Quantum Bounds for Option Prices

Option pricing is the most elemental challenge of mathematical finance. Knowledge of the prices of options at every strike is equivalent to knowing the entire pricing distribution for a security, as derivatives contingent on the security can be replicated using options. The available data may be insufficient to determine this distribution precisely, however, and the question arises: What are the bounds for the option price at a specified strike, given the market-implied constraints? Positivity of the price map imposed by the principle of no-arbitrage is here utilised, via the Gelfand-Naimark-Segal construction, to transform the problem into the domain of operator algebras. Optimisation in this larger context is essentially geometric, and the outcome is simultaneously super-optimal for all commutative subalgebras. This generates an upper bound for the price of a basket option. With innovative decomposition of the assets in the basket, the result is used to create converging families of price bounds for vanilla options, interpolate the volatility smile, price options on cross FX rates, and analyse the relationships between swaption and caplet prices.Comment: 33 pages, 18 figure

The promise of multicyclic control

Several types of rotors which employ multicyclic control are reviewed and compared. Their differences are high-lighted and their potential advantages and disadvantages are discussed. The flow field these rotors must operate in is discussed, and it is shown that simultaneous elimination of vibration and oscillatory blade loads is not an inherent solution to the roughness problem. The use of rotor blades as energy absorbers is proposed. Input-output relations are considered and a gain control for ROMULAN, a multicyclic controlling computer program, is introduced. Implications of the introduction of multicyclic systems into helicopters are discussed

Multicyclic jet-flap control for alleviation of helicopter blade stresses and fuselage vibration

Results of wind tunnel tests of a 12 meter-diameter-rotor utilizing multicyclic jet-flap control deflection are presented. Analyses of these results are shown, and experimental transfer functions are determined by which optimal control vectors are developed. These vectors are calculated to eliminate specific harmonic bending stresses, minimize rms levels (a measure of the peak-to-peak stresses), or minimize vertical vibratory loads that would be transmitted to the fuselage. Although the specific results and the ideal control vectors presented are for a specific jet-flap driven rotor, the method employed for the analyses is applicable to similar investigations. A discussion of possible alternative methods of multicyclic control by mechanical flaps or nonpropulsive jet-flaps is presented

Do You See What I See?: Exploring the Relationship Between OCD Symptomatology and Theory of Mind Ability

A great deal of research supports that Theory of Mind (ToM; the ability to make inferences about the emotions, beliefs, and intentions of others) is impaired in people with symptoms of schizophrenia, autism, bipolar disorder, panic disorder, and obsessive compulsive disorder (OCD), to name a few. The present study focused on OCD, hypothesizing a negative correlation between the presence of OC symptomatology and ToM ability. Participants (N = 179) were undergraduate students from Butler University as well as participants recruited from mental health facilities, hospitals, and other organizations in the Indianapolis area. Participants completed several questionnaires, including measures of ToM (the Reading the Mind in the Eyes test, the Hinting task) and OCD symptoms (the OCI-R). As hypothesized, higher OC levels correlate with lower levels of some aspects of ToM

The Effect of the Third Dimension on Rough Surfaces Formed by Sedimenting Particles in Quasi-Two-Dimensions

The roughness exponent of surfaces obtained by dispersing silica spheres into a quasi-two-dimensional cell is examined. The cell consists of two glass plates separated by a gap, which is comparable in size to the diameter of the beads. Previous work has shown that the quasi-one-dimensional surfaces formed have two distinct roughness exponents in two well-defined length scales, which have a crossover length about 1cm. We have studied the effect of changing the gap between the plates to a limit of about twice the diameter of the beads.Comment: 4 pages, 4 figures, submitted to IJMP

CFD Script for Rapid TPS Damage Assessment

This grid generation script creates unstructured CFD grids for rapid thermal protection system (TPS) damage aeroheating assessments. The existing manual solution is cumbersome, open to errors, and slow. The invention takes a large-scale geometry grid and its large-scale CFD solution, and creates a unstructured patch grid that models the TPS damage. The flow field boundary condition for the patch grid is then interpolated from the large-scale CFD solution. It speeds up the generation of CFD grids and solutions in the modeling of TPS damages and their aeroheating assessment. This process was successfully utilized during STS-134

Effective Computer Programming Instruction for pre-University Albanian Students

The relationship between pre-university students and technology is frequently overrated.While we receive glowing reports about how young people are knowledgeable aboutcomputers, the truth is that their knowledge is typically about computer content and themanipulation of applications. Young students too often treat the actual programming andunderstanding of computers as a sort of magical mystery.In this paper we look at a new Albanian initiative to identify and nurture the mosttalented of our pre-university students. In particular we look at contributions to the goalof making Albanians the most talented programmers in this area of Europe.The study addresses the issue of how to get young people interested in programmingby focusing on non-syntactic procedures. The authors consider two programmingenvironments that teach through the use of objects and problem solving skills

Extrusion of Complex Surface Meshes Utilizing Face Offsetting and Mean Curvature Smoothing

Grids for three-dimensional Computational Fluid Dynamics problems frequently require a prismatic layer of cells, typically extruded in the off-body direction from a two-dimensional surface mesh to properly resolve boundary layers. When the surface geometry is complex, the extrusion process can fail, resulting in the physical boundary layer being thicker than the prismatic layer, leading to under-resolved boundary layers. To address the shortcomings of existing grid generation tools, a new tool has been developed as part of the Mesh Tools suite, that is capable of extruding complex surface meshes. The new tool uses a face offsetting method to preserve surface curvature and a mean curvature smoothing algorithm to prevent the cells from self-intersecting in concave regions. Testing of the new tool found that not only were complex surface meshes able to be extruded to the desired thickness, but extrusion of simple surface meshes was also improved, due to the face offsetting method