The aim of this talk is to provide an overview of the theory on Lambda quantiles and present its versatility via financial applications. Lambda quantiles are generalised quantiles, introduced by Frittelli, Maggis, P. (2014) under the name of Lambda Value at Risk. In particular, Lambda quantiles differ from usual quantiles in that the constant lambda is replaced with a threshold function Lambda allowing for more flexibility of the confidence level. We discuss alternative definitions of Lambda quantiles and derive their fundamental properties. We provide an axiomatic foundation for non-increasing Lambda quantiles based on the well-known locality property of quantiles that here we formalize. As original statistical application, we introduce the so-called Lambda quantile regression. We present the estimation of Lambda quantiles in a market risk setting by comparing methods based on classical assumptions on the return distribution and the Lambda quantile regression. We conclude with a backtesting exercise and discuss how this backtesting framework can be extended to other risk measures.

Ilaria Peri is a lecturer in mathematical finance at the Birkbeck University of London. She earned her doctorate from the University of Milan-Bicocca under the supervision of Marco Frittelli. Prior to joining academics, she worked as a financial consultant gaining experience in risk management and banking operations. Her research focuses on risk measures' theory and applications. Her major contribution is the introduction of the generalized quantile called Lambda value at risk on which she has been conducting theoretical studies and empirical applications. Her research has been published in internationally recognized journals and presented at invited seminars in academic and professional contexts, including regulatory authorities.