Stochastic particle models: mean reversion and burgers dynamics. An application to commodity markets

The aim of this study is to propose a stochastic model for commodity markets linked with the Burgers equation from fluid dynamics. We construct a stochastic particles method for commodity markets, in which particles represent market participants. A discontinuity in the model is included through an interacting kernel equal to the Heaviside function and its link with the Burgers equation is given. The Burgers equation and the connection of this model with stochastic differential equations are also studied. Further, based on the law of large numbers, we prove the convergence, for large N, of a system of stochastic differential equations describing the evolution of the prices of N traders to a deterministic partial differential equation of Burgers type. Numerical experiments highlight the success of the new proposal in modeling some commodity markets, and this is confirmed by the ability of the model to reproduce price spikes when their effects occur in a sufficiently long period of time.

The effects of quinpirole in eliciting 50 kHz calls from the rat nucleus accumbens /

Fifty kHz rat vocalizations are theorized to reflect a positive affective state, and index the reward value of stimuli (Knutson, Burgdorf & Panksepp, 2002; Panksepp & Burgdorf, 2003; Brudzynski,2005). Previous studies have identified the neurochemical substrate of this behaviour to be dependent on dopaminergic activity at the nucleus accumbens shell (Burgdorf, Knutson, Panksepp & Ikemoto, 2001; Thompson, Leonard & Brudzynski, 2006). The utilization of d-amphetamine (a non-selective dopamine agonist) in these studies does not address the specific dopamine receptor types involved. The present study aims to identify the role of the D2- like family of receptors in the nucleus accumbens shell in the production of 50 kHz vocalizations in adult rats. Single injections of quinpirole in a saline vehicle were administered to the nucleus accumbens shell of 57 rats, and the number of 50 kHz vocalizations were recorded. An inverted V-shaped relationship was found between quinpirole dose (0.5 ~g, 3 ~g, 6 ~g, 1 0 ~g and 20 ~g, all in 0.2~1 saline) and the mean number of 50 kHz calls produced. Quinpirole successfully elicited significantly more 50 kHz calls than did a saline control at the 6 ~g dose, as did 7 ~g/0.2 ~l of d-amphetamine injections into the same brain site. To test whether a selective D2 antagonist could reverse elicited 50 kHz calling, double injections were given that used either saline or raclopride as a pretreatment before quinpirole injections. Saline followed by 6 ~g/0.2 ~l of quinpirole elicited significantly more 50 kHz vocalizations than did a double injection of saline, while pretreatment with an equimolar dose of raclopride reduced elicited calls to control levels. Raclopride was also used as a pretreatment of 7 ~g/0.2 ~l d-amphetamine, which elicited significantly fewer 50 kHz vocalizations than saline followed by amphetamine, replicating the finding of Thompson, Leonard & Brudzynski (2006).Subcutaneous injections of 0.5 mg/kg and 1.5 mg/kg of quinpirole produced a similar number of 50 kHz vocalizations as subcutaneous injection of saline. Wider dose ranges may be explored in fiiture research. Thus, direct activation of the Da-like receptors in the nucleus accumbens shell was sufficient to elicit 50 kHz vocalizations in adult rats, an effect which was reversed with selective local antagonism of Da-like receptors. The Da-like receptor family also appears necessary for pharmacological activation of 50 kHz calling, as d-amphetamine was no longer able to effectively elicit these vocalizations from the nucleus accumbens shell when the Da-receptor family was antagonized with raclopride. The acoustic parameters of elicited vocalizations remained typical of rat 50 kHz calls. Detailed analyses of the acoustic characteristics of elicited calls indicated significant increases in call duration and peak frequency across drug injection groups, particularly among quinpirole dose groups. The implications of these findings are not yet clear, but may represent an important direction for future research into the coding of semiotic content into affective signals in rats.

A treatment of atomic mean square displacement in higher order perturbation theory

A general derivation of the anharmonic coefficients for a periodic lattice invoking the special case of the central force interaction is presented. All of the contributions to mean square displacement (MSD) to order 14 perturbation theory are enumerated. A direct correspondance is found between the high temperature limit MSD and high temperature limit free energy contributions up to and including 0(14). This correspondance follows from the detailed derivation of some of the contributions to MSD. Numerical results are obtained for all the MSD contributions to 0(14) using the Lennard-Jones potential for the lattice constants and temperatures for which the Monte Carlo results were calculated by Heiser, Shukla and Cowley. The Peierls approximation is also employed in order to simplify the numerical evaluation of the MSD contributions. The numerical results indicate the convergence of the perturbation expansion up to 75% of the melting temperature of the solid (TM) for the exact calculation; however, a better agreement with the Monte Carlo results is not obtained when the total of all 14 contributions is added to the 12 perturbation theory results. Using Peierls approximation the expansion converges up to 45% of TM• The MSD contributions arising in the Green's function method of Shukla and Hubschle are derived and enumerated up to and including 0(18). The total MSD from these selected contributions is in excellent agreement with their results at all temperatures. Theoretical values of the recoilless fraction for krypton are calculated from the MSD contributions for both the Lennard-Jones and Aziz potentials. The agreement with experimental values is quite good.

Molecular dynamics calculation of mean square displacement in alkali metals and rare gas solids and comparison with lattice dynamics

Molec ul ar dynamics calculations of the mean sq ua re displacement have been carried out for the alkali metals Na, K and Cs and for an fcc nearest neighbour Lennard-Jones model applicable to rare gas solids. The computations for the alkalis were done for several temperatures for temperature vol ume a swell as for the the ze r 0 pressure ze ro zero pressure volume corresponding to each temperature. In the fcc case, results were obtained for a wide range of both the temperature and density. Lattice dynamics calculations of the harmonic and the lowe s t order anharmonic (cubic and quartic) contributions to the mean square displacement were performed for the same potential models as in the molecular dynamics calculations. The Brillouin zone sums arising in the harmonic and the quartic terms were computed for very large numbers of points in q-space, and were extrapolated to obtain results ful converged with respect to the number of points in the Brillouin zone.An excellent agreement between the lattice dynamics results was observed molecular dynamics and in the case of all the alkali metals, e~ept for the zero pressure case of CSt where the difference is about 15 % near the melting temperature. It was concluded that for the alkalis, the lowest order perturbation theory works well even at temperat ures close to the melting temperat ure. For the fcc nearest neighbour model it was found that the number of particles (256) used for the molecular dynamics calculations, produces a result which is somewhere between 10 and 20 % smaller than the value converged with respect to the number of particles. However, the general temperature dependence of the mean square displacement is the same in molecular dynamics and lattice dynamics for all temperatures at the highest densities examined, while at higher volumes and high temperatures the results diverge. This indicates the importance of the higher order (eg. ~* ) perturbation theory contributions in these cases.

On the equation of state and atomic mean square displacement of crystals

We have presented a Green's function method for the calculation of the atomic mean square displacement (MSD) for an anharmonic Hamil toni an . This method effectively sums a whole class of anharmonic contributions to MSD in the perturbation expansion in the high temperature limit. Using this formalism we have calculated the MSD for a nearest neighbour fcc Lennard Jones solid. The results show an improvement over the lowest order perturbation theory results, the difference with Monte Carlo calculations at temperatures close to melting is reduced from 11% to 3%. We also calculated the MSD for the Alkali metals Nat K/ Cs where a sixth neighbour interaction potential derived from the pseudopotential theory was employed in the calculations. The MSD by this method increases by 2.5% to 3.5% over the respective perturbation theory results. The MSD was calculated for Aluminum where different pseudopotential functions and a phenomenological Morse potential were used. The results show that the pseudopotentials provide better agreement with experimental data than the Morse potential. An excellent agreement with experiment over the whole temperature range is achieved with the Harrison modified point-ion pseudopotential with Hubbard-Sham screening function. We have calculated the thermodynamic properties of solid Kr by minimizing the total energy consisting of static and vibrational components, employing different schemes: The quasiharmonic theory (QH), ).2 and).4 perturbation theory, all terms up to 0 ().4) of the improved self consistent phonon theory (ISC), the ring diagrams up to o ().4) (RING), the iteration scheme (ITER) derived from the Greens's function method and a scheme consisting of ITER plus the remaining contributions of 0 ().4) which are not included in ITER which we call E(FULL). We have calculated the lattice constant, the volume expansion, the isothermal and adiabatic bulk modulus, the specific heat at constant volume and at constant pressure, and the Gruneisen parameter from two different potential functions: Lennard-Jones and Aziz. The Aziz potential gives generally a better agreement with experimental data than the LJ potential for the QH, ).2, ).4 and E(FULL) schemes. When only a partial sum of the).4 diagrams is used in the calculations (e.g. RING and ISC) the LJ results are in better agreement with experiment. The iteration scheme brings a definitive improvement over the).2 PT for both potentials.

Phonon dispersion curves and atomic mean square displacement for several fcc and bcc materials

The atomic mean square displacement (MSD) and the phonon dispersion curves (PDC's) of a number of face-centred cubic (fcc) and body-centred cubic (bcc) materials have been calclllated from the quasiharmonic (QH) theory, the lowest order (A2 ) perturbation theory (PT) and a recently proposed Green's function (GF) method by Shukla and Hiibschle. The latter method includes certain anharmonic effects to all orders of anharmonicity. In order to determine the effect of the range of the interatomic interaction upon the anharmonic contributions to the MSD we have carried out our calculations for a Lennard-Jones (L-J) solid in the nearest-neighbour (NN) and next-nearest neighbour (NNN) approximations. These results can be presented in dimensionless units but if the NN and NNN results are to be compared with each other they must be converted to that of a real solid. When this is done for Xe, the QH MSD for the NN and NNN approximations are found to differ from each other by about 2%. For the A2 and GF results this difference amounts to 8% and 7% respectively. For the NN case we have also compared our PT results, which have been calculated exactly, with PT results calculated using a frequency-shift approximation. We conclude that this frequency-shift approximation is a poor approximation. We have calculated the MSD of five alkali metals, five bcc transition metals and seven fcc transition metals. The model potentials we have used include the Morse, modified Morse, and Rydberg potentials. In general the results obtained from the Green's function method are in the best agreement with experiment. However, this improvement is mostly qualitative and the values of MSD calculated from the Green's function method are not in much better agreement with the experimental data than those calculated from the QH theory. We have calculated the phonon dispersion curves (PDC's) of Na and Cu, using the 4 parameter modified Morse potential. In the case of Na, our results for the PDC's are in poor agreement with experiment. In the case of eu, the agreement between the tlleory and experiment is much better and in addition the results for the PDC's calclliated from the GF method are in better agreement with experiment that those obtained from the QH theory.

Determinants of bankruptcy protection duration for Canadian firms

The present thesis examines the determinants of the bankruptcy protection duration for Canadian firms. Using a sample of Canadian firms that filed for bankruptcy protection between the calendar years 1992 and 2009, we fmd that the firm age, the industry adjusted operating margin, the default spread, the industrial production growth rate or the interest rate are influential factors on determining the length of the protection period. Older firms tend to stay longer under protection from creditors. As older firms have more complicated structures and issues to settle, the risk of exiting soon the protection (the hazard rate) is small. We also find that firms that perform better than their benchmark as measured by the industry they belong to, tend to leave quickly the bankruptcy protection state. We conclude that the fate of relatively successful companies is determined faster. Moreover, we report that it takes less time to achieve a final solution to firms under bankrupt~y when the default spread is low or when the appetite for risk is high. Conversely, during periods of high default spreads and flight for quality, it takes longer time to resolve the bankruptcy issue. This last finding may suggest that troubled firms should place themselves under protection when spreads are low. However, this ignores the endogeneity issue: high default spread may cause and incidentally reflect higher bankruptcy rates in the economy. Indeed, we find that bankruptcy protection is longer during economic downturns. We explain this relation by the natural increase in default rate among firms (and individuals) during economically troubled times. Default spreads are usually larger during these harsh periods as investors become more risk averse since their wealth shrinks. Using a Log-logistic hazard model, we also fmd that firms that file under the Companies' Creditors Arrangement Act (CCAA) protection spend longer time restructuring than firms that filed under the Bankruptcy and Insolvency Act (BIA). As BIA is more statutory and less flexible, solutions can be reached faster by court orders.

“You Know What I Mean?”- Language and Cultural Retention in Luso-Canadian Mothers in the Greater Toronto Area

The Portuguese community is one of the largest diasporic groups in the Greater Toronto Area and the choice of retention and transmission of language and culture to Luso-Canadians is crucial to the development and sustainability of the community. The overall objective of this study is to learn about the factors that influence Luso-Canadian mothers’ inclination to teach Portuguese language and cultural retention to their children. To explore this topic I employed a qualitative research design that included in-depth interviews conducted in 2012 with six Luso-Canadian mothers. Three central arguments emerged from the findings. First, Luso-Canadian mothers interviewed posses a pronounced desire for their children to succeed academically, and to provide opportunities that their children that they did not have. Second, five of the mothers attempt to achieve this mothering objective partly by disconnecting from their Portuguese roots, and by disassociating their children from the Portuguese language and culture. Third, the disconnection they experience and enact is influenced by the divisions evident in the Portuguese community in the GTA that divides regions and hierarchically ranks dialects, and groups. I conclude that the children in these households inevitably bear the prospects of maintaining a vibrant Portuguese community in the GTA and I propose that actions by the community in ranking dialects influence mothers’ decisions about transmitting language and culture to their children.

Canada’s new Open Access Policy: what does it mean for Brock researchers?

Presentation at Brock Library Spring Symposium 2015: What's really going on?

The Bootstrap of Mean for Dependent Heterogeneous Arrays.

Presently, conditions ensuring the validity of bootstrap methods for the sample mean of (possibly heterogeneous) near epoch dependent (NED) functions of mixing processes are unknown. Here we establish the validity of the bootstrap in this context, extending the applicability of bootstrap methods to a class of processes broadly relevant for applications in economics and finance. Our results apply to two block bootstrap methods: the moving blocks bootstrap of Künsch ( 989) and Liu and Singh ( 992), and the stationary bootstrap of Politis and Romano ( 994). In particular, the consistency of the bootstrap variance estimator for the sample mean is shown to be robust against heteroskedasticity and dependence of unknown form. The first order asymptotic validity of the bootstrap approximation to the actual distribution of the sample mean is also established in this heterogeneous NED context.

Reported Job Satisfaction : What Does It Mean?

By reporting his satisfaction with his job or any other experience, an individual does not communicate the number of utils that he feels. Instead, he expresses his posterior preference over available alternatives conditional on acquired knowledge of the past. This new interpretation of reported job satisfaction restores the power of microeconomic theory without denying the essential role of discrepancies between one’s situation and available opportunities. Posterior human wealth discrepancies are found to be the best predictor of reported job satisfaction. Static models of relative utility and other subjective well-being assumptions are all unambiguously rejected by the data, as well as an \"economic\" model in which job satisfaction is a measure of posterior human wealth. The \"posterior choice\" model readily explains why so many people usually report themselves as happy or satisfied, why both younger and older age groups are insensitive to current earning discrepancies, and why the past weighs more heavily than the present and the future.

Testing Mean-Variance Efficiency in CAPM with Possibly Non-Gaussian Errors : An Exact Simulation-Based Approach

In this paper we propose exact likelihood-based mean-variance efficiency tests of the market portfolio in the context of Capital Asset Pricing Model (CAPM), allowing for a wide class of error distributions which include normality as a special case. These tests are developed in the frame-work of multivariate linear regressions (MLR). It is well known however that despite their simple statistical structure, standard asymptotically justified MLR-based tests are unreliable. In financial econometrics, exact tests have been proposed for a few specific hypotheses [Jobson and Korkie (Journal of Financial Economics, 1982), MacKinlay (Journal of Financial Economics, 1987), Gib-bons, Ross and Shanken (Econometrica, 1989), Zhou (Journal of Finance 1993)], most of which depend on normality. For the gaussian model, our tests correspond to Gibbons, Ross and Shanken’s mean-variance efficiency tests. In non-gaussian contexts, we reconsider mean-variance efficiency tests allowing for multivariate Student-t and gaussian mixture errors. Our framework allows to cast more evidence on whether the normality assumption is too restrictive when testing the CAPM. We also propose exact multivariate diagnostic checks (including tests for multivariate GARCH and mul-tivariate generalization of the well known variance ratio tests) and goodness of fit tests as well as a set estimate for the intervening nuisance parameters. Our results [over five-year subperiods] show the following: (i) multivariate normality is rejected in most subperiods, (ii) residual checks reveal no significant departures from the multivariate i.i.d. assumption, and (iii) mean-variance efficiency tests of the market portfolio is not rejected as frequently once it is allowed for the possibility of non-normal errors.

Development of the Physical Activity Interactive Recall (PAIR) for Aboriginal children

Affiliation: Margaret Cargo : Département de médecine sociale et préventive, Faculté de médecine, Université de Montréal