A theoretical framework for the pricing of contingent claims in the presence of model uncertainty

The aim of this work is to evaluate the cheapest superreplication price of a general (possibly path-dependent) European contingent claim in a context where the model is uncertain. This setting is a generalization of the uncertain volatility model (UVM) introduced in by Avellaneda, Levy and Paras. The uncertainty is specified by a family of martingale probability measures which may not be dominated. We obtain a partial characterization result and a full characterization which extends Avellaneda, Levy and Paras results in the UVM case.Comment: Published at http://dx.doi.org/10.1214/105051606000000169 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Homomorphisms of binary Cayley graphs

A binary Cayley graph is a Cayley graph based on a binary group. In 1982, Payan proved that any non-bipartite binary Cayley graph must contain a generalized Mycielski graph of an odd-cycle, implying that such a graph cannot have chromatic number 3. We strengthen this result first by proving that any non-bipartite binary Cayley graph must contain a projective cube as a subgraph. We further conjecture that any homo- morphism of a non-bipartite binary Cayley graph to a projective cube must be surjective and we prove some special case of this conjecture

Deep wide field HI imaging of Messier 31

We report on preliminary results from a new deep 21-cm survey of the Andromeda galaxy, based on observations performed with the Synthesis Telescope and the 26-m antenna at DRAO. The HI distribution and kinematics of the disc are analyzed and basic dynamical properties are derived. New HI structures are discovered, like thin HI spur-like structures and an external arm in the disc outskirts. The HI spurs are related to perturbed stellar clumps outside the main disc of M31. The external arm lies on the far, receding side of the galaxy and has no obvious counterpart in the opposite side. These HI perturbations probably result from tidal interactions with companions. It is found a dynamical mass of 4.7 +/- 0.5 x10^11 Msol enclosed within a radius R = 38 kpc and a total mass of ~1 x10^12 Msol inside the virial radius.Comment: 4 pages, 1 figure, proceeding of the conference "Panoramic Radio Astronomy: Wide-field 1-2 GHz research on galaxy evolution", June 02 - 05 2009, Groninge

Dark matter in low mass surface density galaxies

Low mass surface density spiral and irregular galaxies like low surface brightness (LSB) and dwarf galaxies are unique laboratories to study the dynamical properties of Dark Matter halos because their mass is generally dominated by dark matter at all galactocentric radii. We present results from the largest sample ever assembled of high resolution Halpha velocity fields of LSB and dwarf galaxies in order to study their mass distributions.Comment: 2 pages, 1 figure, proceedings of the conference "Pathways Through an Eclectic Universe", Johan Knapen, Terry Mahoney, and Alexandre Vazdekis ed

A mathematical model for the Fermi weak interactions

We consider a mathematical model of the Fermi theory of weak interactions as patterned according to the well-known current-current coupling of quantum electrodynamics. We focuss on the example of the decay of the muons into electrons, positrons and neutrinos but other examples are considered in the same way. We prove that the Hamiltonian describing this model has a ground state in the fermionic Fock space for a sufficiently small coupling constant. Furthermore we determine the absolutely continuous spectrum of the Hamiltonian and by commutator estimates we prove that the spectrum is absolutely continuous away from a small neighborhood of the thresholds of the free Hamiltonian. For all these results we do not use any infrared cutoff or infrared regularization even if fermions with zero mass are involved

Hybridation of Bayesian networks and evolutionary algorithms for multi-objective optimization in an integrated product design and project management context

A better integration of preliminary product design and project management processes at early steps of system design is nowadays a key industrial issue. Therefore, the aim is to make firms evolve from classical sequential approach (first product design the project design and management) to new integrated approaches. In this paper, a model for integrated product/project optimization is first proposed which allows taking into account simultaneously decisions coming from the product and project managers. However, the resulting model has an important underlying complexity, and a multi-objective optimization technique is required to provide managers with appropriate scenarios in a reasonable amount of time. The proposed approach is based on an original evolutionary algorithm called evolutionary algorithm oriented by knowledge (EAOK). This algorithm is based on the interaction between an adapted evolutionary algorithm and a model of knowledge (MoK) used for giving relevant orientations during the search process. The evolutionary operators of the EA are modified in order to take into account these orientations. The MoK is based on the Bayesian Network formalism and is built both from expert knowledge and from individuals generated by the EA. A learning process permits to update probabilities of the BN from a set of selected individuals. At each cycle of the EA, probabilities contained into the MoK are used to give some bias to the new evolutionary operators. This method ensures both a faster and effective optimization, but it also provides the decision maker with a graphic and interactive model of knowledge linked to the studied project. An experimental platform has been developed to experiment the algorithm and a large campaign of tests permits to compare different strategies as well as the benefits of this novel approach in comparison with a classical EA

Conductance and absolutely continuous spectrum of 1D samples

We characterize the absolutely continuous spectrum of the one-dimensional Schr\"odinger operators $h=-\Delta+v$ acting on $\ell^2(\mathbb{Z}_+)$ in terms of the limiting behavior of the Landauer-B\"uttiker and Thouless conductances of the associated finite samples. The finite sample is defined by restricting $h$ to a finite interval $[1,L]\cap\mathbb{Z}_+$ and the conductance refers to the charge current across the sample in the open quantum system obtained by attaching independent electronic reservoirs to the sample ends. Our main result is that the conductances associated to an energy interval $I$ are non-vanishing in the limit $L\to\infty$ iff ${\rm sp}_{\rm ac}(h)\cap I=\emptyset$. We also discuss the relationship between this result and the Schr\"odinger Conjecture

Landauer-B\"uttiker and Thouless conductance

In the independent electron approximation, the average (energy/charge/entropy) current flowing through a finite sample S connected to two electronic reservoirs can be computed by scattering theoretic arguments which lead to the famous Landauer-B\"uttiker formula. Another well known formula has been proposed by Thouless on the basis of a scaling argument. The Thouless formula relates the conductance of the sample to the width of the spectral bands of the infinite crystal obtained by periodic juxtaposition of S. In this spirit, we define Landauer-B\"uttiker crystalline currents by extending the Landauer-B\"uttiker formula to a setup where the sample S is replaced by a periodic structure whose unit cell is S. We argue that these crystalline currents are closely related to the Thouless currents. For example, the crystalline heat current is bounded above by the Thouless heat current, and this bound saturates iff the coupling between the reservoirs and the sample is reflectionless. Our analysis leads to a rigorous derivation of the Thouless formula from the first principles of quantum statistical mechanics

Crystalline conductance and absolutely continuous spectrum of 1D samples

We characterize the absolutely continuous spectrum of half-line one-dimensional Schr\"odinger operators in terms of the limiting behavior of the Crystaline Landauer-B\"uttiker conductance of the associated finite samples

Decorated proofs for computational effects: Exceptions

We define a proof system for exceptions which is close to the syntax for exceptions, in the sense that the exceptions do not appear explicitly in the type of any expression. This proof system is sound with respect to the intended denotational semantics of exceptions. With this inference system we prove several properties of exceptions.Comment: 11 page