Optimal selling time in stock market over a finite time horizon

In this paper, we examine the best time to sell a stock at a price being as close as possible to its highest price over a finite time horizon [0, T ], where the stock price is modelled by a geometric Brownian motion and the ’closeness’ is measured by the relative error of the stock price to its highest price over [0, T ]. More precisely, we want to optimize the expression: where (V t ) t≥0 is a geometric Brownian motion with constant drift α and constant volatility σ > 0, M t = max Vs is the running maximum of the stock price, and the supremum is taken over all possible stopping times 0 ≤τ≤ T adapted to the natural filtration (F t ) t≥0 of the stock price. The above problem has been considered by Shiryaev, Xu and Zhou (2008) and Du Toit and Peskir (2009). In this paper we provide an independent proof that when α = 1 2 σ 2 , a selling strategy is optimal if and only if it sells the stock either at the terminal time T or at the moment when the stock price hits its maximum price so far. Besides, when α > 1 2 σ 2 , selling the stock at the terminal time T is the unique optimal selling strategy. Our approach to the problem is purely probabilistic and has been inspired by relating the notion of dominant stopping ρτ of a stopping time τ to the optimal stopping strategy arisen in the classical "Secretary Problem".     

Linear-scaling quantum mechanical methods for excited states

The poor scaling of many existing quantum mechanical methods with respect to the system size hinders their applications to large systems. In this tutorial review, we focus on latest research on linear-scaling or O(N) quantum mechanical methods for excited states. Based on the locality of quantum mechanical systems, O(N) quantum mechanical methods for excited states are comprised of two categories, the time-domain and frequency-domain methods. The former solves the dynamics of the electronic systems in real time while the latter involves direct evaluation of electronic response in the frequency-domain. The localized density matrix (LDM) method is the first and most mature linear-scaling quantum mechanical method for excited states. It has been implemented in time- and frequency-domains. The O(N) time-domain methods also include the approach that solves the time-dependent Kohn-Sham (TDKS) equation using the non-orthogonal localized molecular orbitals (NOLMOs). Besides the frequency-domain LDM method, other O(N) frequency-domain methods have been proposed and implemented at the first-principles level. Except one-dimensional or quasi-one-dimensional systems, the O(N) frequency-domain methods are often not applicable to resonant responses because of the convergence problem. For linear response, the most efficient O(N) first-principles method is found to be the LDM method with Chebyshev expansion for time integration. For off-resonant response (including nonlinear properties) at a specific frequency, the frequency-domain methods with iterative solvers are quite efficient and thus practical. For nonlinear response, both on-resonance and off-resonance, the time-domain methods can be used, however, as the time-domain first-principles methods are quite expensive, time-domain O(N) semi-empirical methods are often the practical choice. Compared to the O(N) frequency-domain methods, the O(N) time-domain methods for excited states are much more mature and numerically stable, and have been applied widely to investigate the dynamics of complex molecular systems.     

Labelling and binding of poly-( -lysine) to functionalised gold surfaces. Combined FT-IRRAS and XPS characterisation

We compare herein the interfacial reactivity of self-assembled monolayers (SAMs) of 11-mercaptoundecanoic acid (MUA), 1-undecanethiol (UDT) and 11-mercaptoundecanol (MUD) on gold surfaces towards aqueous solutions of poly-( -lysine) (PL). Liquid-phase labelling of PL with the alkyne dicobalt hexacarbonyl cluster 1 combined with analysis of the substrates by Fourier transform infrared reflection–absorption spectroscopy (FT-IRRAS) and X-ray photoelectron spectroscopy (XPS) revealed that irreversible binding of PL occurred in all cases. However, the mechanism of binding involved differed markedly from one monolayer to the other. The main mode of interaction of PL to MUA SAM was of electrostatic nature between the terminal carboxylate of MUA and the ammonium groups of PL. For a similar number of bound thiolate molecules, the UDT adsorbed layer was found less continuous than the MUA one, allowing a higher fraction of PL to directly bind to the gold surface. As for MUD, very little thiolate molecules were adsorbed, leaving bare gold surface areas for non specific adsorption of PL.     

Electronic and resonance Raman spectra of [Au2(CS3)2]2-. Spectroscopic properties of a "short" Au(I)-Au(I) bond

The anion [Au2(CS3)2]2- has an unusually short Au-Au distance (2.80 A) for a binuclear Au(I) complex. We report detailed Raman studies of the nBu4N+ salt of this complex, including FT-Raman of the solid and UV/vis resonance Raman of dimethyl sulfoxide solutions. All five totally symmetric vibrations of the anion have been located and assigned. A band at delta nu = 125 cm-1 is assigned to nu (Au2). The visible-region electronic absorption bands (384 (epsilon 30,680) and 472 nm (epsilon 610 M-1 cm-1)) are attributable to CS3(2-) localized transitions, as confirmed by the dominance of nu sym(C-Sexo) (delta nu = 951 cm-1) in RR spectra measured in this region. An absorption band at 314 nm (22,250 M-1 cm-1) is assigned as the metal-metal 1(d sigma*-->p sigma) transition, largely because nu sym(C-Sexo) is not strongly enhanced in RR involving this band. Observation of the expected strong resonance enhancement of nu (Au2) was precluded as a result of masking by intense solvent Rayleigh scattering in the UV.     

Luminescence Behavior of Polynuclear Alkynylcopper(I) Phosphines

A series of soluble trinuclear and tetranuclear copper(I) complexes containing ₃-^l acetylides , and have been synthesized and shown to exhibit rich photoluminescent behavior at room temperature. The electrochemistry of the trinuclear Cu(I) acetylide complexes and the excited-state redox properties of have been investigated. The X-ray crystal structures of and have been determined.     

Three-dimensional mode shapes of a tire using experimental modal analysis

Experimental modal analysis of a tire was carried out. Mode shapes in the radial, tangential and lateral directions of the tire under radial and tangential excitation, respectively, were obtained for the first time. The consistency of tire experimental modal frequencies in three directions was observed after careful design and adjustment of the test method. This indicates the accuracy of the experiments. The phenomena discovered in this experimental study, such as the mode shapes of the rim and the complex modes of the tire, are discussed in detail. The modal parameters acquired from experimental modal analysis of the tire can be used for the modeling of tire dynamics.     

Cobalt-catalysed asymmetric hydrovinylation of 1,3-dienes

In the presence of bidentate 1,n-bis-diphenylphosphinoalkane-CoCl₂ complexes {Cl₂Co[P ∼ P]} and Me₃Al or methylaluminoxane, acyclic (E)-1,3-dienes react with ethylene (1 atmosphere) to give excellent yields of hydrovinylation products. The regioselectivity (1,4- or 1,2-addition) and the alkene configuration (E- or Z-) of the resulting product depend on the nature of the ligand and temperature at which the reaction is carried out. Cobalt(ii)-complexes of 1,1-diphenylphosphinomethane and similar ligands with narrow bite angles give mostly 1,2-addition, retaining the E-geometry of the original diene. Complexes of most other ligands at low temperature (–40 °C) give almost exclusively a single branched product, (Z)-3-alkylhexa-1,4-diene, which arises from a 1,4-hydrovinylation reaction. A minor product is the linear adduct, a 6-alkyl-hexa-1,4-diene, also arising from a 1,4-addition of ethylene. As the temperature is increased, a higher proportion of the major branched-1,4-adduct appears as the (E)-isomer. The unexpectedly high selectivity seen in the Co-catalysed reaction as compared to the corresponding Ni-catalysed reaction can be rationalized by invoking the intermediacy of an η⁴-[(diene)[P ∼ P]CoH]⁺-complex and its subsequent reactions. The enhanced reactivity of terminal E-1,3-dienes over the corresponding Z-dienes can also be explained on the basis of the ease of formation of this η⁴-complex in the former case. The lack of reactivity of the X₂Co(dppb) (X = Cl, Br) complexes in the presence of Zn/ZnI₂ makes the Me₃Al-mediated reaction different from the previously reported hydroalkenylation of dienes. Electron-rich phospholanes, bis-oxazolines and N-heterocyclic carbenes appear to be poor ligands for the Co(ii)-catalysed hydrovinylation of 1,3-dienes. An extensive survey of chiral ligands reveals that complexes of DIOP, BDPP and Josiphos ligands are quite effective for these reactions even at –45 °C and enantioselectivities in the range of 90–99% ee can be realized for a variety of 1,3-dienes. Cobalt(ii)-complex of an electron-deficient Josiphos ligand is especially active, requiring only <1 mol% catalyst to effect the reactions.