Faculty of Actuarial Science & Insurance Seminar with Dr Stephen Mildenhall

Pricing Insurance Risk: Theory and Practice

Abstract
This presentation discusses the main results from my monograph with John Major published earlier this year. It focuses on portfolio pricing and its allocation to individual units. We show how the standard assumption of a constant cost of capital (which goes back to Adam Smith) requires two risk measures, not one, and is inconsistent with observed bond credit spreads and cat bond pricing. We then explain how spectral risk measures provide a theoretically satisfying pricing model, but one that doesn't hold in practice because of subtle non-differentiability problems, which manifest themselves to practitioners as the "order problem." The theoretical model is also hard to calibrate. Next, we invert the calibration problem and provide a concrete description of the set of spectral risk measures that determine the same price for a given portfolio. We show how pricing functionals in this set can be interpreted as tail-centric or volatility-centric. They give different allocations to a net sub-portfolio over a range material to real-world decision-making. These findings are interpreted in light of current catastrophe reinsurance market dislocations.