A new approach for studying stochastic ordering of risks

Wednesday, April 2, 2014 - 11:00
703 Thackeray Hall
Speaker Information
Liang Hong
Robert Morris University

Abstract or Additional Information

Stochastic orders have been widely applied in actuarial science, insurance, quantitative finance and risk management. In this talk, we introduce a new approach for studying stochastic ordering of risks. This approach has two potential advantages: (1) it may lead to simple proofs of complicated theorems; (2) it provides an opportunity of studying many different stochastic orders under a unified framework. As an illustration, we will apply this approach to prove separation theorems for three commonly-used risk orders: stochastic dominance order, stop-loss order and convex order.

In particular, our proof of the separation theorem for convex order is simpler than the one in the existing literature. Furthermore, we will also show that this approach yields a decomposition theorem as well as a countable approximation property for each of the three risk orders under consideration.