The paper presents a unified framework where a simple structural model of the macroeconomy is combined with an affine model of corporate default intensities. The main innovation of the paper is that the authors use structural macroeconomic framework, rather than starting from a reduced form representation and incorporate the structural model of macroeconomy in multivariate dynamics risk-neutral default intensities. The approach shows estimation of default intensity parameters from macroeconomic prospective. The combined model allows getting more precise corporate default intensities parameters and recovery rates that could be used for the fair CDS premium calculation.

The paper proposes both statistical and simulation-based analysis and evaluation of the bullwhip effect in supply chains. The demand distortion, called the bullwhip effect, is considered as an important characteristic of supply chain operation stability. A mathematical justification of the stochastic demand as a cause of the bullwhip effect is discussed. Results of simulation studies to analyse the impact of information sharing strategies on the magnification of demand fluctuations as orders move up the supply chain are presented. An approach to measuring the bullwhip effect for the entire supply chain is proposed and practically applied for comparison of different supply chain's configurations.

A mathematical model presented in this paper describes the separation of pourable materials into two components. We prove that there is a quantitative convergence of each grain-size class at every stage of separation and obtain a calculation formula for finding the degree of fractional extraction for each narrow class.