Illinois Mobile App Master Calendar

Title:
Worst-case risk with unspecified risk preferences

Abstract:
In this talk, I will first give an introduction of the worst-case distortion risk measure when information about distortion functions is partially available. Then I will show you the explicit forms of the worst-case distortion functions for different sets of plausible distortion functions. Specifically, when there is no concavity constraint on distortion functions, the worst-case distortion function is independent of the risk to be measured and the corresponding worst-case distortion risk measure is a combination of several VaR's at different confidence levels. When the concavity constraint is imposed on distortion functions and the set of concave distortion functions is defined by the riskiness of one single risk,  the  explicit form of the worst-case distortion function is obtained, which is related to the risk to be measured. When the set of concave distortion functions is defined by the riskiness of multiple risks, the infinite-dimensional optimization problem is reduced to a finite-dimensional optimization problem which can be solved numerically.

Speaker's Bio:
Dr. Haiyan Liu is an associate professor in the department of mathematics and the department of statistics and probability at Michigan State University. Her research interests are in risk measurement and management, model uncertainty, and reinsurance.