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This paper is devoted to the study of qualitative geometrical properties of stochastic dynamical systems, namely their symmetries, reduction, and integrability. In particular, we show that an SDS that is diffusion-wise symmetric with respect to a proper Lie group action can be diffusion-wise reduced to an SDS on the quotient space. We also show necessary and sufficient conditions for an SDS to be projectable via a surjective map. We then introduce the notion of integrability of SDS's, and extend the results on the existence and structure-preserving property of Liouville torus actions from the classical case to the case of integrable SDS's. We also show how integrable SDS's are related to compatible families of integrable Riemannian metrics on manifolds., UDC 519.216.73 Dedicated to Anatoly Timofeevich Fomenko on the occasion of his 70th birthday 1. Introduction The aim of this paper is to study the reduction and integrability of stochastic [...]

Purpose – The purpose of this paper is to examine the interrelationships among default risk, capital and efficiency of the Indian banking system over 1990-2011. This study also took into account the impact of ownership on these interrelationships Design/methodology/approach – This paper employed Data Envelopment Analysis (DEA) Windows Analysis to estimate efficiency levels and trends of individual banks. This paper then used a model of seemingly unrelated regression equations (SURE) to examine the interrelationships among default risk, capital and efficiency. Findings – This study found a two-way negative association between efficiency and default risk, and between capital ratio and default risk. However, this study found a two-way positive relationship between capital ratio and only profit efficiency. Public banks behaved differently from private banks regarding the association between capital and efficiency. Moreover, public banks had greater probability of default risk, lower capital ratio but higher efficiency level than private banks. Further, default risk, capital ratio and efficiency of the Indian banking system increased over time, but the two formers were driven by public banks while the latter was driven by private banks. Practical implications – The findings of this study appear to favour capital ratio as an efficient tool to improve efficiency and reduce default risk of the Indian banking system. Originality/value – This paper is the first investigating the interrelationships between bank risk, capital and efficiency of the Indian banking system, where bank risk is measured by Z-score value and efficiency is captured by cost, revenue and profit efficiencies, and then considering the impact of agency issues on these interrelationships. [ABSTRACT FROM AUTHOR]