A Kolmogorov-Smirnov type test for shortfall dominance against parametric alternatives

This paper proposes a Kolmogorov-type test for the shortfall order (also known in the literature as the right-spread or excess-wealth order) against parametric alternatives. In the case of the null hypothesis corresponding to the Negative Exponential distribution, this provides a test for the new better than used in expectation (NBUE) property. Such a test is particularly useful in reliability applications as well as duration and income distribution analysis. The theoretical properties of the testing procedure are established. Simulation studies reveal that the test proposed in this paper performs well, even with moderate sample sizes. Applications to real data, namely chief executive officer (CEO) compensation data and flight delay data, illustrate the empirical relevance of the techniques described in this paper.Right-spread order; Excess-wealth order; New better than used in expectation; Bootstrap; Reliability; CEO compensation; Flight delay

Designating market maker behaviour in Limit Order Book markets

Financial exchanges provide incentives for limit order book (LOB) liquidity provision to certain market participants, termed designated market makers or designated sponsors. While quoting requirements typically enforce the activity of these participants for a certain portion of the day, we argue that liquidity demand throughout the trading day is far from uniformly distributed, and thus this liquidity provision may not be calibrated to the demand. We propose that quoting obligations also include requirements about the speed of liquidity replenishment, and we recommend use of the Threshold Exceedance Duration (TED) for this purpose. We present a comprehensive regression modelling approach using GLM and GAMLSS models to relate the TED to the state of the LOB and identify the regression structures that are best suited to modelling the TED. Such an approach can be used by exchanges to set target levels of liquidity replenishment for designated market makers

A characterization of the multivariate excess wealth ordering

In this paper, some new properties of the upper-corrected orthant of a random vector are proved. The univariate right-spread or excess wealth function, introduced by Fernández-Ponce et al. (1996), is extended to multivariate random vectors, and some properties of this multivariate function are studied. Later, this function was used to define the excess wealth ordering by Shaked and Shanthikumar (1998) and Fernández-Ponce et al. (1998). The multivariate excess wealth function enable us to define a new stochastic comparison which is weaker than the multivariate dispersion orderings. Also, some properties relating the multivariate excess wealth order with stochastic dependence are describe

Tests for exponentiality against NBUE alternatives: a Monte Carlo comparison

Testing of various classes of life distributions has been addressed in the literature for more than 45 years. In this paper, we consider the problem of testing exponentiality (which essentially implies no ageing) against positive ageing which is captured by the fairly large class of new better than used in expectation (NBUE) distributions. These tests of exponentiality against NBUE alternatives are discussed and compared. The empirical size of the tests is obtained by simulations. Power comparisons for different popular alternatives are done using Monte Carlo simulations. These comparisons are made for both small and large sample sizes. The paper concludes with a discussion in which suggestions are made regarding the choices of the test when a particular alternative is suspected

Real-time growth rate for general stochastic SIR epidemics on unclustered networks

Networks have become an important tool for infectious disease epidemiology. Most previous theoretical studies of transmission network models have either considered simple Markovian dynamics at the individual level, or have focused on the invasion threshold and final outcome of the epidemic. Here, we provide a general theory for early real-time behaviour of epidemics on large configuration model networks (i.e. static and locally unclustered), in particular focusing on the computation of the Malthusian parameter that describes the early exponential epidemic growth. Analytical, numerical and Monte-Carlo methods under a wide variety of Markovian and non-Markovian assumptions about the infectivity profile are presented. Numerous examples provide explicit quantification of the impact of the network structure on the temporal dynamics of the spread of infection and provide a benchmark for validating results of large scale simulations.Comment: 45 pages, 8 figures, submitted to Mathematical Biosciences on 29/11/2014; Version 2: resubmitted on 15/04/2015; accepted on 17/04/2015. Changes: better explanations in introduction; restructured section 3.3 (3.3.3 added); section 6.3.1 added; more precise terminology; typos correcte

Ballistic aggregation for one-sided Brownian initial velocity

We study the one-dimensional ballistic aggregation process in the continuum limit for one-sided Brownian initial velocity (i.e. particles merge when they collide and move freely between collisions, and in the continuum limit the initial velocity on the right side is a Brownian motion that starts from the origin $x=0$). We consider the cases where the left side is either at rest or empty at $t=0$. We derive explicit expressions for the velocity distribution and the mean density and current profiles built by this out-of-equilibrium system. We find that on the right side the mean density remains constant whereas the mean current is uniform and grows linearly with time. All quantities show an exponential decay on the far left. We also obtain the properties of the leftmost cluster that travels towards the left. We find that in both cases relevant lengths and masses scale as $t^2$ and the evolution is self-similar.Comment: 18 pages, published in Physica

Triggering Active Galactic Nuclei in Hierarchical Galaxy Formation: Disk instability vs. Interactions

Using a semi analytic model for galaxy formation we investigate the effects of Black Hole accretion triggered by disk instabilities (DI) in isolated galaxies on the evolution of AGN. Specifically, we took on, developed and expanded the Hopkins & Quataert (2011) model for the mass inflow following disk perturbations, and compare the corresponding evolution of the AGN population with that arising in a scenario where galaxy interactions trigger AGN (IT mode). We extended and developed the DI model by including different disk surface density profiles, to study the maximal contribution of DI to the evolution of the AGN population. We obtained the following results: i) for luminosities corresponding to $M_{1450}\gtrsim -26$ the DI mode can provide the BH accretion needed to match the observed AGN luminosity functions up to $z \approx 4.5$; in such a luminosity range and redshift, it can compete with the IT scenario as the main driver of cosmological evolution of AGN; ii) The DI scenario cannot provide the observed abundance of high-luminosity QSO with $M_{1450}\lesssim -26$ AGN, as well as the abundance of high-redhshift $z \approx 4.5$ QSOs with $M_{1450}\lesssim -24$, while the IT scenario provides an acceptable match up to $z \approx 6$, as found in our earliest works; iii) The dispersion of the distributions of Eddington ratio for low- and intermediate-luminosity AGN (bolometric $L_{AGN}$ = $10^{43}$ - $10^{45}$ erg/s) is predicted to be much smaller in the DI scenario compared to the IT mode; iv) The above conclusions are robust with respect to the explored variants of the Hopkins & Quataert (2011) model. We discuss the physical origin of our findings, and how it is possible to pin down the dominant fueling mechanism in the low-intermediate luminosity range $M_{1450}\gtrsim -26$ where both the DI and the IT modes are viable candidates as drivers for the AGN evolution.Comment: Accepted for publication in Astronomy & Astrophysics, 24 pages, 8 figures; updated reference