In this paper, we study various ways of changing probability measures with applications to Finance and Insurance. Changes of numéraire and Esscher transforms are considered, just as pricing kernels which are, in a complementary direction, a means of keeping a privileged probability measure....

While a lot of research concentrates on the respective merits of VaR and TCE, which are the two most classic risk indicators used by financial institutions, little has been written on the equivalence between such indicators. Further, TCE, despite its merits, may not be the most accurate...

This article focuses on the computation of VaR and CTE. It provides a very accurate and fast method, based on Fourier analysis and following Boyarchenko and Levendorskii (2000). Once the characteristic function of a marginal law is known, the computation of VaR or CTE is performed using a Fast...

In this paper we review existing statistical measures for systemic risk and discuss their strengths and weaknesses. Among them we discuss the Conditional Value-at-Risk (CoVaR) introduced by Adrian and Brunnermeier (2010) and the Systemic Expected Shortfall (SES) of Acharya, Pedersen, Philippon...

Robustness of risk measures to changes in underlying loss distributions (distributional uncertainty) is of crucial importance when making well-informed risk management decisions. In this paper, we quantify for any given distortion risk measure its robustness to distributional uncertainty by...