Diffusion in a linear potential in the presence of position-dependent killing is used to mimic a default process. Different assumptions regarding transport coefficients, initial conditions, and elasticity of the killing measure lead to diverse models of bankruptcy. One “stylized fact” is...

We study the probability distributions of daily leverage returns of 520 North American industrial companies that survive de-listing during the financial crisis, 2006-2012. We provide evidence that distributions of unbiased leverage returns of all individual firms belong to the class of...

Fat tails of q-Gaussian distributions of daily log-leverage-returns of 520 North American industrial firms reported by Katz and Tian (2013) imply a significantly higher credit risk at short time-horizons and/or large initial distances to the default barrier than forecasted by traditional...

We analyze four major cryptocurrencies (Bitcoin, Ethereum, Litecoin, and Ripple) before the digital asset market crash at the beginning of 2018. We also analyze Bitcoin before some of the mini-crashes that occurred during the period 2016 - 2018. All relevant time series exhibited a highly...

Topological data analysis provides a new perspective on many problems in the domain of complex systems. Here, we establish the dependency of the mean value of functional $p$-norms of 'persistence landscapes' on a uniform scaling of the underlying multivariate distribution. Furthermore, we...

We study the relationships between the mean of functional L^p-norms of persistence topological landscapes of noisy datasets and statistical properties of the underlying probability distributions. We establish a functional relationship of the average L^p-norms to variability of datasets sampled...

We explore the evolution of daily returns of four major US stock market indices during the technology crash of 2000, and the financial crisis of 2007-2009. Our methodology is based on topological data analysis (TDA). We use persistence homology to detect and quantify topological patterns that...

We study average topological summaries of Vietoris–Rips complexes built on top of random point clouds in the D-dimensional Euclidian space in two setups: i) a homogeneous Poisson point process (HPPP) with intensity n and ii) N i.i.d. points sampled from a uniform elliptical distribution. In...