Edward Furman and Zinoviy Landsman
Abstract
This paper explores two tail-based premium calculation principles, the tail standard deviation (TSD) premium and the tail conditional expectation (TCE) premium, in their risk-adjusted and unadjusted forms. They are risk-adjusted using so-called distortion functions. We prove that the proportional hazard (PH) risk-adjusted TCE premium is larger than the unadjusted TCE premium. Additionally, given a risk distribution with location and scale parameters, we prove that the PH risk-adjusted TCE premium reduces to the unadjusted TSD premium.
Key words and phrases: tail conditional expectation, tail standard deviation, distortion function, Wang's premium principle, risk-adjusted tail standard deviation, risk-adjusted tail conditional expectation
Corresponding Author:
Edward Furman
Department of Statistics
E-mail: efurman@stat.haifa.ac.il
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