Related papers: Threshold levels in Economics
We combine general equilibrium theory and theorie generale of stochastic processes to derive structural results about equilibrium state prices.
The Convolution and Master equations governing the time behavior of the term structure of Interest Rates are set up both for continuous variables and for their discretised forms. The notion of Seed is introduced. The discretised theoretical…
The problem of convergence in law of normed sums of exchangeable random variables is examined. First, the problem is studied w.r.t. arrays of exchangeable random variables, and the special role played by mixtures of products of stable laws…
For any length category, we establish a set of rules (necessary and sufficient) that ensure a partial order on the isomorphism classes of simple objects such that the category is equivalent to the category of finite dimensional…
We introduce a broad class of equations that are described by a graph, which includes many well-studied systems. For these, we show that the number of solutions (or the dimension of the solution set) can be bounded by studying certain…
In complex systems, external parameters often determine the phase in which the system operates, i.e., its macroscopic behavior. For nearly a century, statistical physics has extensively studied systems' transitions across phases,…
Context: Advances in technical debt research demonstrate the benefits of applying the financial debt metaphor to support decision-making in software development activities. Although decision-making during requirements engineering has…
We introduce the notion of limiting theories, giving examples and providing a sufficient condition under which the first order theory of a structure is the limit of the first order theories of a collection of substructures. We also give a…
We provide here a proof theoretic account of constraint programming that attempts to capture the essential ingredients of this programming style. We exemplify it by presenting proof rules for linear constraints over interval domains, and…
Prices of commodities or assets produce what is called time-series. Different kinds of financial time-series have been recorded and studied for decades. Nowadays, all transactions on a financial market are recorded, leading to a huge amount…
The present paper presents some reflections of the author on divergent series and their role and place in mathematics over the centuries. The point of view presented here is limited to differential equations and dynamical systems.
The instability of the financial system as experienced in recent years and in previous periods is often linked to credit defaults, i.e., to the failure of obligors to make promised payments. Given the large number of credit contracts, this…
We answer an open question in the theory of transducer degrees initially posed in [1] on the existence of a diamond structure in the transducer hierarchy. Transducer degrees are the equivalence classes formed by word transformations which…
Evaluation of systemic risk in networks of financial institutions in general requires information of inter-institution financial exposures. In the framework of Debt Rank algorithm, we introduce an approximate method of systemic risk…
We argue that there is a hierarchy of levels describing to that particular level relevant features of reality behind the content and behavior of blockchain and smart contracts in their realistic deployment. Choice, design, audit and legal…
`What more than its truth do we know if we have a proof of a theorem in a given formal system?' We examine Kreisel's question in the particular context of program termination proofs, with an eye to deriving complexity bounds on program…
We provide a setting-independent definition of reals by introducing the notion of a streak. We show that various standard constructions of reals satisfy our definition. We study the structure of reals by noting that its pieces correspond to…
The conditions are found that all solutions of a systems dynamic equations on time scales tends to finite limits as $t\to\infty$.
The main objective of the paper is to establish explicit estimates on some applicable inequalities in two variables on time scales which can be used in the study of certain qualitative properties of dynamical equations on time scales.
We survey systemic risks to financial markets and present a high-level description of an algorithm that measures systemic risk in terms of coupled networks.