Vladimir Rankovic

Market risk management in a post-Basel II regulatory environment

We propose a novel method of Mean-Capital Requirement portfolio optimization. The optimization is performed using a parallel framework for optimization based on the Nondominated Sorting Genetic Algorithm II. Capital requirements for market risk include an additional stress component introduced by the recent Basel 2.5 regulation. Our optimization with the Basel 2.5 formula in the objective function produces superior results to those of the old (Basel II) formula in stress scenarios in which the correlations of asset returns change considerably. These improvements are achieved at the expense of reduced cardinality of Pareto-optimal portfolios. This reduced cardinality (and thus portfolio diversification) in periods of relatively low market volatility may have unintended consequences for banks’ risk exposure.

Mathematical analysis of the heart rate performance curve during incremental exercise testing.

In this study we performed laboratory treadmill protocols of increasing load. Heart rate was continuously recorded and blood lactate concentration was measured for determination of lactate threshold by means of LTD-max and LT4.0 methods.Our results indicate that the shape of heart rate performance curve (HRPC) during incremental testing depends on the applied exercise protocol (change of initial speed and the step of running speed increase, with the constant stage duration). Depending on the applied protocol, the HRPC can be described by linear, polynomial (S-shaped), and exponential mathematical expression.We presented mathematical procedure for estimation of heart rate threshold points at the level of LTD-max and LT4.0, by means of exponential curve and its relative deflection from the initial trend line (tangent line to exponential curve at the point of starting heart rate). The relative deflection of exponential curve from the initial trend line at the level of LTD-max and/or LT4.0 can be defined, based on the slope of the initial trend line. Using originally developed software that allows mathematical analysis of heart rate-load relation, LTD-max and/or LT4.0 can be estimated without direct measurement of blood lactate concentration.

Mean-univariate GARCH VaR portfolio optimization

In accordance with Basel Capital Accords, the Capital Requirements (CR) for market risk exposure of banks is a nonlinear function of Value-at-Risk (VaR). Importantly, the CR is calculated based on a banks actual portfolio, i.e. the portfolio represented by its current holdings. To tackle mean-VaR portfolio optimization within the actual portfolio framework (APF), we propose a novel mean-VaR optimization method where VaR is estimated using a univariate Generalized AutoRegressive Conditional Heteroscedasticity (GARCH) volatility model. The optimization was performed by employing a Nondominated Sorting Genetic Algorithm (NSGA-II). On a sample of 40 large US stocks, our procedure provided superior mean-VaR trade-offs compared to those obtained from applying more customary mean-multivariate GARCH and historical VaR models. The results hold true in both low and high volatility samples. We introduce mean-univariate GARCH VaR actual portfolio optimization in accordance with Basel Capital Accords.We develop optimization software that combines NSGA-II algorithm and R statistical software.Computational results show that our approach provides better mean-univariate GARCH VaR trade-offs of actual portfolios in comparison to benchmarks estimated by analytical methods.Empirical tests cover both low and high volatility samples.

Supplier Selection using NSGA-II Technique

In modern manufacturing industries, supplier selection is increasingly recognized as a critical decision in supply chain management. Supplier selection problem is a typical multiple criteria decision making problem involving a number of different and usually conflicting objectives. Because of that, modern supplier selection techniques imply solving of multi-objective optimization problems. In this paper supplier selection using evolutionary algorithm (NSGA-II method) is presented. Recent investigations show that quality and costs are among the most important selection factors. In this paper the authors used variance of quality and total costs as criteria for selection optimization. Results show that described methodology can be applicable for the practical purposes. DOI: 10.4018/jwp.2012100103 36 International Journal of Web Portals, 4(4), 35-47, October-December 2012 Copyright

Supplier Selection Using Multiobjective Evolutionary Algorithm

Supplier selection is one of the most critical activities of purchasing management. Nowadays, supplier selection includes a number of different and usually conflicting objectives. Because of that, modern supplier selection techniques imply solving of multiobjective optimization problems. In this paper supplier selection using evolutionary algorithm (SPEA method) is presented. As criteria for selection optimization we used variance of quality and total costs. Results show that described methodology can be applicable for the practical purposes.