Related papers: Threshold levels in Economics
Many economic theory models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. We provide a principled framework for scaling results from such models by removing these finiteness…
Cluster indices describe extremal behaviour of stationary time series. We consider runs estimators of cluster indices. Using a modern theory of multivariate, regularly varying time series, we obtain central limit theorems under conditions…
We define reflective numbers and their iterative summations. We provide classification of reflective numbers based on their iterative cyclical limits.
We established the rate of convergence in the central limit theorem for stopped sums of a class of martingale difference sequences.
The 2008 financial crisis illustrated the need for a thorough, functional understanding of systemic risk in strongly interconnected financial structures. Dynamic processes on complex networks being intrinsically difficult, most recent…
Asset price bubbles are situations where asset prices exceed the fundamental values defined by the present value of dividends. This paper presents a conceptually new perspective: the necessity of bubbles. We establish the Bubble Necessity…
In this note, we study a certain class of trigonometric series which is important in many problems. An unproved statement in Zygmund's book [5] will be proved and generalized. Further discussions based on this problem will also be made…
Here we obtain the exact asymptotics for large and moderate deviations, strong law of large numbers and central limit theorem for chains with unbounded variable length memory.
An axiomatic approach to macroeconomics based on the mathematical structure of thermodynamics is presented. It deduces relations between aggregate properties of an economy, concerning quantities and flows of goods and money, prices and the…
In this paper relations among some kinds of cumulative entropies and moments of order statistics are presented. By using some characterizations and the symmetry of a non negative and absolutely continuous random variable X, lower and upper…
Some limit theorems of the type $\int_{\Omega}f_n dm_n -- --> \int_{\Omega}f dm$ are presented for scalar, (vector), (multi)-valued sequences of m_n-integrable functions f_n. The convergences obtained, in the vector and multivalued…
The seniority of debt, which determines the order in which a bankrupt institution repays its debts, is an important and sometimes contentious feature of financial crises, yet its impact on system-wide stability is not well understood. We…
This paper proves an instability theorem for dynamical systems. As one adds interactions between subystems in a complex system, structured or random, a threshold of connectivity is reached beyond which the overall dynamics inevitably goes…
We develop the concept of character level for the complex irreducible characters of finite, general or special, linear and unitary groups. We give characterizations of the level of a character in terms of its Lusztig's label and in terms of…
Public debt is one of the important economic variables that quantitatively describes a nation's economy. Because bankruptcy is a risk faced even by institutions as large as governments (e.g. Iceland), national debt should be strictly…
Models to price long term loans in the securities lending business are developed. These longer horizon deals can be viewed as contracts with optionality embedded in them. This insight leads to the usage of established methods from…
In this letter, I consider the issue of pricing risky debt by following Merton's approach. I generalize Merton's results to the case where the interest rate is modeled by the CIR term structure. Exact closed forms are provided for the risky…
The fragility of financial systems was starkly demonstrated in early 2023 through a cascade of major bank failures in the United States, including the second, third, and fourth largest collapses in the US history. The highly interdependent…
A new definition for the notion of a (general) $\infty$-category is given.
A digraph whose degree sequence has a unique vertex labeled realization is called threshold. In this paper we present several characterizations of threshold digraphs and their degree sequences, and show these characterizations to be…