Particle Resuspension in Turbulent Boundary Layers and the Influence of Non-Gaussian Removal Forces

The work described is concerned with the way micron-size particles attached to a surface are resuspended when exposed to a turbulent flow. An improved version of the Rock'n'Roll model (Reeks and Hall, 2001) is developed where this model employs a stochastic approach to resuspension involving the rocking and rolling of a particle about surface asperities arising from the moments of the fluctuating drag forces acting on the particle close to the surface. In this work, the model is improved by using values of both the streamwise fluid velocity andacceleration close to the wall obtained from Direct Numerical Simulation (DNS) of turbulentchannel flow. Using analysis and numerical calculations of the drag force on a sphere near a wall in shear flow (O'Neill (1968) and Lee and Balachandar (2010)) these values are used to obtain the joint distribution of the moments of the fluctuating drag force and its time derivative acting on a particle attached to a surface. In so doing the influence of highly non-Gaussian forces (associated with the sweeping and ejection events in a turbulent boundary layer) on short and long term resuspension rates is examined for a sparse monolayer coverage of particles, along with the dependence of the resuspension upon the timescale of the particle motion attached to the surface, the ratio of the rms/ mean of the removal force and the distribution of adhesive forces. Model predictions of the fraction resuspended are compared with experimental results.Comment: 31 pages 21 figure

Wavelength Dependent PSFs and their impact on Weak Lensing Measurements

We measure and model the wavelength dependence of the PSF in the Hyper Suprime-Cam (HSC) Subaru Strategic Program (SSP) survey. We find that PSF chromaticity is present in that redder stars appear smaller than bluer stars in the $g, r,$ and $i$-bands at the 1-2 per cent level and in the $z$ and $y$-bands at the 0.1-0.2 per cent level. From the color dependence of the PSF, we fit a model between the monochromatic PSF trace radius, $R$, and wavelength of the form $R(\lambda)\propto \lambda^{b}$. We find values of $b$ between -0.2 and -0.5, depending on the epoch and filter. This is consistent with the expectations of a turbulent atmosphere with an outer scale length of $\sim 10-100$ m, indicating that the atmosphere is dominating the chromaticity. We find evidence in the best seeing data that the optical system and detector also contribute some wavelength dependence. Meyers and Burchat (2015) showed that $b$ must be measured to an accuracy of $\sim 0.02$ not to dominate the systematic error budget of the Large Synoptic Survey Telescope (LSST) weak lensing (WL) survey. Using simple image simulations, we find that $b$ can be inferred with this accuracy in the $r$ and $i$-bands for all positions in the LSST field of view, assuming a stellar density of 1 star arcmin$^{-2}$ and that the optical PSF can be accurately modeled. Therefore, it is possible to correct for most, if not all, of the bias that the wavelength-dependent PSF will introduce into an LSST-like WL survey.Comment: 14 pages, 10 figures. Submitted to MNRAS. Comments welcom

Dynamic modeling of mean-reverting spreads for statistical arbitrage

Statistical arbitrage strategies, such as pairs trading and its generalizations, rely on the construction of mean-reverting spreads enjoying a certain degree of predictability. Gaussian linear state-space processes have recently been proposed as a model for such spreads under the assumption that the observed process is a noisy realization of some hidden states. Real-time estimation of the unobserved spread process can reveal temporary market inefficiencies which can then be exploited to generate excess returns. Building on previous work, we embrace the state-space framework for modeling spread processes and extend this methodology along three different directions. First, we introduce time-dependency in the model parameters, which allows for quick adaptation to changes in the data generating process. Second, we provide an on-line estimation algorithm that can be constantly run in real-time. Being computationally fast, the algorithm is particularly suitable for building aggressive trading strategies based on high-frequency data and may be used as a monitoring device for mean-reversion. Finally, our framework naturally provides informative uncertainty measures of all the estimated parameters. Experimental results based on Monte Carlo simulations and historical equity data are discussed, including a co-integration relationship involving two exchange-traded funds.Comment: 34 pages, 6 figures. Submitte

Hedging tranches index products : illustration of model dependency

In this paper, index tranches'properties and several hedging strategies are discussed. Model risk and correlation risk are analysed through the study of the efficiency of several factor based copula models, like the Gaussian, the double-t and the double NIG using implied correlation and a particular NIG one factor model, using historical data in terms of hedging capabilities.CDO – Factor models – NIG distribution

Rational Multi-Curve Models with Counterparty-Risk Valuation Adjustments

We develop a multi-curve term structure setup in which the modelling ingredients are expressed by rational functionals of Markov processes. We calibrate to LIBOR swaptions data and show that a rational two-factor lognormal multi-curve model is sufficient to match market data with accuracy. We elucidate the relationship between the models developed and calibrated under a risk-neutral measure Q and their consistent equivalence class under the real-world probability measure P. The consistent P-pricing models are applied to compute the risk exposures which may be required to comply with regulatory obligations. In order to compute counterparty-risk valuation adjustments, such as CVA, we show how positive default intensity processes with rational form can be derived. We flesh out our study by applying the results to a basis swap contract.Comment: 34 pages, 9 figure

Risk Assessment for a Structured Product Specific to the CO2 Emission Permits Market

The aim of this work is to use a new modelling technique for CO2 emission prices, in order to estimate the risk associated with a related, structured product. After a short discussion of the specificities of this market, we investigate several modelling methods for CO2 emission prices. We use these results for risk modeling of the swap between two CO2 related instruments : the European Union Allowances and the Certified Emission Reductions. We estimate the counterparty risk for this kind of transaction and evaluate the impact of different models on the risk measure and the allocated capital.Carbon ; Generalized Hyperbolic Distribution ; CER ; EUA ; Swap ; Value at Risk

A model for hedging load and price risk in the Texas electricity market

Energy companies with commitments to meet customers’ daily electricity demands face the problem of hedging load and price risk. We propose a joint model for load and price dynamics, which is motivated by the goal of facilitating optimal hedging decisions, while also intuitively capturing the key features of the electricity market. Driven by three stochastic factors including the load process, our power price model allows for the calculation of closed-form pricing formulas for forwards and some options, products often used for hedging purposes. Making use of these results, we illustrate in a simple example the hedging benefit of these instruments, while also evaluating the performance of the model when fitted to the Texas electricity market