Abstract
Christofides (1998) studies the proportional hazards (PH) transform of Wang (I 995) and shows that for some parametric families, the PH premium principle reduces to the standard deviation (SD) premium principle. Christofides conjectures that for a parametric family of distributions with constant skewness, the PH premium principle reduces to the SD principle. I will show that this conjecture is false in general but that it is true for location-scale families and for certain other families.
Wang's premium principle has been established as a sound measure of risk in Wang (1995, 1996), Wang, Young, and Panjer (1997), and Wang and Young (1998). Determining when the SD premium principle is a special case of Wang's premium principle is important because it will help identify circumstances under which the more easily applied SD premium principle is a reliable measure of risk.
Volume
29:2
Page
191-196
Year
1999
Categories
Actuarial Applications and Methodologies
Ratemaking
Financial and Statistical Methods
Risk Measures
Financial and Statistical Methods
Risk Pricing and Risk Evaluation Models
Financial and Statistical Methods
Statistical Models and Methods
Publications
ASTIN Bulletin
