Admissible Risks and Convex Order

Series: 
Mathematical Finance/Financial Engineering Seminar
Wednesday, April 17, 2013 - 15:05
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
University of Waterloo

Hosts: Christian Houdre and Liang Peng

We introduce the admissible risk class as the set of possible aggregate risks when the marginal distributions of individual risks are given but the dependence structure among them is unspecified. The convex ordering upper bound on this class is known to be attained by the comonotonic scenario, but a sharp lower bound is a mystery for dimension larger than 2. In this talk we give a general convex ordering lower bound over this class. In the case of identical marginal distributions, we give a sufficient condition for this lower bound to be sharp. The results are used to identify extreme scenarios and calculate bounds on convex risk measures and other quantities of interest, such as expected utilities, stop-loss premiums, prices of European options and TVaR. Numerical illustrations are provided for different settings and commonly-used distributions of risks.