Computations for constrained linear models

The article presents an algorithm for linear regression computations subject to linear parametric equality constraints, linear parametric inequality constraints, or a mixture of the two. No rank conditions are imposed on the regression specification or the constraint specification. The algorithm requires a full Moore-Penrose g-inverse which entails extra computational effort relative to other orthonormalization type algorithms. In exchange, auxiliary statistical information is generated: feasibility of a set of constraints may be checked, estimability of a linear parametric function may be checked, and bias and variance may be decomposed by source.     

细长柱垂直度验算及施工质量控制措施

通过对某细长装饰柱不同受力方向挠度的计算分析,提出了保证该柱垂直度的施工方案及质量控制措施。对类似工程具有一定的借鉴与参考作用。     

Value-at-Risk (VaR) Computations Under Various VaR Models and Stress Testing

SUMMARY

Bank for International Settlements (BIS) proposes that all banks calculate and report amount of market risk they incur and allocate sufficient amount of capital starting at the beginning of year 2002. BIS also suggests that value-at-risk (VaR) models in computing market risk should be used. The Turkish Bank Regulation and Supervision Agency already required all Turkish banks to compute and periodically report market risk and reserve adequate amount of capital since January, 2002. This study mimics an average trading marketable securities portfolio subject to market risk of the four largest Turkish banks. The publicly available quarterly financial reports of year 2001 for Isbank, Garanti, Yapi Kredi and Akbank are examined, and a mimicking portfolio composition is determined as bond investments; 60% in Turkish currency (TRL), 20% in American dollar (USD) and 20%in Euro (EUR). The VaR amounts of the mimicking portfolio are computed by applying Historical Simulation, Monte Carlo Simulation, Delta-Normal and Standard Methods. Finally, stress test is applied for each of the models by using crisis scenarios. The Turkish financial crises of November 2000 and February 2001 are simulated as stress scenarios. The results of stress testing reveal that all methods except standard method can stand the crisis in November 2000, but none of the models can stand the crisis in February 2001.