Department of Mathematics

Colloquium

  •  Haiyan Liu, University of Waterloo
  •  Risk sharing and risk aggregation via risk measures
  •  11/21/2016
  •  4:10 PM - 5:00 PM
  •  C304 Wells Hall

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.

 

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Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
Fax: (517) 432-1562

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