On Logical Depth and the Running Time of Shortest Programs

The logical depth with significance $b$ of a finite binary string $x$ is the shortest running time of a binary program for $x$ that can be compressed by at most $b$ bits. There is another definition of logical depth. We give two theorems about the quantitative relation between these versions: the first theorem concerns a variation of a known fact with a new proof, the second theorem and its proof are new. We select the above version of logical depth and show the following. There is an infinite sequence of strings of increasing length such that for each $j$ there is a $b$ such that the logical depth of the $j$th string as a function of $j$ is incomputable (it rises faster than any computable function) but with $b$ replaced by $b+1$ the resuling function is computable. Hence the maximal gap between the logical depths resulting from incrementing appropriate $b$'s by 1 rises faster than any computable function. All functions mentioned are upper bounded by the Busy Beaver function. Since for every string its logical depth is nonincreasing in $b$, the minimal computation time of the shortest programs for the sequence of strings as a function of $j$ rises faster than any computable function but not so fast as the Busy Beaver function.Comment: 12 pages LaTex (this supercedes arXiv:1301.4451

Linking Financial and Macroeconomic Factors to Credit Risk Indicators of Brazilian Banks

This study constructs a set of credit risk indicators for 39 Brazilian banks, using the Merton framework and balance sheet information on the banks’ total assets and liabilities. Despite the simplifying assumptions, the methodology captures well several stylized facts in the recent history of Brazil. In particular, it identifies deterioration in the credit risk indicators of the banking sector, following the crisis in the early 2000s. The risk indicators were regressed against a number of macro-financial variables at both individual and systemic level, showing that an increase in the system EDF, interest rates, and CDS spreads will lead to a deterioration of the individual expected default probability.

A Macro Stress Test Model of Credit Risk for the Brazilian Banking Sector

This paper proposes a model to conduct macro stress test of credit risk for the banking system based on scenario analysis. We employ an original bank level data set with disaggregated credit loans for business and consumer loans. The results corroborate the presence of a strong procyclical behavior of credit quality, and show a robust negative relationship between (the logistic transformation of) NPLs and GDP growth, with a lag response up to three quarters. The models also indicate substantial variations in the cyclical behavior of NPLs across credit types. Stress tests suggest that the banking system is well prepared to absorb the credit losses associated with a set of distressed macroeconomic scenarios without threatening financial stability.

On sectional paths in a category of complexes of fixed size

We show how to build the Auslander-Reiten quiver of the category Cn(proj A)of complexes of size n ≥ 2, for any artin algebra A. We also give conditions over the complexes in Cn(proj A) under which the composition of irreducible morphisms in sectional paths vanishes.Fil: Chaio, Claudia Alicia. Universidad Nacional de Mar del Plata; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; ArgentinaFil: Pratti, Nilda Isabel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; Argentina. Universidad Nacional de Mar del Plata; ArgentinaFil: Souto-Salorio, M. José. Universidad de Coruña; Españ