Mathematical Models or My Kingdom for a Lotus
The specialized mathematical models that we had
built for our many diverse projects were beginning to cover every
aspect of our operation and the impulse to connect them into one
grand comprehensive construct was irresistible to any dreamer
of castles. In our lunchtime scheming, KGH had been sketching
coming crises and rumors of fears in the market. The outlines of
the missing towers and moats, together with strategies of their
use, were taking shape.
We would only need to add modules to produce
estimates of expense and investment income. Those would
complete our picture of the company's status. The links to
connect these modules to our main models, Crystalball for exposures
and Houdini for claims behavior, already existed. When the
technical details of the programming connections were
tested and assembled, we would hope for a balance of
robustness and sensitivity.
Because of the growth capacity inherent in accounting's
computerization, the expense module could be built around the
written policy count using incremental rates and staff
productivities. Acquisition costs could be treated as a spinoff
from the same policy count along with the premium rates, the two
mainsprings of our exposure model. Investment income that
flowed from the unearned premium reserves, specifically the
use of premium funds until related claims occurred and were
reported for payment, could be based on the complement of our
exposure calculations of earned premiums; the arrival of claims
being, in a sense, the earning of our premium and the end of its
initial availability for investment. This part of our investment
income, as well as the expenses, acquisition costs, and the
premiums themselves would flow to the bottom line at the
appropriate points in time. The earned exposures would flow to
the claims model on their own timetable.
The claims model would then produce the tables of
simulated, reported claims, their payment histories, their
reserves and their so-called runoff, that excess over, or
shortfall from, those reserves as the claims settled over time.
The remaining part of investment income, that part arising
from the use of moneys held for the eventual payment of
reported claims, could be simulated from the tables of reserves
generated by our claims model. This component of the
investment income along with the claims' impacts then flowed
to the bottom line at their appointed times.
The whole structure would only require input about the
rates, the resulting policy counts and projections of claims count
per policy. Elegantly manageable. But before we would ask
this grand model to draw the picture of the company's future
bottom line emerging from choices of these few considered inputs,
there would be a wealth of parameters to fine tune, such as
various inflation rates, commission rates, interest rates, staff
productivity. We would need to know what size changes in
each of these parameters, or combinations of them, made
substantive changes in the company future. If any proved
sensitive, they would need to be treated as variable rather
Because of the myriad delays inherent in the claims model,
identifying the possible impact of any combination of
input variables on the future would require an examination of
the bottom line over an extended time frame. Our resulting
picture of net status would need to be a sequence of yearends in
order to describe the full impact of a given combination of rate
strategy and market reaction. The perfect summary values to
decorate the ends of a decision tree's branches!
As we put this model through testing, it exhibited such
realistic behavior as we flexed its inputs and parameters, that
it was more orrery; too mobile to envision it as stolid structure.
It was sheer pleasure to watch it perform. To seek its insights
was to approach a soothsayer and we so christened it. Our
Oracle would be Houdini with a Crystalball, in a Pear Tree.
Rumors of our successes had been entertaining Home Office
for some time now and, in spite of our titles, London
summoned us for an audience with their chiefs to see what we
provincials were like, to see for themselves what magic we
possessed, that they had found nowhere else. Not only were
our systems, models and techniques very exciting but the tools
we had at our disposal were the rough leading edge of
technology and esoteric new languages; no such creatures yet as
spreadsheets or modeling systems.
We had a couple of months to prepare our exhibits, to
gather our programs, to pack our bags and still when the days
grew short there were surprises...