Numerical Methods for the Pricing of Swing Options: A Stochastic Control Approach

In the natural gas market, many derivative contracts have a large degree of flexibility. These are known as Swing or Take-Or-Pay options. They allow their owner to purchase gas daily, at a fixed price and according to a volume of their choice. Daily, monthly and/or annual constraints on the purchased volume are usually incorporated. Thus, the valuation of such contracts is related to a stochastic control problem, which we solve in this paper using new numerical methods. Firstly, we extend the Longstaff–Schwarz methodology (originally used for Bermuda options) to our case. Secondly, we propose two efficient parameterizations of the gas consumption, one is based on neural networks and the other on finite elements. It allows us to derive a local optimal consumption law using a stochastic gradient ascent. Numerical experiments illustrate the efficiency of these approaches. Furthermore, we show that the optimal purchase is of bang-bang type.      

Statistical physics of inference: thresholds and algorithms

Many questions of fundamental interest in today's science can be formulated as inference problems: some partial, or noisy, observations are performed over a set of variables and the goal is to recover, or infer, the values of the variables based on the indirect information contained in the measurements. For such problems, the central scientific questions are: Under what conditions is the information contained in the measurements sufficient for a satisfactory inference to be possible? What are the most efficient algorithms for this task? A growing body of work has shown that often we can understand and locate these fundamental barriers by thinking of them as phase transitions in the sense of statistical physics. Moreover, it turned out that we can use the gained physical insight to develop new promising algorithms. The connection between inference and statistical physics is currently witnessing an impressive renaissance and we review here the current state-of-the-art, with a pedagogical focus on the Ising model which, formulated as an inference problem, we call the planted spin glass. In terms of applications we review two classes of problems: (i) inference of clusters on graphs and networks, with community detection as a special case and (ii) estimating a signal from its noisy linear measurements, with compressed sensing as a case of sparse estimation. Our goal is to provide a pedagogical review for researchers in physics and other fields interested in this fascinating topic.     

Ab initio study of the mechanism for photoinduced Yl-oxygen exchange in uranyl(VI) in acidic aqueous solution

The mechanism for the photochemically induced isotope-exchange reaction U(17/18)O2(2+)(aq) + H2(16)O <==> U(16)O2(2+)(aq) + H2(17/18)O has been studied using quantum-chemical methods. There is a dense manifold of states between 22,000 and 54,000 cm(-1) that results from excitations from the sigma(u) and pi(u) bonding orbitals in the (1)Sigma(g)(+) ground state to the nonbonding f(delta) and f(phi) orbitals localized on uranium. On the basis of investigations of the reaction profile in the (1)Sigma(g)(+) ground state and the excited states (3)Delta(g) (the lowest triplet state) and (3)Gamma(g) (one of the several higher triplet states), the latter two of which have the electron configurations sigma(u)f(delta) and pi(u)f(phi), respectively, we suggest that the isotope exchange takes place in one of the higher triplet states, of which the (3)Gamma(g) state was used as a representative. The geometries of the luminescent (3)Delta(g) state, the lowest in the sigma(u)f(delta,phi) manifold (the "sigma" states), and the (1)Sigma(g)(+) ground state are very similar, except that the bond distances are slightly longer in the former. This is presumably a result of transfer of a bonding electron to a nonbonding f orbital, which makes the excited state in some respects similar to uranyl(V). As is the case for all of the states of the pi(u)f(delta,phi) manifold (the "pi" states), the geometry of the (3)Gamma(g) state is very different from that of the (3)Delta(g) "sigma" state and has nonequivalent U-O(yl) distances of 1.982 and 1.763 A; in the (3)Gamma(g) state, the yl-exchange takes place by transfer of a proton or hydrogen from water to the more distant yl-oxygen. The activation barriers for proton/hydrogen transfer in the ground state and the (3)Delta(g) and (3)Gamma(g) states are 186, 219, and 84 kJ/mol, respectively. The relaxation energy for the (3)Gamma(g) state in the solvent after photoexcitation is -86 kJ/mol, indicating that the energy barrier can be overcome; the "pi" states are therefore the most probable route for proton/hydrogen transfer. They can be populated after UV irradiation but are too high in energy (approximately 36,000-40,000 cm(-1)) to be reached by a single-photon absorption at 436 nm (22,900 cm(-1)), where experimental data have demonstrated that exchange can take place. Okuyama et al. [Bull. Res. Lab. Nucl. React. (Tokyo Inst. Technol.) 1978, 3, 39-50] have demonstrated that an intermediate is formed when an acidic solution of UO2(2+)(aq) is flash-photolyzed in the UV range. The absorption spectrum of this short-lived intermediate (which has a maximum at 560 nm) indicates that this species arises from 436 nm excitation of the luminescent (3)Delta(g) state (which has a lifetime of approximately 2 x 10(-6) s); this is sufficient to reach the reactive "pi" states. It has been speculated that the primary reaction in acidic solutions of UO2(2+)(aq) is the formation of a uranyl(V) species; our results indicate that the structure in the luminescent state has some similarity to that of UO2(+) but that the reactive species in the "pi" states is a cation radical with a distinctly different structure.     

Aggregation and self-assembly of amphiphilic block copolymers in aqueous dispersions of carbon nanotubes

The self-assembly (SA) of amphiphilic block copolymers (poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide)) was investigated in dispersions of single-walled and multiwalled carbon nanotubes (SWNT and MWNT, respectively) as a function of temperature. Differential scanning calorimetry (DSC) was used for characterization of the thermal behavior of the combined polymers-nanostructures system, and spin-probe electron paramagnetic resonance (EPR) was employed for probing the local dynamic and polarity of the polymer chains in the presence of nanostructures. It was found that SWNT and MWNT modify the temperature, enthalpy, and dynamic behavior of polymer SA. In particular, SWNT were found to increase the cooperativity of aggregating chains and dominate aggregate dynamics. MWNT reduced the cooperativity, while colloidal carbon black additives, studied for comparison, did not show similar effects. The experimental observations are consistent with the suggestion that dimensional matching between the characteristic radius of the solvated polymer chains and the dimensions of additives dominate polymer SA in the hybrid system.     

Calix[n]arenes as components for the construction of micellar systems: synthesis and self-assembly properties of 5,11,17-Tris[(dimethylamino)methyl]-25-monoalkoxy-26,27,28-trihydroxycalix[4]arene derivatives

A series of mono-O-alkylated calix [4] arenes derivatives, with alkyl chain lengths of between 1 and 12 carbon atoms are reported. Monoalkylation is best achieved using potassium carbonate as the weak base and the respective alkyl iodide for chain lengths of one to three carbon atoms and using caesium fluoride as the base and the respective alkyl iodide for longer chain lengths. The mono-alkylated derivatives were converted into the tri-para-dimethylaminomethylene derivatives by the para-quinonemethide reaction in good yields. Surface tension measurements showed that at pH 2, 4, 6 and 8 all the tri-dimethylaminomethylene derivatives showed surfactant behaviour, and at pH 2 all show a Critical Micellar Concentration values. No correlation between Critical Micellar Concentration values and chain length is observed. Dynamic Light Scattering measurements showed that the CMC behaviour may be correlated with the observed aggregate sizes. The solid state structure of mono-O-ethoxy-calix[4]arene is described, in this structure a 1-D inclusion polymer is observed.     

Modeling of HeN+ clusters. II. Calculation of He3+ vibrational spectrum

We have computed the vibrational spectrum of the helium ionized trimer He(3)(+) using three different potential energy surfaces [D. T. Chang and G. L. Gellene, J. Chem. Phys. 119, 4694 (2003); E. Scifoni et al., ibid. 125, 164304 (2006); I. Paidarova et al., Chem. Phys. 342, 64 (2007)]. Differences in the details of these potential energy surfaces induce discrepancies between bound state energies of the order of 0.01 eV. The effects of the geometric phase induced by the conical intersection between the ground electronic potential energy surface and the first excited one are studied by computing vibrational spectra with and without this phase. The six lowest vibrational bound states are negligibly affected by the geometric phase. Indeed, they correspond to wavefunctions localized in the vicinity of the linear symmetric configurations and can be assigned well defined vibrational quantum numbers. On the other hand, higher excited states are delocalized, cannot be assigned definite vibrational quantum numbers, and the geometric phase shifts their energies by approximately 0.005 eV.     

Control of the regioselectivity for new fluorinated amphiphilic cyclodextrins: synthesis of di- and tetra(6-deoxy-6-alkylthio)- and 6-(perfluoroalkypropanethio)-alpha-cyclodextrin derivatives

Twelve new di- and tetraderivatized alpha-cyclodextrin molecules having either alkylthio and perfluoroalkylpropanethio functions at the primary face have been synthesized by using the procedure of Sinay for di-O-debenzylation of perbenzylated alpha-cyclodextrins. A new strategy of protection/deprotection has been developed for introducing the lipophilic chains. The coupling reaction involves the reaction between the appropriate alpha-cyclodextin derivative, regioselectively modified at C-6 positions by a good leaving group (O-mesityl for disubstituted or iodine for tetrasubstituted derivatives), with the thioalkyl or the thioperfluoroakylpropane chains. These nucleophilic reagents are obtained from the in situ basic hydrolysis of the alkylisothiouronium bromides or perfluoalkylropropane and the isothiouronium iodides. These multistep reactions give the desired amphiphilic alpha-cyclodextrins in good overall yields of 33% to 58%.     

Outliers in the Single Ring Theorem

This text is about spiked models of non-Hermitian random matrices. More specifically, we consider matrices of the type \({\mathbf {A}}+{\mathbf {P}}\), where the rank of \({\mathbf {P}}\) stays bounded as the dimension goes to infinity and where the matrix \({\mathbf {A}}\) is a non-Hermitian random matrix, satisfying an isotropy hypothesis: its distribution is invariant under the left and right actions of the unitary group. The macroscopic eigenvalue distribution of such matrices is governed by the so called Single Ring Theorem, due to Guionnet, Krishnapur and Zeitouni. We first prove that if \({\mathbf {P}}\) has some eigenvalues out of the maximal circle of the single ring, then \({\mathbf {A}}+{\mathbf {P}}\) has some eigenvalues (called outliers) in the neighborhood of those of \({\mathbf {P}}\), which is not the case for the eigenvalues of \({\mathbf {P}}\) in the inner cycle of the single ring. Then, we study the fluctuations of the outliers of \({\mathbf {A}}\) around the eigenvalues of \({\mathbf {P}}\) and prove that they are distributed as the eigenvalues of some finite dimensional random matrices. Such kind of fluctuations had already been shown for Hermitian models. More surprising facts are that outliers can here have very various rates of convergence to their limits (depending on the Jordan Canonical Form of \({\mathbf {P}}\)) and that some correlations can appear between outliers at a macroscopic distance from each other (a fact already noticed by Knowles and Yin in (Ann Probab 42:1980–2031, 2014) in the Hermitian case, but only for non Gaussian models, whereas spiked Gaussian matrices belong to our model and can have such correlated outliers). Our first result generalizes a result by Tao proved specifically for matrices with i.i.d. entries, whereas the second one (about the fluctuations) is new.     

Flash Latex Production in a Continuous Helical Photoreactor: Releasing the Brake Pedal on Acrylate Chain Radical Polymerization

The continuous photopolymerization of acrylate and methacrylate monomer miniemulsions (25% solids content) is investigated at room temperature in a compact helix minireactor. Using n‐butyl acrylate, the process yields 95% conversion after only 27 s residence time, and gel‐free high‐molecular‐weight products. Under optimized conditions, a 25‐fold increase in efficiency is obtained when compared to a batch photopolymerization. The reaction set‐up offers a frugal process because of moderate irradiance (2.6 mW cm^?2), photoinitiator concentration (0.75 wt%), and low‐power UV‐A fluorescent lamp.