Related papers: Radical Complexity
Hierarchical analysis is considered and a multilevel model is presented in order to explore causality, chance and complexity in financial economics. A coupled system of models is used to describe multilevel interactions, consistent with…
The thesis is composed of three parts. Part I introduces the mathematical and statistical tools that are relevant for the study of dependences, as well as statistical tests of Goodness-of-fit for empirical probability distributions. I…
Models characterized by autoregressive structure and random coefficients are powerful tools for the analysis of high-frequency, high-dimensional and volatile time series. The available literature on such models is broad, but also sectorial,…
This is a review about financial dependencies which merges efforts in econophysics and financial economics during the last few years. We focus on the most relevant contributions to the analysis of asset markets' dependencies, especially…
Detailed study of multifractal characteristics of the financial time series of asset values and of its returns is performed using a collection of the high frequency Deutsche Aktienindex data. The tail index ($\alpha$), the Renyi exponents…
We explore a stochastic model that enables capturing external influences in two specific ways. The model allows for the expression of uncertainty in the parametrisation of the stochastic dynamics and incorporates patterns to account for…
In complex systems, crucial parameters are often subject to unpredictable changes in time. Climate, biological evolution and networks provide numerous examples for such non-stationarities. In many cases, improved statistical models are…
The role of cryptocurrencies within the financial systems has been expanding rapidly in recent years among investors and institutions. It is therefore crucial to investigate the phenomena and develop statistical methods able to capture…
In the recent years a lot of attention is focused on unconventional string compactifications. A variety of different but related frameworks was developed in order to address issues such as duality invariance, non-geometry and…
We derive computationally tractable formulations of the robust counterparts of convex quadratic and conic quadratic constraints that are concave in matrix-valued uncertain parameters. We do this for a broad range of uncertainty sets. In…
The simplest field theory description of the multivariate statistics of forward rate variations over time and maturities, involves a quadratic action containing a gradient squared rigidity term. However, this choice leads to a spurious kink…
We analyze the spectral properties of correlation matrices between distinct statistical systems. Such matrices are intrinsically non symmetric, and lend themselves to extend the spectral analyses usually performed on standard Pearson…
We study the dependence structure of market states by estimating empirical pairwise copulas of daily stock returns. We consider both original returns, which exhibit time-varying trends and volatilities, as well as locally normalized ones,…
We set up a structural model to study credit risk for a portfolio containing several or many credit contracts. The model is based on a jump--diffusion process for the risk factors, i.e. for the company assets. We also include correlations…
We consider microstructure as an arbitrary contamination of the underlying latent securities price, through a Markov kernel $Q$. Special cases include additive error, rounding and combinations thereof. Our main result is that, subject to…
This paper investigates how two important sources of risk -- market tail risk and extreme market volatility risk -- are priced into the cross-section of asset returns across various investment horizons. To identify such risks, we propose a…
We review a collection of models of random simplicial complexes together with some of the most exciting phenomena related to them. We do not attempt to cover all existing models, but try to focus on those for which many important results…
Linear Recurrence Sequences (LRS) are a fundamental mathematical primitive for a plethora of applications such as the verification of probabilistic systems, model checking, computational biology, and economics. Positivity (are all terms of…
The study of mereology (parts and wholes) in the context of formal approaches to vagueness can be approached in a number of ways. In the context of rough sets, mereological concepts with a set-theoretic or valuation based ontology acquire…
We discuss several aspects of creation of adequate mathematical models in other sciences. In particular, many difficulties stem from great complexity of the source systems and the presence of a variety of uncertain factors. We illustrate…