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Using Stochastic Optimization to Underwrite a Portfolio of Insurance Linked Securities
November 1, 2016
By: Morton N. Lane, President
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Optimal Insurance and Reinsurance Portfolios... |
Sept. 24, 2007
By: Morton N. Lane, President; Jerome Kreuser
Some reinsurers use optimization procedures to generate
underwriting portfolios, maximizing expected returns which are
perfectly aligned with their stated risk preferences. Similar
objectives apply to those who use simulation or DFA techniques.
However, beyond the optimal portfolio itself, optimizers as part of
their output also generate marginal economic signals, such as “implied”
or “risk adjusted” probabilities which are important but underused and
often misunderstood management tools. The purpose of this paper is to
further illustrate the power of those economic signals.
In an earlier paper4 we illustrated how implied or risk-adjusted
probabilities from optimal solutions may be derived and used in a
simple single risk zone example. In this paper we continue the same
simplifying universe but with multiple risk zones. We then use the
marginal outputs to illustrate how to price indifference points for
traditional retrocession purchases, which complement the optimum
portfolio. In addition, we show how the implied probabilities may be
used to allocate retrocession costs to the respective zones. Of course,
allocating retrocession costs is an important sub-species of allocating
capital costs in general. Actually we also believe the marginal outputs
are the key to unlocking general capital allocation decisions.
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An Introduction to the Benefits… |
June 2, 2006
By: Morton N. Lane, President; Jerome Kreuser
The use of optimizing models for portfolio selection and construction in the context of insurance is relatively new. Investment portfolio managers regularly rely on optimization, but underwriters are much more likely to use good old fashion trial and error, with some admittedly quite sophisticated, simulation techniques to developing underwriting portfolio strategies. The unique characteristics of insurance risk, e.g. long tails, one sided correlations etc, did not lend themselves to early optimization models but, certain technical breakthroughs have advanced optimization modeling and insurance risk is now a potentially important application. Moreover, once adopted, optimization techniques have considerable informational benefits over simulation.
The purpose of this paper is to illustrate these benefits. We do this in two ways. First by tracing out the numerical implications with a simple practical application; second, by introducing some of the algebra4 necessary to extract the benefits in more general and complicated cases. The techniques have been successfully applied in several large scale real situations and further technical details will be forthcoming in subsequent papers
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