Title: Risk sharing and risk aggregation via risk measures

Date: 11/21/2016

Time: 4:10 PM - 5:00 PM

Place: C304 Wells Hall

Speaker: Haiyan Liu, University of Waterloo

In this talk, we discuss two problems in risk management using the tools of risk
measures.
In the first part of the talk, we address the problem of risk sharing among agents using
a two-parameter class of quantile-based risk measures, the so-called RangeValue-at-Risk
(RVaR), as their preferences. We first establish an inequality for RVaRbased
risk aggregation, showing that RVaR satisfies a special form of subadditivity.
Then, the risk sharing problem is solved through explicit construction.
Comonotonicty and robustness of the optimal allocations are investigated. We
show that, in general, a robust optimal allocation exists if and only if none of the risk
measures is a VaR. Practical implications of our main results for risk management
and policy makers will be discussed.
In the second part of the talk, we study the aggregation of inhomogeneous risks with
a special type of model uncertainty, called dependence uncertainty, evaluated by a
generic risk measure. We establish general asymptotic equivalence results for the
classes of distortion risk measures and convex risk measures under different mild
conditions. The results implicitly suggest that it is only reasonable to implement a
coherent risk measure for the aggregation of a large number of risks with uncertainty
in the dependence structure, a relevant situation for risk management practice.