European Option Pricing with Liquidity Shocks

We study the valuation and hedging problem of European options in a market subject to liquidity shocks. Working within a Markovian regime-switching setting, we model illiquidity as the inability to trade. To isolate the impact of such liquidity constraints, we focus on the case where the market is completely static in the illiquid regime. We then consider derivative pricing using either equivalent martingale measures or exponential indifference mechanisms. Our main results concern the analysis of the semi-linear coupled HJB equation satisfied by the indifference price, as well as its asymptotics when the probability of a liquidity shock is small. We then present several numerical studies of the liquidity risk premia obtained in our models leading to practical guidelines on how to adjust for liquidity risk in option valuation and hedging.Comment: 25 pages, 6 figure

Distinct modes of floor plate induction in the chick embryo

To begin to reconcile models of floor plate formation in the vertebrate neural tube, we have performed experiments aimed at understanding the development of the early floor plate in the chick embryo. Using real-time analyses of cell behaviour, we provide evidence that the principal contributor to the early neural midline, the future anterior floor plate, exists as a separate population of floor plate precursor cells in the epiblast of the gastrula stage embryo, and does not share a lineage with axial mesoderm. Analysis of the tissue interactions associated with differentiation of these cells to a floor plate fate reveals a role for the nascent prechordal mesoderm, indicating that more than one inductive event is associated with floor plate formation along the length of the neuraxis. We show that Nr1, a chick nodal homologue, is expressed in the nascent prechordal mesoderm and we provide evidence that Nodal signalling can cooperate with Shh to induce the epiblast precursors to a floor-plate fate. These results indicate that a shared lineage with axial mesoderm cells is not a pre-requisite for floor plate differentiation and suggest parallels between the development of the floor plate in amniote and anamniote embryos

Functional redundancy of EGF-CFC genes in epiblast and extraembryonic patterning during early mouse embryogenesis

AbstractDuring early mouse embryogenesis, multiple patterning and differentiation events require the activity of Nodal, a ligand of the transforming growth factor-beta (TGFβ) family. Although Nodal signaling is known to require activity of EGF-CFC co-receptors in many contexts, it has been unclear whether all Nodal signaling in the early mouse embryo is EGF-CFC dependent. We have investigated the double null mutant phenotypes for the EGF-CFC genes Cripto and Cryptic, which encode co-receptors for Nodal, and have found that they have partially redundant functions in early mouse development. Expression of Cripto and Cryptic is non-overlapping prior to gastrulation, since Cripto is expressed solely in the epiblast whereas Cryptic is expressed in the primitive endoderm of the late blastocyst and the visceral endoderm after implantation. Despite these non-overlapping expression patterns, Cripto; Cryptic double mutants display severe defects in epiblast, extraembryonic ectoderm, and anterior visceral endoderm (AVE), resulting in phenotypes that are highly similar to those of Nodal null mutants. Our results indicate that both Cripto and Cryptic function non-cell-autonomously during normal development, and that most if not all Nodal activity in early mouse embryogenesis is EGF-CFC-dependent

Rapid Response of an Academic Surgical Department to the COVID-19 Pandemic: Implications for Patients, Surgeons, and the Community.

BackgroundAs the coronavirus disease 2019 (COVID-19) pandemic continues to spread, swift actions and preparation are critical for ensuring the best outcomes for patients and providers. We aim to describe our hospital and Department of Surgery's experience in preparing for the COVID-19 pandemic and caring for surgical patients during this unprecedented time.Study designThis is a descriptive study outlining the strategy of a single academic health system for addressing the following 4 critical issues facing surgical departments during the COVID-19 pandemic: developing a cohesive leadership team and system for frequent communication throughout the department; ensuring adequate hospital capacity to care for an anticipated influx of COVID-19 patients; safeguarding supplies of blood products and personal protective equipment to protect patients and providers; and preparing for an unstable workforce due to illness and competing personal priorities, such as childcare.ResultsThrough collaborative efforts within the Department of Surgery and hospital, we provided concise and regular communication, reduced operating room volume by 80%, secured a 4-week supply of personal protective equipment, and created reduced staffing protocols with back-up staffing plans.ConclusionsBy developing an enabling infrastructure, a department can nimbly respond to crises like COVID-19 by promoting trust among colleagues and emphasizing an unwavering commitment to excellent patient care. Sharing principles and practical applications of these changes is important to optimize responses across the country and the world

The size distribution of galaxies in the Sloan Digital Sky Survey

abridged: We use a complete sample of about 140,000 galaxies from the Sloan Digital Sky Survey (SDSS) to study the size distribution of galaxies and its dependence on their luminosity, stellar mass, and morphological type. The large SDSS database provides statistics of unprecedented accuracy. For each type of galaxy, the size distribution at given luminosity (or stellar mass) is well described by a log-normal function, characterized by its median $\bar{R}$ and dispersion $\sigma_{\ln R}$. For late-type galaxies, there is a characteristic luminosity at $M_{r,0}\sim -20.5$ (assuming $h=0.7$) corresponding to a stellar mass M_0\sim 10^{10.6}\Msun. Galaxies more massive than $M_0$ have $\bar{R}\propto M^{0.4}$ and $\sigma_{\ln R}\sim 0.3$, while less massive galaxies have $\bar{R}\propto M^{0.15}$ and $\sigma_{\ln R}\sim 0.5$. For early-type galaxies, the $\bar{R}$ - $M$ relation is significantly steeper, $\bar{R}\propto M^{0.55}$, but the $\sigma_{\ln R}$ - $M$ relation is similar to that of late-type galaxies. Faint red galaxies have sizes quite independent of their luminosities.Comment: 42 pages, 18 figures, 2 tables; replaced with the version accepted by MNRA

Do broad absorption line quasars live in different environments from ordinary quasars?

We select a sample of $\sim 4200$ traditionally defined broad absorption line quasars (BALQs) from the Fifth Data Release quasar catalog of the Sloan Digital Sky Survey. For a statistically homogeneous quasar sample with $1.7\le z\le 4.2$, the BAL quasar fraction is $\sim 14$ and is almost constant with redshift. We measure the auto-correlation of non-BAL quasars (nonBALQs) and the cross-correlation of BALQs with nonBALQs using this statistically homogeneous sample, both in redshift space and using the projected correlation function. We find no significant difference between the clustering strengths of BALQs and nonBALQs. Assuming a power-law model for the real space correlation function $\xi(r)=(r/r_0)^{-1.8}$, the correlation length for nonBALQs is $r_0=7.6\pm 0.8 h^{-1}{\rm Mpc}$; for BALQs, the cross-correlation length is $r_0=7.4\pm 1.1 h^{-1}{\rm Mpc}$. Our clustering results suggest that BALQs live in similar large-scale environments as do nonBALQs.Comment: accepted for publication in Ap

Convergence Analysis of the Best Response Algorithm for Time-Varying Games

This paper studies a class of strongly monotone games involving non-cooperative agents that optimize their own time-varying cost functions. We assume that the agents can observe other agents' historical actions and choose actions that best respond to other agents' previous actions; we call this a best response scheme. We start by analyzing the convergence rate of this best response scheme for standard time-invariant games. Specifically, we provide a sufficient condition on the strong monotonicity parameter of the time-invariant games under which the proposed best response algorithm achieves exponential convergence to the static Nash equilibrium. We further illustrate that this best response algorithm may oscillate when the proposed sufficient condition fails to hold, which indicates that this condition is tight. Next, we analyze this best response algorithm for time-varying games where the cost functions of each agent change over time. Under similar conditions as for time-invariant games, we show that the proposed best response algorithm stays asymptotically close to the evolving equilibrium. We do so by analyzing both the equilibrium tracking error and the dynamic regret. Numerical experiments on economic market problems are presented to validate our analysis