Optimal portfolio for a small investor in a market model with discontinuous prices

A consumption-investment problem is considered for a small investor in the case of a market model in which prices evolve according to a stochastic equation with a jump-process component. The techniques we use include the martingale representation theorem, Lagrange multiplier methods, and Markovian methods for the resolution of stochastic differential equations. We establish a Black-Scholes formula.     

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Sans résumé     

Overcoming Crystallinity Limitations of Aluminium Metal-Organic Frameworks by Oxalic Acid Modulated Synthesis

A modulated synthesis approach based on the chelating properties of oxalic acid (H₂C₂O₄) is presented as a robust and versatile method to achieve highly crystalline Al-based metal-organic frameworks. A comparative study on this method and the already established modulation by hydrofluoric acid was conducted using MIL-53 as test system. The superior performance of oxalic acid modulation in terms of crystallinity and absence of undesired impurities is explained by assessing the coordination modes of the two modulators and the structural features of the product. The validity of our approach was confirmed for a diverse set of Al-MOFs, namely X-MIL-53 (X=OH, CH₃O, Br, NO₂), CAU-10, MIL-69, and Al(OH)ndc (ndc=1,4-naphtalenedicarboxylate), highlighting the potential benefits of extending the use of this modulator to other coordination materials.     

Chromatographic behaviour of steroidal saponins studied by high-performance liquid chromatography-mass spectrometry

The chromatographic behaviour of steroidal saponins found in Anemarrhena asphodeloides, Asparagus officinalis, Convallaria majalis, Digitalis purpurea and Ruscus aculeatus was studied by HPLC-MS using a C-18 reversed-phase column and aqueous acetonitrile or aqueous methanol mobile phase gradients, with or without the addition of 1% acetic acid. The behaviour was compared to that of triterpene saponins found in Aesculus hippocastanum, Centella asiatica, Panax notoginseng and Potentilla tormentilla. Inclusion of methanol in the mobile phase under acidic conditions was found to cause furostanol saponins hydroxylated at C-22 to chromatograph as broad peaks, whereas the peak shapes of the spirostanol saponins and triterpene saponins studied remained acceptable. In aqueous methanol mobile phases without the addition of acid, furostanol saponins chromatographed with good peak shape, but each C-22 hydroxylated furostanol saponin was accompanied by a second chromatographic peak identified as its C-22 methyl ether. Methanolic extracts analysed in non-acidified aqueous acetonitrile mobile phases also resolved pairs of C-22 hydroxy and C-22 methoxy furostanol saponins. The C-22 methyl ether of deglucoruscoside was found to convert to deglucoruscoside during chromatography in acidified aqueous acetonitrile, or by dissolving in water. Poor chromatography of furostanol saponins in acidified aqueous methanol is due to the interconversion of the C-22 hydroxy and C-22 methoxy forms. It is recommended that initial analysis of saponins by HPLC-MS using a C-18 stationary phase is performed using acidified aqueous acetonitrile mobile phase gradients. The existence of naturally-occurring furostanol saponins methoxylated at C-22 can be investigated with aqueous acetonitrile mobile phases and avoiding methanol in the extraction solvent.     

Electrochromatography in poly(dimethyl)siloxane microchips using organic monolithic stationary phases

This paper shows the in situ synthesis of an hexyl acrylate monolith in PDMS microfluidic devices and its subsequent use as stationary phase for electrochromatography on chip. To overcome the ability of PDMS material to absorb organic monomers, surface modification of the enclosed channels was realized by UV-mediated graft polymerization. This grafting procedure is based on the preliminary adsorption of a photoinitiator onto the PDMS surface and polymerization of charged monomers. Next, hexyl acrylate monoliths were cast in situ using photopolymerization process. The chromatographic behavior of the monolithic column was confirmed by the successful separation of derivatized catecholamines in the PDMS device using a 30 mm effective separation length (100 microm x 100 microm section). Efficiencies reached up to 200,000 plates per meter.     

Information,no-arbitrage and completeness for asset price models with a change point

We consider a general class of continuous asset price models where the drift and the volatility functions, as well as the driving Brownian motions, change at a random time τ$\tau$. Under minimal assumptions on the random time and on the driving Brownian motions, we study the behavior of the model in all the filtrations which naturally arise in this setting, establishing martingale representation results and characterizing the validity of the NA1 and NFLVR no-arbitrage conditions.     

Medium range optimization of copper extraction planning under uncertainty in future copper prices

Deterministic mine planning models along a time horizon have proved to be very effective in supporting decisions on sequencing the extraction of material in copper mines. Some of these models have been developed for, and used successfully by CODELCO, the Chilean state copper company. In this paper, we wish to consider the uncertainty in a very volatile parameter of the problem, namely, the copper price along a given time horizon. We represent the uncertainty by a multistage scenario tree. The resulting stochastic model is then converted into a mixed 0–1 Deterministic Equivalent Model using a compact representation. We first introduce the stochastic model that maximizes the expected profit along the time horizon over all scenarios (i.e., as in a risk neutral environment). We then present several approaches for risk management in a risk averse environment. Specifically, we consider the maximization of the Value-at-Risk and several variants of the Conditional Value-at-Risk (one of them is new), the maximization of the expected profit minus the weighted probability of having an undesirable scenario in the solution provided by the model, and the maximization of the expected profit subject to stochastic dominance constraints recourse-integer for a set of profiles given by the pairs of target profits and bounds on either the probability of failure or the expected profit shortfall. We present an extensive computational experience on the actual problem, by comparing the risk neutral approach, the tested risk averse strategies and the performance of the traditional deterministic approach that uses the expected value of the uncertain parameters. The results clearly show the advantage of using the risk neutral strategy over the traditional deterministic approach, as well as the advantage of using any risk averse strategy over the risk neutral one.     

Perturbations for Delaunay and weighted Delaunay 3D triangulations

The Delaunay triangulation and the weighted Delaunay triangulation are not uniquely defined when the input set is degenerate. We present a new symbolic perturbation that allows to always define these triangulations in a unique way, as soon as the points are not all coplanar. No flat tetrahedron exists in the defined triangulation. The perturbation scheme is easy to code. It is implemented in cgal, and guarantees that both vertex insertion and vertex removal are fully robust.     

Some Lower Bounds in the B. and M. Shapiro Conjecture for Flag Varieties

The B. and M. Shapiro conjecture stated that all solutions of the Schubert Calculus problems associated with real points on the rational normal curve should be real. For Grassmannians, it was proved by Mukhin, Tarasov, and Varchenko. For flag varieties, Sottile found a counterexample and suggested that all solutions should be real under certain monotonicity conditions. In this paper, we compute lower bounds on the number of real solutions for some special cases of the B. and M. Shapiro conjecture for flag varieties, when Sottile’s monotonicity conditions are not satisfied.     

NMR parameters in alkali, alkaline earth and rare earth fluorides from first principle calculations

(19)F isotropic chemical shifts for alkali, alkaline earth and rare earth of column 3 basic fluorides are measured and the corresponding isotropic chemical shieldings are calculated using the GIPAW method. When using the PBE exchange-correlation functional for the treatment of the cationic localized empty orbitals of Ca(2+), Sc(3+) (3d) and La(3+) (4f), a correction is needed to accurately calculate (19)F chemical shieldings. We show that the correlation between experimental isotropic chemical shifts and calculated isotropic chemical shieldings established for the studied compounds allows us to predict (19)F NMR spectra of crystalline compounds with a relatively good accuracy. In addition, we experimentally determine the quadrupolar parameters of (25)Mg in MgF(2) and calculate the electric field gradients of (25)Mg in MgF(2) and (139)La in LaF(3) using both PAW and LAPW methods. The orientation of the EFG components in the crystallographic frame, provided by DFT calculations, is analysed in terms of electron densities. It is shown that consideration of the quadrupolar charge deformation is essential for the analysis of slightly distorted environments or highly irregular polyhedra.