Special Algorithm for Stability Analysis of Multistable Biological Regulatory Systems

We consider the problem of counting (stable) equilibriums of an important family of algebraic differential equations modeling multistable biological regulatory systems. The problem can be solved, in principle, using real quantifier elimination algorithms, in particular real root classification algorithms. However, it is well known that they can handle only very small cases due to the enormous computing time requirements. In this paper, we present a special algorithm which is much more efficient than the general methods. Its efficiency comes from the exploitation of certain interesting structures of the family of differential equations.Comment: 24 pages, 5 algorithms, 10 figure

Statistical Thermodynamics of General Minimal Diffusion Processes: Constuction, Invariant Density, Reversibility and Entropy Production

The solution to nonlinear Fokker-Planck equation is constructed in terms of the minimal Markov semigroup generated by the equation. The semigroup is obtained by a purely functional analytical method via Hille-Yosida theorem. The existence of the positive invariant measure with density is established and a weak form of Foguel alternative proven. We show the equivalence among self-adjoint of the elliptic operator, time-reversibility, and zero entropy production rate of the stationary diffusion process. A thermodynamic theory for diffusion processes emerges.Comment: 23 page

Market conditions, default risk and credit spreads

This study empirically examine the impact of market conditions on credit spreads as motivated by recently developed structural credit risk models. Using credit default swap (CDS) spreads, we find that, in the time series, average credit spreads are decreasing in GDP growth rate, but increasing in GDP growth volatility. We document that credit spreads are lower when investor sentiment is high and when the systematic jump risk is low. In the cross section, we confirm that firm-level cash flow volatility raises credit spreads. More importantly, we demonstrate that the impact of market conditions on credit spreads is substantially affected by firm heterogeneity. During economic expansions, ceteris paribus, firms with high cash flow betas have lower credit spreads than those with low cash flow betas. This relation disappears during economic recessions, consistent with theoretical predictions. -- In diesem Arbeitspapier untersuchen wir empirisch, wie die gesamtwirtschaftlichen Bedingungen die Renditeabstände von Unternehmensanleihen, die mit einem Ausfallrisiko behaftet sind, beeinflussen. Dabei verwenden wir Spreads von Kreditausfallswaps (Credit Default Swap, CDS) als Näherungswert für Kreditspreads und stellen fest, dass die durchschnittlichen Kreditspreads im Zeitverlauf bei wirtschaftlicher Expansion niedriger und bei wirtschaftlicher Rezession höher sind. Wenn das Wirtschaftswachstum volatiler ist, führt dies ebenfalls zu höheren Kreditspreads. Wir stellen fest, dass Kreditspreads bei positiver Anlegerstimmung und geringem Risiko eines marktweiten Sprungs niedriger ausfallen. Firmenübergreifend stellen wir fest, dass ein auf Unternehmensebene volatiler Cashflow zu einer Erhöhung der Kreditspreads führt. Was noch entscheidender ist, wir zeigen, dass in Zeiten wirtschaftlicher Expansion ? bei ansonsten gleichen Bedingungen ? Unternehmen, deren Cashflow stark mit dem gesamtwirtschaftlichen Wachstum korreliert, geringere Kreditspreads aufweisen als solche mit einer schwachen Cashflow-Korrelation. Im Einklang mit den theoretischen Voraussagen verschwindet dieser Zusammenhang in Zeiten wirtschaftlicher Rezession.Credit Risk,Credit Default Swaps,Credit Spreads,Market Conditions

Ramsey Fiscal Policy and Endogenous Growth: A Comment

Recently, Park (2009, Economic Theory 39, 377--398) extended the Barro endogenous growth model (1990) by assuming that tax rate is optimally chosen by the government and labor supply is elastic. Park claimed to have proved the existence of multiple balanced growth paths that exhibit zero growth rate and local indeterminacy. In this comment, it is shown that his claim is incorrect. The model has a unique balanced growth path that may exhibit positive growth, and the model has no transitional dynamics.Fiscal Policy; Elastic Labor Supply; Growth