Comparison of conditional distributions in portfolios of dependent risks

• Published in: Insurance, mathematics & economics mathematics & economics, 2015-03, Vol.61, p.62-69
• Main Authors: Sordo, Miguel A., Suárez-Llorens, Alfonso, Bello, Alfonso J.
• Format: Article
• Language: English
• Subjects: Comonotonic vectors; Conditional distribution; Conditionally increasing; Dependence; Distorted random variables; Distortion function; Economic behaviour; Portfolio analysis; Probability distribution; Random variables; Risk assessment; Risk theory; Stochastic models; Stochastic orders; Stochastic processes; Studies; Vector space
• ISSN: 0167-6687; 1873-5959
• DOI: 10.1016/j.insmatheco.2014.11.008

Given a portfolio of risks, we study the marginal behavior of the ith risk under an adverse event, such as an unusually large loss in the portfolio or, in the case of a portfolio with a positive dependence structure, to an unusually large loss for another risk. By considering some particular conditional risk distributions, we formalize, in several ways, the intuition that the ith component of the portfolio is riskier when it is part of a positive dependent random vector than when it is considered alone. We also study, given two random vectors with a fixed dependence structure, the circumstances under which the existence of some stochastic orderings among their marginals implies an ordering among the corresponding conditional risk distributions. •Conditional distributions describing marginal risks under adverse events are studied.•We consider PDS and conditionally increasing random vectors.•Different location and variability stochastic orders are considered.