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Activity Number: 375
Type: Topic Contributed
Date/Time: Wednesday, August 1, 2007 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract - #308406
Title: Risk Measures, Distortion Parameters, and their Empirical Estimation
Author(s): Bruce Jones*+ and Ricardas Zitikis
Companies: University of Western Ontario and University of Western Ontario
Address: Dept of Stats and Act Sci, London, ON, N6A 5B7, Canada
Keywords: Premium principle ; risk measure ; distortion parameter ; proportional hazards transform ; Wang transform ; conditional tail expectation
Abstract:

Risk measures are of considerable current interest. Among other uses, they allow an insurer to calculate a risk-loaded premium for a random loss. However, the premium principle in use by the insurer may be, at least in part, based on considerations other than risk. It is then important to quantify the degree to which the premium compensates the insurer for the risk associated with the loss. This can be done by choosing a suitable risk measure and solving for the parameter that leads to the insurer's premium. When the loss distribution is unknown, this becomes a statistical estimation problem. I will discuss the nonparametric estimation of the parameter associated with a distortion-based risk measure. It is assumed that the premium principle is known, but no information is assumed about the loss distribution, and therefore empirical estimators are used.

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Revised September, 2007