The problem of arbitrary pole placement via dynamic decentralized output feedback is studied for minimal systems described by a proper transfer function matrix P(s) ∈ R^{m× p}(s) (m = ∑ m_i and p = ∑ p_i), with McMillan degree n. The family of controllers to be used includes those decentralized controllers with κ channels whose ith channel has maximum observability index at most d_i. The method presented here is based on asymptotic linearization around a decentralized degenerate compensator of the pole placement map related to the problem. It is shown that the method works generically when m⁺p > n, where m⁺ = min{d_i(p_i + m_i – 1) + m_i}, i = 1, …, κ, and the smallest d_i of the compensator of the ith channel is the integral part of (n – pm_i)/p(p_i + m_i – 1).

Purpose: – The IRB capital requirements of Basel II define the minimum level of capital that the bank has to retain to cover the current risks of its portfolio. The major risk that many banks are facing is credit risk and Basel II provides an approach to calculate its capital requirement. It is well known that Pillar I Basel II approach for credit risk capital requirements does not include concentration risk. The paper aims to propose a model modifying Basel II methodology (IRB) to include name concentration risk. Design/methodology/approach: – The model is developed on data based on a portfolio of Greek companies that are financed by Greek commercial banks. Based on the initial portfolio, new portfolios were simulated having a range of different credit risk parameters. Subsequently, the credit VaR of various portfolios was regressed against the credit risk indicators such as Basel II capital requirements, modified Herfindahl Index and a non-linear model was developed. This model modifies the Pillar I IRB capital requirements model of Basel II to include name concentration risk. Findings: – As the Pillar I IRB capital requirements model of Basel II does not include concentration risk, the credit VaR calculations performed in the present work appeared to have gaps with the Basel II capital requirements. These gaps were more apparent when there was high concentration risk in the credit portfolios. The new model bridges this gap providing with a correction coefficient. Practical implications: – The credit VaR of a loan portfolio could be calculated from the bank easily, without the use of additional complicated algorithms and systems. Originality/value: – The model is constructed in such a way as to provide an approximation of credit VaR satisfactory for business loan portfolios whose risk parameters lie within the range of those in a realistic bank credit portfolio and without the application of Monte Carlo simulations.

The Athens Stock Exchange (ASE) is a dynamic financial market with complex interactions and inherent volatility. Traditional models often fall short in capturing the intricate dependencies and long memory effects observed in real-world financial data. In this study, we explore the application of fractional Brownian motion (fBm) to model stock price dynamics within the ASE, specifically utilizing the Athens General Composite (ATG) index. The ATG is considered a key barometer of the overall health of the Greek stock market. Investors and analysts monitor the index to gauge investor sentiment, economic trends, and potential investment opportunities in Greek companies. We find that the Hurst exponent falls outside the range typically associated with fractal Brownian motion. This, combined with the established non-normality of increments, disfavors both geometric Brownian motion and fractal Brownian motion models for the ATG index.

In this article, we study the Cournot-Theocharis duopoly with variable marginal cost. We present sufficient conditions such that, both firms enter the market at any stage, remain in the market, and maximize their profit at any stage. We suggest cost implementation strategies, under which the market might benefit from the variability of marginal cost. We exhibit strategies, for which, the variability of marginal cost might be hazardous for the duopoly competitors. We prove that there exist cases, in which the market forms cycles of length six. Within each cycle, there is an interchange between monopolies and duopolies. Finally, we present some new ideas to establish monopoly convergence under certain monopoly conditions.