2016-Risk Measures in Actuarial Science

Risk Measures in Actuarial Science 
Organizer and Chair: Jun Cai (University of Waterloo) 

EDWARD FURMAN, York University
A New Risk Measure for Heavy Tailed Risks [PDF]
I will introduce a new tail-based risk measure, the Tail Gini (TG) risk measure, and discuss its properties and links to Solvency II. The TG risk measure aims to catch the variability along the (right) tail of the risk's distribution, but unlike the Tail Standard Deviation risk measure ([Furman, E. and Landsman, Z. (2006). Tail variance premium with applications for Elliptical portfolio of risks. ASTIN Bulletin, 36(2), 433 - 462]), the TG risk measure only requires the finiteness of the first moment. I will suggest an economic capital allocation rule induced by the TG and show explicit expressions in the context of risk portfolios with jointly elliptical risk components. This is a joint work with Ricardas Zitikis of Western University. 
MÉLINA MAILHOT, Concordia University
Multivariate TVaR Risk Decomposition Techniques [PDF]
In this talk, different methods of calculating the contribution of each risk within a portfolio with dependent business lines that are not aggregated will be presented. From an enterprise wide risk management point of view, it has become important to calculate the contribution of each risk and provide conservative provisions. The multivariate Value-at-Risk and Tail-Value-at-Risk will be presented, and we focus on three different methods to calculate optimal finite sets for the contribution of each risk within the sums of random vectors to the overall portfolio, which could particularly apply in actuarial science. Approximations methods and empirical estimators will also be presented. 
RUODU WANG, University of Waterloo
Risk Aversion in Monetary Risk Measures  [PDF]
We incorporate the notion of risk aversion favoring prudent decisions from financial institutions into the concept of monetary risk measures. The class of monetary risk measures representing this risk aversion is referred to as consistent risk measures. We characterize the class of consistent risk measures by establishing an Expected Shortfall-based representation. The results obtained suggest that for the determination of regulatory capital, every regulator in favor of risk-averse financial decisions is essentially using a combination of Expected Shortfalls up to some adjustments. This reveals important advantages of the Expected Shortfall for prudent regulation as compared to the Value-at-Risk, a topic very much under discussion in Basel III.