Clearing price distributions in call auctions

We propose a model for price formation in financial markets based on clearing of a standard call auction with random orders, and verify its validity for prediction of the daily closing price distribution statistically. The model considers random buy and sell orders, placed following demand- and supply-side valuation distributions; an equilibrium equation then leads to a distribution for clearing price and transacted volume. Bid and ask volumes are left as free parameters, permitting possibly heavy-tailed or very skewed order flow conditions. In highly liquid auctions, the clearing price distribution converges to an asymptotically normal central limit, with mean and variance in terms of supply/demand-valuation distributions and order flow imbalance. By means of simulations, we illustrate the influence of variations in order flow and valuation distributions on price/volume, noting a distinction between high- and low-volume auction price variance. To verify the validity of the model statistically, we predict a year's worth of daily closing price distributions for 5 constituents of the Eurostoxx 50 index; Kolmogorov-Smirnov statistics and QQ-plots demonstrate with ample statistical significance that the model predicts closing price distributions accurately, and compares favourably with alternative methods of prediction

The Bayesian Score Statistic

We propose a novel Bayesian test under a (noninformative) Jeffreys’ prior speciï¬ca- tion. We check whether the ï¬xed scalar value of the so-called Bayesian Score Statistic (BSS) under the null hypothesis is a plausible realization from its known and standard- ized distribution under the alternative. Unlike highest posterior density regions the BSS is invariant to reparameterizations. The BSS equals the posterior expectation of the classical score statistic and it provides an exact test procedure, whereas classical tests often rely on asymptotic results. Since the statistic is evaluated under the null hypothe- sis it provides the Bayesian counterpart of diagnostic checking. This result extends the similarity of classical sampling densities of maximum likelihood estimators and Bayesian posterior distributions based on Jeffreys’ priors, towards score statistics. We illustrate the BSS as a diagnostic to test for misspeciï¬cation in linear and cointegration models.bayesian statistics

The Bayesian Score Statistic

We propose a novel Bayesian test under a (noninformative) Jeffreys' prior specification. We check whether the fixed scalar value of the so- called Bayesian Score Statistic (BSS) under the null hypothesis is a plausible realization from its known and standardized distribution under the alternative. Unlike highest posterior density regions the BSS is invariant to reparameterizations. The BSS equals the posterior expectation of the classical score statistic and it provides an exact test procedure, whereas classical tests often rely on asymptotic results. Since the statistic is evaluated under the null hypothesis it provides the Bayesian counterpart of diagnostic checking. This result extends the similarity of classical sampling densities of maximum likelihood estimators and Bayesian posterior distributions based on Jeffreys' priors, towards score statistics. We illustrate the BSS as a diagnostic to test for misspecification in linear and cointegration models.

Marangoni driven turbulence in high energy surface melting processes

Experimental observations of high-energy surface melting processes, such as laser welding, have revealed unsteady, often violent, motion of the free surface of the melt pool. Surprisingly, no similar observations have been reported in numerical simulation studies of such flows. Moreover, the published simulation results fail to predict the post-solidification pool shape without adapting non-physical values for input parameters, suggesting the neglect of significant physics in the models employed. The experimentally observed violent flow surface instabilities, scaling analyses for the occurrence of turbulence in Marangoni driven flows, and the fact that in simulations transport coefficients generally have to be increased by an order of magnitude to match experimentally observed pool shapes, suggest the common assumption of laminar flow in the pool may not hold, and that the flow is actually turbulent. Here, we use direct numerical simulations (DNS) to investigate the role of turbulence in laser melting of a steel alloy with surface active elements. Our results reveal the presence of two competing vortices driven by thermocapillary forces towards a local surface tension maximum. The jet away from this location at the free surface, separating the two vortices, is found to be unstable and highly oscillatory, indeed leading to turbulence-like flow in the pool. The resulting additional heat transport, however, is insufficient to account for the observed differences in pool shapes between experiment and simulations

Analysis and improvement of the vector quantization in SELP (Stochastically Excited Linear Prediction)

The Stochastically Excited Linear Prediction (SELP) algorithm is described as a speech coding method employing a two-stage vector quantization. The first stage uses an adaptive codebook which efficiently encodes the periodicity of voiced speech, and the second stage uses a stochastic codebook to encode the remainder of the excitation signal. The adaptive codebook performs well when the pitch period of the speech signal is larger than the frame size. An extension is introduced, which increases its performance for the case that the frame size is longer than the pitch period. The performance of the stochastic stage, which improves with frame length, is shown to be best in those sections of the speech signal where a high level of short-term correlations is present. It can be concluded that the SELP algorithm performs best during voiced speech where the pitch period is longer than the frame length

Droplets on Inclined Plates: Local and Global Hysteresis of Pinned Capillary Surfaces

Local contact line pinning prevents droplets from rearranging to minimal global energy, and models for droplets without pinning cannot predict their shape. We show that experiments are much better described by a theory, developed herein, that does account for the constrained contact line motion, using as example droplets on tilted plates. We map out their shapes in suitable phase spaces. For 2D droplets, the critical point of maximum tilt depends on the hysteresis range and Bond number. In 3D, it also depends on the initial width, highlighting the importance of the deposition history.Comment: 5 pages, 5 figures, accepted for publication in Phys. Rev. Let

Dependencies and Simultaneity in Membrane Systems

Membrane system computations proceed in a synchronous fashion: at each step all the applicable rules are actually applied. Hence each step depends on the previous one. This coarse view can be refined by looking at the dependencies among rule occurrences, by recording, for an object, which was the a rule that produced it and subsequently (in a later step), which was the a rule that consumed it. In this paper we propose a way to look also at the other main ingredient in membrane system computations, namely the simultaneity in the rule applications. This is achieved using zero-safe nets that allows to synchronize transitions, i.e., rule occurrences. Zero-safe nets can be unfolded into occurrence nets in a classical way, and to this unfolding an event structure can be associated. The capability of capturing simultaneity of zero-safe nets is transferred on the level of event structure by adding a way to express which events occur simultaneously

Using break quantities for tactical optimisation in multistage distribution systems

In this chapter we discuss a tactical optimisation problem that arises in a multistage distribution system where customer orders can be delivered from any stockpoint. A simple rule to allocate orders to locations is a break quantity rule, which routes large orders to higher-stage stockpoints and small orders to end-stockpoints. A so-called break quantity determines whether an order is small or large. We present a qualitative discussion on the implications of this rule for the marketing process, and a qualitative and quantitative analysis on the implications for the transportation and inventory costs. Furthermore, we present a case study for a company that implemented a break quantity rule. Finally, in the last section the main results are summarised.marketing;inventory;transportation;break quantity rule;distribution systems