On the surface I don't agree with allocating surplus in proportion to
the loss portion of the unearned premium reserve for startup business.
The loss reserve number by itself does not say how long the reserve must
be held and the longer you hold the reserve, the greater the (dollar)
cost of the capital needed to support it.
Looking a little deeper and remembering a version of Murphy's law -
Constants aren't - I can see a way to wiggle out of this one by varying
the constant of proportionality with duration.
Actually, I prefer formulas with less wiggle room. At the very least
you learn something when things go wrong. Let me expose a formula to
the virtual arrows of CASNet.
Allocated Surplus for a line of insurance is proportional to:
Expected Loss times
Duration times
Marginal Surplus of the line (which implicitly allows for covariance and
parameter uncertainty.)
I will tighten this up by stating that the constant of proportionality
should be the same for all lines - in defiance of Murphy.
I will leave some wiggle room in my definition of total surplus. My
favorite surplus formula is to make it a function of the insurer's
aggregate variance. But I do not want to make a hard stand here.
Glenn Meyers
Insurance Services Office, Inc.
Internet: gmeyers@iso.com
Voice:(212) 898-5938
Fax: (212) 898-6060
----------
From: Ruhm, David [SMTP:David.Ruhm@aig.com]
Sent: Monday, June 29, 1998 10:16 AM
To: 'Meyers, Glenn G.'
Cc: 'casnet(a)lists.casact.org'
Subject: RE: Allocating Surplus and Risk Loads
Glenn,
In fact, I have worked through the math somewhat
extensively, since I built a surplus allocation model for a prior
employer which was based on these concepts (including the duration
concept).
I respectfully disagree with your claim that there would
be a problem with a startup or growing line of business, as long as you
are also allocating surplus in proportion to the loss portion of the
unearned premium reserve. If one does not include this additional loss
element in the allocation process, your point does appear valid. Does
this seem correct to you? - David Ruhm
----------
From: Bradford S. Gile [SMTP:kgecorp@ix.netcom.com]
Sent: Monday, June 29, 1998 9:45 PM
To: Meyers, Glenn G.
Cc: 'Ruhm, David'; 'casnet@lists.casact.org'
Subject: Re: Allocating Surplus and Risk Loads
The basic ideas that I have been following are:
1. Surplus allocated to a given line should be proportional to loss
duration, because surplus should not be released until the last loss
dollar has ben paid.
2. Volatility in losses and/or pricing inaccuracy (parameter risk)
must be reflected. I suggest the simple idea that surplus should be
directly proportional to the (historical) coefficient of variation on
loss ratios.
If these measures are adopted, I fail to see how a percentage of
loss reserves, including unearned premium, can be reasonable for
volatile long-tailed lines.
Brad Gile
Visit the CAS Web Site at http://www.casact.org
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