Section: ArticlesTitle: Capital requirements with defaultable securities / Walter Farkas, Pablo Koch-Medina, Cosimo MunariAuthor: Farkas, WalterNotes: Sumario: We study capital requirements for bounded financial positions defined as the minimum amount of capital to invest in a chosen eligible asset targeting a pre-specified acceptability test. We allow for general acceptance sets and general eligible assets, including defaultable bonds. Since the payoff of these assets is not necessarily bounded away from zero, the resulting risk measures cannot be transformed into cash-additive risk measures by a change of numéraire. However, extending the range of eligible assets is important because, as exemplified by the recent financial crisis, assuming the existence of default-free bonds may be unrealistic. We focus on finiteness and continuity properties of these general risk measures. As an application, we discuss capital requirements based on Value-at-Risk and Tail-Value-at-Risk acceptability, the two most important acceptability criteria in practice. Finally, we prove that there is no optimal choice of the eligible asset. Our results and our examples show that a theory of capital requirements allowing for general eligible assets is richer than the standard theory of cash-additive risk measures.Related records: En: Insurance : mathematics and economics. - Oxford : Elsevier, 1990- = ISSN 0167-6687. - 03/03/2014 Volumen 55 Número 1 - marzo 2014 Other categories: 6Rights: In Copyright (InC)Referencias externas:
