Re: Allocating Surplus and Risk Loads

Bradford S. Gile ( (no email) )
Fri, 26 Jun 1998 20:22:47 -0500

An approach that I have been working with can briefly described as follows:
1. Determine, using risk theoretic considerations, the aggregate surplus
needed to support existing business for all lines.
2. Allocate this surplus by line, for pricing purposes only, according to
the following criteria:
(a) Line Surplus, as a percentage of Line Premium, is directly proportional
to the coefficient of variation on loss ratios and loss duration, and (b)
the sum of line surpluses is the aggregate surplus.
This is a simple statement, but not easy to do.

I wholeheartedly agree with the idea that the model used for pricing should
be consistent with that used for profitability analysis.

Brad Gile

Meyers, Glenn G. wrote:

> I would like to comment on the allocation of surplus discussion.
>
> First - I hope that most of us would agree that the allocation of
> surplus is a pricing tool, and is not directly connected to the safety
> of the insurance policy that is "supported" by the allocated surplus.
> To quote Chuck McClenehan "A monoline auto company with $100 million of
> surplus is not the same as a multiline company with $100 million of
> surplus allocated to its auto line."
>
> Second - The real purpose of allocating surplus is to calculate a risk
> load. Conversely, you can allocate surplus in proportion to your
> favorite risk load. That is to say allocating surplus (as it is used)
> is equivalent to a risk load formula.
>
> The difference between the approaches is that pricing by allocating
> surplus is a "top-down" method and the risk load approach is a
> "bottom-up" method. There are probably some insights that the surplus
> allocaters can gain from looking at risk loads.
>
> I like to view risk load as the cost of marginal surplus. I offer three
> ideas related to some of the knottier problems involved in allocating
> surplus.
>
> 1. You have to hold surplus longer to support long tailed lines.
> Therefore the risk load should depend (among other things) on a factor
> times the duration of the losses - - at least as a first approximation.
>
> 2. Marginal surplus methods can account for correlations between
> lines. Suppose, for example, you assume that the total needed surplus
> is a function of the variance. If Y is the random loss of the policy in
> question and X the random loss for the rest of the insurer's business,
> then the marginal variance is Var[Y] + 2Cov[X,Y].
> You can also treat correlations between losses and
> assets by marginal methods.
>
> 3. You can treat "surplus substitutes", such as reinsurance, very
> much the same as surplus. For example, you can calculate the marginal
> cost of reinsurance.
>
> I suspect there are some things that the surplus allocaters can tell us
> riskies.
>
> Here are some papers for those who want more information on marginal
> surplus risk loads.
>
> Rodney Kreps - "Reinsurer Risk Loads from Marginal Surplus Requirements"
> - 1990 PCAS
>
> Glenn Meyers - "The Competitive Market Equilibrium Risk Load Formula for
> Catastrophe Ratemaking" 1996 PCAS. This is available on the CAS web
> site under "Publications"
>
>
> Glenn Meyers
> Insurance Services Office, Inc.
> Internet: gmeyers@iso.com
> Voice:(212) 898-5938
> Fax: (212) 898-6060
>
> Visit the CAS Web Site at http://www.casact.org
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