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#1
12-12-2018, 03:51 PM
 uyttrefds CAS SOA Non-Actuary Join Date: Nov 2018 College: Robert Morris University Posts: 2

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Last edited by uyttrefds; 12-13-2018 at 11:49 AM..
#2
12-12-2018, 06:15 PM
 Jim Daniel Member SOA Join Date: Jan 2002 Location: Davis, CA College: Wabash College B.A. 1962, Stanford Ph.D. 1965 Posts: 2,702

Quote:
 Originally Posted by uyttrefds Given a model is inverse Gamma and prior is Gamma, calculate the Bayesian premium and credibility premium (given sample size is n). The concrete example given is: X1,X2…,Xn∼IG(α=4,θ)θ∼Γ(α=50,θ=5000)n=25 From this, Z=100103, Pc=1008+50103, and a Bayesian premium of: (4n+0.5)[(α−1)(.01+∑xi)] However, not much work is shown, and I'm struggling to figure out a general formula for this case. How can I apply this to a general formula for Bayesian and Credibility premium with Inverse Gamma and a Gamma prior? Thanks so much!
What you have written makes no sense. Z must be between 0 and 1, and you wrote that Z = 100103. Can't be.

Also, you can't get the credibility premium (Buhlmann?) without knowing the observations.

Finally, you write the Bayesian estimate as a formula in "a" and "n", but previously wrote that a=4 once and a=50 another time and n=25.

Might you look again at the problem and then carefully restate your question?
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#3
12-12-2018, 09:14 PM
 uyttrefds CAS SOA Non-Actuary Join Date: Nov 2018 College: Robert Morris University Posts: 2

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Last edited by uyttrefds; 12-13-2018 at 11:50 AM..
#4
12-12-2018, 10:14 PM
 Jim Daniel Member SOA Join Date: Jan 2002 Location: Davis, CA College: Wabash College B.A. 1962, Stanford Ph.D. 1965 Posts: 2,702

The data and answer still make little sense. Might you scan the printed version of the problem and "solution" and post it? I suspect you have typed some things incorrectly.
__________________
Jim Daniel
Jim Daniel's Actuarial Seminars
www.actuarialseminars.com
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 Tags bayesian, bayesian premium, credibility premium, gamma

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