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\def\astin{{\sc Astin}}
\def\afir{{\sc Afir}}
\rightline{25. September 1997}
\bigskip\bigskip\bigskip
\centerline{\large Report on the International ASTIN/AFIR
Colloquia 1997}
\bigskip\bigskip\noindent
The 28$^{\rm th}$ \astin\ International Colloquium and the
7$^{\rm th}$ International \afir\ Colloquium where held in the
same week from August 11$^{\rm th}$ to August 15$^{\rm th}$
1997, in the Cairns International Hotel, North Queensland,
Australia. This first ever joint meeting culminated in a 
\lq\lq joint day\rq\rq\ on the Wednesday, recognising the fact that
\astin\ and \afir\ delegates have an increasing number of
interests in common and that both actuarial and financial skills
are necessary to cope with the new challenges of today. The CNN
announcement of the merger of the Winterthur Insurance company and
the Credit Suisse Group, news of which spread rapidly among
delegates, emphasised this point.

The joint meeting was also an excellent opportunity to celebrate
the 100$^{\rm th}$ anniversary of the Institute of Actuaries of
Australia. The first gathering of Australian actuaries to discuss
the formation of an institute took place on August
12$^{\rm th}$ 1897.

This historic meeting (and possibly also the chance to visit the
Great Barrier Reef and the tropical rain forest, two of
Australia's World Heritage Areas) attracted a large audience: 193
people registered for \astin\ and 209 registered for \afir; both
numbers include 126 people who took the opportunity to register
for both colloquia. The delegates came from 31 different
countries with groups of at least ten delegates from Australia,
Belgium, Canada, Denmark, Germany, Japan, Netherlands, Norway,
Sweden, Switzerland, United Kingdom and the USA.

Eight internationally recognised keynote speakers gave lectures 
during the week; 21 speakers presented papers during the two
\astin\ days, nine during the afternoon of the joint day; 31
speakers presented their research, partly in concurrent sessions,
during the two \afir\ days. The combined proceedings of both
colloquia have an approximate length of two thousand pages.
Obviously, we can only mention the general themes and some
highlights of the colloquia, which reflect our personal tastes and
understanding.

The \astin\ colloquium opened with a session on the topical
subject of catastrophe risk. Bruce Harper held an entertaining
invited address on the modelling of wind hazards and insurance
risks in Australia. This talk was impressive in showing how, in
the absence of reliable data on the losses caused by tropical
storms, insurance events could be simulated using physical models
for storms and for the damage caused by storms with different
characteristics.

In the second invited address Prof.~Paul Embrechts, ETH Z\"urich,
outlined the possibilities offered by extreme value theory
in the modelling of catastrophic losses in the situation where
some data are available. The basic message of extreme value theory
is that there are natural probability distributions and models for
extremely large observations in the same way that there are
natural models for average values (such as the well known Gaussian
normal distribution). Further contributed talks on extreme values
by Alexander McNeil and Dietmar Pfeifer indicated that this
interesting branch of probability theory is now coming to the
attention of practising actuaries.

A second major topic on the first day was classification of risks,
and this session showed the broad palette of statistical techniques
now being used in insurance research. Talks ranged from the
application of cluster analysis in the formation of tariff classes
using neural network-based implementations to the evaluation of
occupational risks using methods from survival analysis. Greg
Taylor, who later in the week became the recipient of the first
ever gold medal of the Institute of Actuaries of Australia,
submitted two papers in this section, one on the use of Whitaker
spatial smoothing to obtain good estimates of risks which vary
geographically, the second on the setting up of a bonus--malus
scale of premiums in the presence of additional rating factors. 

The final session of the day consisted of papers on the subject of
premium rating in which one identifiable theme was the use of
Markov state models. Papers presented by Jose Garrido and by
Ermanno Pitacco addressed the use of such models in tarifying
disability and health insurance. The day ended with delegates
enjoying dinners at one of two exotic locations. One party sampled
traditional Queensland fare at the Riverstone Homestead, a
historical sugar plantation house; a second group dined at the
luxury Paradise Palms Golf Course.

In view of the copiousness and excellence of the food and wine it
was all the more remarkable that attendance had not declined on
the second morning when delegates reconvened to hear talks in two
sessions entitled statistics and reserving. In the
former session David Dickson described an alternative to the
classical compound Poisson risk process; he derived results for
the probability and the extent of ruin when claims occur as a more
general renewal processes. In the latter session two papers
looked at different aspects of the calculation of development
factors, or link ratios, in the loss development problem. The
first paper by Glen Barnett and Ben Zehnwirth focussed on the use
of diagnostics in the selection of competing models for loss
development; the second paper by Erhard Kremer looked at a robust
version of the classical chain-ladder model. After these short
but intensive scientific sessions delegates spent the afternoon
on an enjoyable excursion with the Kuranda historical railway
from the coast up to Kuranda, passing the Barron Falls, and down
again with Skyrail above the canopy of the tropical rainforest.
This provided a most unusual but congenial backdrop for the
important conference activity of catching up and networking with
colleagues.

The joint \astin/\afir\ day was mainly devoted to the
securitization of insurance risk, the issue which best
represents the convergence of \astin\ and \afir\ interests. The
first keynote lecture by James A. Tilley addressed the
securitization of catastrophic property risks, the second by
Prof.\ Neil Doherty, University of Pennsylvania, was about
financial innovation in the management of catastrophe risk.

For \astin\ delegates the first talk followed nicely from the
discussion of catastrophe risk on day one. The interest in
securitization arises because of increased exposure to
catastrophes and the empirical observation that frequency and
severity of large losses are on the increase. Insurance companies
alone may not have the capacity to handle the mega-catastrophes
of the future.

A possible way to pass the insurance risk to investors (in return
for a corresponding risk premium) are catastrophe bonds.
Investors can use these bonds to diversify their portfolios
because natural disasters, for example, have a very small
correlation with financial market risk. 
Catastrophe bonds can be classified as

\item{--} Pure catastrophe bonds, when the principal and the
coupons are at risk,
\item{--} Principal-protected catastrophe bonds, when only
the coupons are at risk,
\item{--} Deferred catastrophe bonds, when no payment as
such is at risk, but the date of the payments can be deferred,
leaving the issuer of the bond an interest gain in case of a
catastrophe.

James Tilley described some products which have so far been
developed, such as the California Earthquake Authority risk bonds
(an example of the second type of bond above), and looked at
reasons why the market for securitized products has generally
developed slowly. Among these reasons are the favourable
catastrophe experience since 1994, the rehabilitation of Lloyds
and the weaknesses of proposed securitization structures.
However, he suggested there was still a potential need for cost
efficient products with flexible annual renewal possibilities and
more of the simplicity which makes traditional reinsurance
arrangements appealing.

In the afternoon presentations of the joint day, several points
raised in the keynote lectures were studied more deeply. The
correspondence of catastrophe bonds and defaultable bonds was
discussed, both leading to an incomplete market setting which
causes difficulties in the pricing methodology. An approach,
advocated by Prof.~Martin Schweizer, is to decompose the risk of
say a catastrophe bond into a hedgeable part and a residual part,
which is treated by standard actuarial methods to obtain a price.
This leads to a bid--ask price spread  for the catastrophe bond.
A specific principal-protected catastrophe bond, the Winterthur
Insurance convertible bond with WinCat coupons \lq\lq hail\rq\rq,
was considered by Uwe~Schmock and several methods for the
estimation of the coupon values were presented; model risk for
the statistical analysis and the corresponding pricing of the
bond were investigated. Further talks addressed selected topics of
asset liability modelling, risk-based capital allocation,
risk-adjusted performance management and reserving for future
claims taking stochastic interest rates into account.

The joint day ended with a lavish \astin/\afir\ colloquia banquet
in the Great Hall of the Cairns Convention Centre, where the
gold medal was awarded to Greg Taylor, the chairman of the
\astin\ scientific committee.

The first pure \afir\ day started with Prof.~Phelim Boyle's
keynote lecture on quasi-Monte Carlo methods for numerical
integration. He showed that deterministic low discrepancy
sequences outperform crude Monte Carlo methods in low dimensions,
but that this superiority diminishes for high dimensions or 
discontinuous integrands. Randomisation of low discrepancy
sequences and reduction of the effective dimension of the
integration problem can come in handy in these cases. 

After morning tea, the \afir\ prize winning papers were presented
and the certificates awarded. The first \afir\ prize was given
to Glen R. Harris, AMP Society, Australia, for his paper on
\lq\lq Regime switching vector autoregressions: a Bayesian
Markov chain Monte Carlo approach.\rq\rq\ The second \afir\ price
was divided between D. J. F. Nonnenmacher and Jochen Russ,
University of Ulm, Germany, for their paper \lq\lq Equity-linked
life insurance in Germany: quantifying the risk of additional
policy reserves\rq\rq\ and Ken Seng Tan and Prof.~Phelim Boyle,
University of Waterloo, Canada, for their paper \lq\lq
Applications of scrambled low discrepancy sequences to exotic
options.\rq\rq\ 

Prof.~Stanley Pliska, University of Illinois, gave his keynote
lecture on a model for risk-sensitive dynamic asset allocation.
For measuring the performance of the model, he presented various
infinite-horizon criteria: expected growth rate of the portfolio,
expected utility growth rate of the portfolio and a risk-sensitive
growth rate criterion. A major aim of this model was to combine
the statistical work for parameter estimation with the forecast
for asset management. Applied to a historic data set, the
corresponding management strategy showed an impressive
performance.

Several contributed talks also presented and compared
asset/liability management strategies for various settings such
as continuous-time pension fund models or portfolios of
defaultable assets. Some further themes ranged from inflation
modelling to an axiomatic classification of usurious loans and
tax-efficient, option-based compensation packages for employees.

The last day of the colloquium started with the keynote lecture by
Prof.\ J. David Cummins, University of Pennsylvania, about the use
of financial derivatives in corporate risk management,
participation and volume decisions in the insurance industry.
According to this talk, the main reasons for the use of
derivatives in the insurance industry are to avoid
\item{--}Financial distress costs like bankruptcy costs,
additional regulatory restrictions and reputational losses
affecting relationships with key employees, supplies and
customers,
\item{--}Duration problems in the asset/liability management,
including the liquidity risk of private placements or real estate,
\item{--}Foreign exchange risk, and
\item{--}Losses due to the convexity of income tax schedules.

In the contributed talks on Friday, partly in concurrent
sessions, Peter Antal applied ideas mentioned on the joint day to
the pricing of regular options, arguing that option prices should
contain a risk premium in any case because a dynamic hedge as in
the Black--Scholes model is not possible in practice.
Godfrey Perrott presented policyholder considerations for the
demutualisation of a company. David Wilkie showed that different
prices of risk and different portfolios cause a failure
of the capital asset pricing model in a multi-currency world.
Robert Clarkson critically discussed the financial risk in the
Markowitz and Black--Scholes worlds, explaining that
investors would not accept a certain level of risk (bankruptcy for
example), no matter how high the offered risk premium is; a
comparison with the risk of death in some dangerous sports made
his point clear. Further talks concerned the fitting of the term
structure, pricing rate of return guarantees, the use of genetic
algorithms, the Italian pension plan or the social security system
in Indonesia, for example.

The final keynote lecture was given by Dato'Abdul Khalid bin
Ibrahim, currently the Group Chief Executive of Kumpulan Guthrie
Berhad. He gave an overview of the Asian capital markets with
special focus on the development of the capital markets in
Malaysia and Singapore, and he encouraged the audience the invest
in these markets. The colloquium closed with the annual general
meeting of the \afir\ section.

We close with a glimpse of future events.
The 8$^{\rm th}$ International \afir\ Colloquium will take place
in Cambridge, United Kingdom, 15$^{\rm th}$ to 17$^{\rm th}$ of
September 1998. Write to David Golder, \afir\ 1998 Colloquium
Secretariat, Institute of Actuaries, Staple Inn Hall, London,
WC1V~7QJ, United Kingdom, for information. The next General
Insurance Convention \& \astin\ Colloquium will take place in
Glasgow, Scotland, 7$^{\rm th}$ to 10$^{\rm th}$ of October 1998.
For information write to Linda Pritchard at the above address.
The next joint International \astin\ and \afir\ Colloquia are
scheduled to take place in Tokyo, Japan, from 22$^{\rm nd}$ to
25$^{\rm th}$ of August 1999, followed by the Centenary
Convention 29$^{\rm th}$ to 31$^{\rm st}$ of August.
\bigskip\bigskip
\rightline{Alexander McNeil and Uwe Schmock\qquad\qquad}
\end 



