Has anyone done the proof of the tail value at risk for the normal distribution? My integrating is a little rusty so I can't seem to get it to work.
Not an easy proof! Certainly not something you would be asked to do in the exam. (If you want to see the tricky derivation you could refer to "Loss Models - From Data to Decisions" by Klugman, Panjer & Willmot.)
We were asked to derive both the Var formula and the TailVar formula in the CT8 April 2012 exam that I wrote two years ago. This may help, here;- http://www.actuaries.org.uk/research-and-resources/documents/subject-ct8-exam-papers-and-examiners-reports Note that the integral of the product of a z -N(0,1) and f(z) follows by substitution of say u = 1/2z^2
