Valuation of a Financial Claim Contingent on the Outcome of a Quantum Measurement

We consider a rational agent who at time $0$ enters into a financial contract for which the payout is determined by a quantum measurement at some time $T>0$. The state of the quantum system is given in the Heisenberg representation by a known density matrix $\hat p$. How much will the agent be willing to pay at time $0$ to enter into such a contract? In the case of a finite dimensional Hilbert space, each such claim is represented by an observable $\hat X_T$ where the eigenvalues of $\hat X_T$ determine the amount paid if the corresponding outcome is obtained in the measurement. We prove, under reasonable axioms, that there exists a pricing state $\hat q$ which is equivalent to the physical state $\hat p$ on null spaces such that the pricing function $\Pi_{0T}$ takes the form $\Pi_{0T}(\hat X_T) = P_{0T}\,{\rm tr} ( \hat q \hat X_T)$ for any claim $\hat X_T$, where $P_{0T}$ is the one-period discount factor. By "equivalent" we mean that $\hat p$ and $\hat q$ share the same null space: thus, for any $|\xi \rangle \in \mathcal H$ one has $\langle \bar \xi | \hat p | \xi \rangle = 0$ if and only if $\langle \bar \xi | \hat q | \xi \rangle = 0$. We introduce a class of optimization problems and solve for the optimal contract payout structure for a claim based on a given measurement. Then we consider the implications of the Kochen-Specker theorem in such a setting and we look at the problem of forming portfolios of such contracts. Finally, we consider multi-period contracts.Comment: 27 pages, 1 figur

Pricing with Variance Gamma Information

In the information-based pricing framework of Brody, Hughston & Macrina, the market filtration {Ft}_t≥0 is generated by an information process {ξ_t}t≥0 defined in such a way that at some fixed time T an F_T -measurable random variable X_T is “revealed”. A cash flow H_T is taken to depend on the market factor X_T , and one considers the valuation of a financial asset that delivers H_T at T. The value of the asset S_t at any time t ∈ [0, T ) is the discounted conditional expectation of H_T with respect to F_t, where the expectation is under the risk neutral measure and the interest rate is constant. Then S_T− = H_T , and S_t = 0 for t ≥ T. In the general situation one has a countable number of cash flows, and each cash flow can depend on a vector of market factors, each associated with an information process. In the present work we introduce a new process, which we call the normalized variance-gamma bridge. We show that the normalized variance-gamma bridge and the associated gamma bridge are jointly Markovian. From these processes, together with the specification of a market factor X_T , we construct a so-called variance-gamma information process. The filtration is then taken to be generated by the information process together with the gamma bridge. We show that the resulting extended information process has the Markov property and hence can be used to develop pricing models for a variety of different financial assets, several examples of which are discussed in detail

Topological mass in seven dimensions and dualities in four dimensions

The massive topologically and self dual theories en seven dimensions are considered. The local duality between these theories is established and the dimensional reduction lead to the different dualities for massive antisymmetric fields in four dimensions.Comment: 7 page

Temporal visitation patterns of points of interest in cities on a planetary scale: a network science and machine learning approach

We aim to study the temporal patterns of activity in points of interest of cities around the world. In order to do so, we use the data provided by the online location-based social network Foursquare, where users make check-ins that indicate points of interest in the city. The data set comprises more than 90 million check-ins in 632 cities of 87 countries in 5 continents. We analyzed more than 11 million points of interest including all sorts of places: airports, restaurants, parks, hospitals, and many others. With this information, we obtained spatial and temporal patterns of activities for each city. We quantify similarities and differences of these patterns for all the cities involved and construct a network connecting pairs of cities. The links of this network indicate the similarity of temporal visitation patterns of points of interest between cities and is quantified with the Kullback-Leibler divergence between two distributions. Then, we obtained the community structure of this network and the geographic distribution of these communities worldwide. For comparison, we also use a Machine Learning algorithm - unsupervised agglomerative clustering - to obtain clusters or communities of cities with similar patterns. The main result is that both approaches give the same classification of five communities belonging to five different continents worldwide. This suggests that temporal patterns of activity can be universal, with some geographical, historical, and cultural variations, on a planetary scale.Comment: 18 pages, 7 figure

Thermo-rheological-kinetical Study of Compression Molding of Fibre-reinforced Composites

International audienceTo improve the modeling of fiber reinforced composites, we present in this work numerical methods able to compute both fiber-reinforced composites deformation in squeeze flow and thermal-kinetic evolution. The rheology is given by an homogeneous orthotropic model for fiber composites which describes the anisotropy of the in-plane fiber. The thermics is then extended accounting for the reaction here formulated by the Bailleul's model. Both physics are related since the kinetic evolution as well as the temperature profile modify the rheology of the composites, giving raise to the thermo-rheological-kinetical coupling by means of the viscosity temperature dependence. A study case is presented, where the mold temperature is set to 150 • C with a composite sample at 40 • C. Thermal transfer begins as well as sample compression at constant speed. We present the evolution of the reaction, temperature and viscosity at the core and the surface. Reaction in the core of the material is much quicker than in the surface. Which means that a mapping of viscosity values is presented during the reaction modifying the mechanical response

Lévy-Ito Models in Finance

We present an overview of the broad class of financial models in which the prices of assets are L évy-Ito processes driven by an n-dimensional Brownian motion and an independent Poisson random measure. The Poisson random measure is associated with an n-dimensional Lévy process. Each model consists of a pricing kernel, a money market account, and one or more risky assets. We show how the excess rate of return above the interest rate can be calculated for risky assets in such models, thus showing the relationship between risk and return when asset prices have jumps. The framework is applied to a variety of asset classes, allowing one to construct new models as well as interesting generalizations of familiar models

Bioinspired broadband antireflection coatings on GaSb

We report an inexpensive yet scalable templating technique for fabricating moth-eye antireflection gratings on gallium antimonide substrates. Non-close-packed colloidal monolayers are utilized as etching masks to pattern subwavelength-structured nipple arrays on GaSb. The resulting gratings exhibit superior broadband antireflection properties and thermal stability than conventional multilayer dielectric coatings. The specular reflection of the templated nipple arrays match with the theoretical predictions using a rigorous coupled-wave analysis model. The effect of the nipple shape and size on the antireflection properties has also been investigated by the same model. These biomimetic coatings are of great technological importance in developing efficient thermophotovoltaic cells

Application of large area SiPMs for the readout of a plastic scintillator based timing detector

In this study an array of eight 6 mm x 6 mm area SiPMs was coupled to the end of a long plastic scintillator counter which was exposed to a 2.5 GeV/c muon beam at the CERN PS. Timing characteristics of bars with dimensions 150 cm x 6 cm x 1 cm and 120 cm x 11 cm x 2.5 cm have been studied. An 8-channel SiPM anode readout ASIC (MUSIC R1) based on a novel low input impedance current conveyor has been used to read out and amplify SiPMs independently and sum the signals at the end. Prospects for applications in large-scale particle physics detectors with timing resolution below 100 ps are provided in light of the results