Liquidity and its impact on bond prices

In this paper, we propose a theoretical continuous-time model to analyze the impact of liquidity on bond prices. This model prices illiquid bonds relative to liquid bonds and provides a testable theory of illiquidity induced price discounts. The model is tested using 1992-1994 data from bonds issued by the german government.These bonds define a market segment that is homogeneous in bankruptcy risk, taxes, age, and coupons, but the bonds differ with respect to their liquidity. The empirical findings suggest that bond prices not only depend on the dynamics of interest rates, but also on the liquidity of bonds. Therefore, bond liquidity should be used as an additional pricing factor. The findings of the out-of-sample test demonstrate the superiority of the model in comparison with traditional pricing models

Basins of attraction for cascading maps

We study a finite uni-directional array of "cascading" or "threshold coupled" chaotic maps. Such systems have been proposed for use in nonlinear computing and have been applied to classification problems in bioinformatics. We describe some of the attractors for such systems and prove general results about their basins of attraction. In particular, we show that the basins of attraction have infinitely many path components. We show that these components always accumulate at the corners of the domain of the system. For all threshold parameters above a certain value, we show that they accumulate at a Cantor set in the interior of the domain. For certain ranges of the threshold, we prove that the system has many attractors.Comment: 15 pages, 9 figures. To appear in International Journal of Bifurcations and Chao

Escape Rates and Physically Relevant Measures for Billiards with Small Holes

We study the billiard map corresponding to a periodic Lorentz gas in 2-dimensions in the presence of small holes in the table. We allow holes in the form of open sets away from the scatterers as well as segments on the boundaries of the scatterers. For a large class of smooth initial distributions, we establish the existence of a common escape rate and normalized limiting distribution. This limiting distribution is conditionally invariant and is the natural analogue of the SRB measure of a closed system. Finally, we prove that as the size of the hole tends to zero, the limiting distribution converges to the smooth invariant measure of the billiard map.Comment: 39 pages, 4 figure

Lin's method for heteroclinic chains involving periodic orbits

We present an extension of the theory known as Lin's method to heteroclinic chains that connect hyperbolic equilibria and hyperbolic periodic orbits. Based on the construction of a so-called Lin orbit, that is, a sequence of continuous partial orbits that only have jumps in a certain prescribed linear subspace, estimates for these jumps are derived. We use the jump estimates to discuss bifurcation equations for homoclinic orbits near heteroclinic cycles between an equilibrium and a periodic orbit (EtoP cycles)

Retrospective observational RT-PCR analyses on 688 babies born to 843 SARS-CoV-2 positive mothers, placental analyses and diagnostic analyses limitations suggest vertical transmission is possible

Research question: Is there vertical transmission (from mother to baby antenatally or intrapartum) after SARS-CoV-2 (COVID-19) infected pregnancy? Study design: A systematic search related to SARS-CoV-2 (COVID-19), pregnancy, neonatal complications, viral and vertical transmission. The duration was from December 2019 to May 2020. Results: A total of 84 studies with 862 COVID positive women were included. Two studies had ongoing pregnancies while 82 studies included 705 babies, 1 miscarriage and 1 medical termination of pregnancy (MTOP). Most publications (50/84, 59.5%), reported small numbers (<5) of positive babies. From 75 studies, 18 babies were COVID-19 positive. The first reverse transcription polymerase chain reaction (RT-PCR) diagnostic test was done in 449 babies and 2 losses, 2nd RT-PCR was done in 82 babies, IgM tests were done in 28 babies, and IgG tests were done in 28 babies. On the first RT-PCR, 47 studies reported time of testing while 28 studies did not. Positive results in the first RT-PCR were seen in 14 babies. Earliest tested at birth and the average time of the result was 22 hours. Three babies with negative first RT-PCR became positive on the second RT-PCR at day 6, day 7 and at 24 hours which continued to be positive at 1 week. Four studies with a total of 4 placental swabs were positive demonstrating SARS-CoV-2 localised in the placenta. In 2 studies, 10 tests for amniotic fluid were positive for SARS-CoV-2. These 2 babies were found to be positive on RT-PCR on serial testing. Conclusion: Diagnostic testing combined with incubation period and placental pathology indicate a strong likelihood that intrapartum vertical transmission of SARS-CoV-2 (COVID-19) from mother to baby is possible