I think the way you phrase the question is what leads to the
confusion. When you say you are writing 1000 six-month auto
policies evenly throughout the year you seem to mean that you
have 500 in-force policies at any point in time. Some readers may
interpret your statement as meaning that you have 1000 in-force
policies. Note that in-force amounts are a point in time while
premiums are values measured over some period of time, usually
a year.
So if you have 500 in-force policies, your in-force premium is
500*(average premium per policy). Likewise, your in-force
exposures would be 500*(average exposures per policy), which
is 500*(.5car-years) = 250 car years.
Caveat - I last read M-D paper 5 years ago, but perhaps that is
an advantage.
I hope this is enlightening or at least thought provoking to one of you.
Barry Zurbuchen, FCAS
----------
From: Paul_Budde@blanch.com
To: Zurbuchen,Barry C.; studygroup6@lists.casact.org
Subject: Miller-Davis Refined Premium Adjustment
Date: Friday, April 24, 1998 10:44AM
I am trying to understand in-force premium calculations when policy
terms are less than one year.
Suppose I have a book of business writing 1000 six-month auto policies
evenly throughout the year. Since the standard exposure unit is
car-years, my written exposures in the year will be 500, as will my
earned exposures. This tells me that in the notation of Miller-Davis
f(x) = 500
g(x,y) = f(x-0.5*y) = 500
When it comes time to calculate in-force exposures at time x0, M-D says
it should be for k=0.5,
k * INTEGRAL(g(xo,y) dy) from 0 to 1.
This produces an in-force exposure of 250, even though I know I have 500
cars on the road which I am insuring every day of the year.
What gives? Anybody have any insights?
Paul
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