumption and finite horizons. We exploit the equivalence of the transaction cost market to another frictionless market, with a shadow risky asset, in which investment opportunities are stochastic. The shadow price is also found explicitly.Mathematics Subject Classification: (2010) 91G10, 91G80. JEL Classification: G11, G12.

Two-dimensional electron gases (2DEGs) at oxide heterostructures are attracting considerable attention, as these might one day substitute conventional semiconductors at least for some functionalities. Here we present a minimal setup for such a 2DEG--the SrTiO 3 (110)-(4 × 1) surface, natively terminated with one monolayer of tetrahedrally coordinated titania. Oxygen vacancies induced by synchrotron radiation migrate underneath this overlayer; this leads to a confining potential and electron doping such that a 2DEG develops. Our angle-resolved photoemission spectroscopy and theoretical results show that confinement along (110) is strikingly different from the (001) crystal orientation. In particular, the quantized subbands show a surprising "semiheavy" band, in contrast with the analog in the bulk, and a high electronic anisotropy. This anisotropy and even the effective mass of the (110) 2DEG is tunable by doping, offering a high flexibility to engineer the properties of this system. oxide surface | electronic structure | quantum confinement | perovskite | ARPES T he 2D electron gas (2DEG) observed in oxide heterostructures such as LaAlO 3 /SrTiO 3 (1, 2) offers a possible alternative to conventional semiconductors, not only for electronics at the nanoscale (3) but also because of the possibility of spin-polarized (4) and superconducting (5, 6) currents. An even simpler setup is to create a 2DEG directly at SrTiO 3 . Recently this was achieved by irradiating a (001) surface (7, 8) with synchrotron radiation, albeit the origin of the resulting 2DEG is still under debate (7-9). This system has two major drawbacks: (i) surface oxygen vacancies are very reactive and (ii) the (001) surface has no unique surface termination, as TiO 2 and SrO terraces may develop, and the surface structure strongly depends on sample treatment and history (10).Here, we show that a 2DEG can also be induced at SrTiO 3 (110), which is stabilized and covered by a reconstructed overlayer. This overlayer automatically forms to compensate the intrinsic polarity of the system. A SrTiO 3 crystal can be viewed as a stack of alternating (SrTiO) 4+ and (O 2 ) 4− planes along the [110] orientation, resulting in a dipole moment that diverges with increasing crystal thickness (11). As is often true for polar surfaces, this is prevented by one of several compensation mechanisms (11). Specifically, the SrTiO 3 (110) surface spontaneously forms a (4 × 1) reconstruction upon various different sample treatments, including annealing in a tube furnace with flowing high-purity oxygen (12) and standard ultrahigh vacuum preparation procedures (13,14). The reconstruction consists of a 2D, tetrahedrally coordinated titania overlayer (Fig. 1A), which, with a nominal stoichiometry of (Ti 1.5 O 4 ) 2− , quenches the overall dipole moment (12, 15). Because the Ti atoms in the tetrahedral titania surface layer of the reconstruction are saturated by strong, directional bonds, the (4 × 1) surface is chemically quite inert (16). Results and DiscussionExposing the SrTiO 3 ...

The adsorption of Ni, Co, Mn, Ti, and Zr at the (√ 2 × √ 2)R45 •-reconstructed Fe 3 O 4 (001) surface was studied by scanning tunneling microscopy, x-ray and ultraviolet photoelectron spectroscopy, low-energy electron diffraction (LEED), and density functional theory (DFT). Following deposition at room temperature, metals are either adsorbed as isolated adatoms or fill the subsurface cation vacancy sites responsible for the (√ 2 × √ 2)R45 • reconstruction. Both configurations coexist, but the ratio of adatoms to incorporated atoms depends on the metal; Ni prefers the adatom configuration, Co and Mn form adatoms and incorporated atoms in similar numbers, and Ti and Zr are almost fully incorporated. With mild annealing, all adatoms transition to the incorporated cation configuration. At high coverage, the (√ 2 × √ 2)R45 • reconstruction is lifted because all subsurface cation vacancies become occupied with metal atoms, and a (1 × 1) LEED pattern is observed. DFT+U calculations for the extreme cases, Ni and Ti, confirm the energetic preference for incorporation, with calculated oxidation states in good agreement with photoemission experiments. Because the site preference is analogous to bulk ferrite (XFe 2 O 4) compounds, similar behavior is likely to be typical for elements forming a solid solution with Fe 3 O 4 .

Hole distribution for (Sr,Ca,Y,La)14Cu24O41 ladder compounds studied by x-ray absorption spectroscopy Nücker, N.; Merz, M.; Kuntscher, C.A.; Gerhold, S.; Schuppler, S.; Neudert, R.; Golden, M.S.; Fink, J.; Schild, D.

It is known that Heston's stochastic volatility model exhibits moment explosion, and that the critical moment s+ can be obtained by solving (numerically) a simple equation. This yields a leading order expansion for the implied volatility at large strikes: σBS(k, T ) 2 T ∼ Ψ(s+ − 1) × k (Roger Lee's moment formula). Motivated by recent "tail-wing" refinements of this moment formula, we first derive a novel tail expansion for the Heston density, sharpening previous work of Drȃgulescu and Yakovenko [Quant. Finance 2, 6 (2002), 443-453], and then show the validity of a refined expansion of the type σBS(k, T ) 2 T = (β1k 1/2 + β2 + . . . ) 2 , where all constants are explicitly known as functions of s+, the Heston model parameters, spot vol and maturity T . In the case of the "zero-correlation" Heston model such an expansion was derived by Gulisashvili and Stein [Appl. Math. Optim. 61, 3 (2010), 287-315]. Our methods and results may prove useful beyond the Heston model: the entire quantitative analysis is based on affine principles: at no point do we need knowledge of the (explicit, but cumbersome) closed form expression of the Fourier transform of log ST (equivalently: Mellin transform of ST ); what matters is that these transforms satisfy ordinary differential equations of Riccati type. Secondly, our analysis reveals a new parameter ("critical slope"), defined in a model free manner, which drives the second and higher order terms in tail-and implied volatility expansions.