Capital allocation for credit portfolios with kernel estimators

Determining contributions by sub-portfolios or single exposures to portfolio-wide economic capital for credit risk is an important risk measurement task. Often economic capital is measured as Value-at-Risk (VaR) of the portfolio loss distribution. For many of the credit portfolio risk models used in practice, the VaR contributions then have to be estimated from Monte Carlo samples. In the context of a partly continuous loss distribution (i.e. continuous except for a positive point mass on zero), we investigate how to combine kernel estimation methods with importance sampling to achieve more efficient (i.e. less volatile) estimation of VaR contributions.Comment: 22 pages, 12 tables, 1 figure, some amendment

Extinction, Persistence, and Evolution

Extinction can occur for many reasons. We have a closer look at the most basic form, extinction of populations with stable but insufficient reproduction. Then we move on to competing populations and evolutionary suicide