1. Frederik Weber fweber@lmu.de Ludwig-Maximilians-Universität München Institute for Risk and Insurance Management ARIA Annual Meeting · Quebec City 2007 Discussion of Enhanced Annuities, Individual Underwriting, and Adverse Selection – A Solution for the Annuity Puzzle ? by Gudrun Hoermann and Jochen Ruß

2. Institute for Risk and Insurance Management Frederik Weber · Munich School of Management · LMU München Quebec City · August 5-8, 2007 1 Enhanced Annuities, Individual Underwriting, and Adverse Selection – A Solution for the Annuity Puzzle ? by Gudrun Hoermann & Jochen Ruß Setting and Framework In many countries (partial) annuitization is compulsory or tax-favored. However, if annuity prices do not reflect individual life expectancy, persons with impaired health have to buy annuities at “unfair“ rates. If annuitization is not mandatory, these persons may choose not to annuitize. This may be one reason for the “annuity puzzle“. Enhanced annuities offer annuity rates that are adjusted to reflect individual life expectancy or health status: less-than-average-healthy persons receive higher payments, extremely healthy persons have lower payments guaranteed for life. Crucial: How to estimate individual life expectancy at the time of contracting? Quality of underwriting may determine profitability. Akerlof (1970, QJE): Premium discrimination by at least one market player attracts “low risks“, leaves non-discriminating insurers with only “high risks“ – or forces market to offer discriminating products.

3. Institute for Risk and Insurance Management Frederik Weber · Munich School of Management · LMU München Quebec City · August 5-8, 2007 2 Enhanced Annuities, Individual Underwriting, and Adverse Selection – A Solution for the Annuity Puzzle ? by Gudrun Hoermann & Jochen Ruß Summary and Contribution Assessment of profit/loss situation of provider offering enhanced annuities with individual underwriting or not offering them when competitors do so by means of Monte Carlo simulation. Individual mortality variation and varying underwriting quality are combined, and impact of adverse selection arising from discriminating competitors is discussed. Individual underwriting estimates individual mortality (modelled using frailty factor). Estimation is assumed to correlate with actual individual mortality (0<  <1) to reflect quality of underwriting. Assessment of profit/loss situation with varying underwriting quality: -Even poor individual underwriting improves expected profit, but this increase has to be paid for with an increase in the volatily. -Good news: volatily decreases when underwriting quality increases; for  >0.5 volatility of profits below non-discriminating provider‘s.

4. Institute for Risk and Insurance Management Frederik Weber · Munich School of Management · LMU München Quebec City · August 5-8, 2007 3 Enhanced Annuities, Individual Underwriting, and Adverse Selection – A Solution for the Annuity Puzzle ? by Gudrun Hoermann & Jochen Ruß Summary and Contribution Assessment of adverse selection effect: -Competitors offering discriminated (enhanced) annuities attract “low risks“, leaves non-discriminating provider with more-than-avg “high risks“ which in turn leads to losses. -Unlike Akerlof (1970), Rothschild/Stiglitz (1976): Market imperfections incorporated. Real markets exhibit transaction costs, assumption of instant response seems problematic – especially for insurance markets. -Not all “low risks“ choose discriminating provider, only s% of seriously impaired persons (with significantly reduced life expectancy, i.e. mortality above “selection barrier“) choose providers offering enhanced annuities. -Expected value of profits decreases, reduction increases with selection intensity s.

5. Institute for Risk and Insurance Management Frederik Weber · Munich School of Management · LMU München Quebec City · August 5-8, 2007 4 Enhanced Annuities, Individual Underwriting, and Adverse Selection – A Solution for the Annuity Puzzle ? by Gudrun Hoermann & Jochen Ruß Possible extensions and further analysis Illustrate results in absolute terms, not only % of premium volume. Account for different selection barriers for transferring annuitants, having more/less potential transitors than 9% of general population. Include realistic charges; use gross instead of net actuarial premiums. Incorporate age-dependent deviations from life table mortality rates, thus accounting for stronger deviations at older ages. Adjust health distribution and its parametrization to reflect epidemiological or medical knowledge. Assume e.g. DAV2004R table for underwriting, have individual mortality follow “portfolio life table“ of typical (German) provider. Incorporate volatile asset returns in addition to profits/losses from individual underwriting.