Measuring risk when expected losses are unbounded

Measuring risk when expected losses are unbounded
Alejandro Balbás (1) Iván Blanco (1) and José Garrido (2)
(1) University Carlos III of Madrid. C/ Madrid, 126. 28903 Getafe (Madrid, Spain).
alejandro.balbas@uc3m.es and ivan.blanco@uc3m.es
(2) Concordia University. Department of Mathematics and Statistics.
1455 de Maisonneuve Blvd. West, LB-901, Montreal, Quebec, Canada H3G 1M8.
jose.garrido@concordia.ca
Abstract This paper proposes a new method in order to introduce coherent risk
measures applying for risks with infinite expectations, such as those characterized by
some Pareto distributions. Some examples are given, such as extensions of the
Conditional Value at Risk and the Weighted Conditional Value at Risk. Actuarial
applications are analyzed, such as new approaches in Operational Risk and extensions
of the Expected Value Premium Principle when expected losses are unbounded.