John Major and I have given several presentations to actuarial groups on topics related to PIRC since 2020.
They provide helpful background information about distortion functions and the natural
allocation, together with more context and motivation. They also include some detailed
numerical examples and discuss an application to insurance market structure.
The three joint presentations build on work with Don Mango and Jesse Nickerson that we presented at the 2018 CAS Annual Meeting in Las Vegas. A series of eight video presentations is available from those talks.
When is Premium Riskier Than Loss?
Mildenhall/Wright Webinar, November 2021.
Premium to GDP 1923-2020 • cyclical growth post-WW2 • cycle driven by commercial lines • cycle by line • growth by line • surplus and premium dynamics • loss ratio volatility by line • loss and premium dynamics • COVID effect.
Presented with David Wright, host of the Not Unreasonable Podcast.
See PIRC C for more details.
A Modern Approach to Pricing for Risk
Mildenhall Talk, November 2021.
Avoid Arbitrary Assumptions! • the wisdom of Adam Smith • three market actors • problems with additive pricing functionals • buyer motivation and bid-ask spreads • insurers as transformers and intermediaries • working with Bernoulli risks • distortions and spreads • adding up to price realistic risks • the problems with capital allocation • marginal and risk decomposition are the same (Delbaen's theorem) • the problems caused by limited liability
Charging
for Diversifiable Risk and Proud to Do It: Multiline Insurance Pricing with a Distortion
Risk Measure
Major/Mildenhall, CAS Webinar, September 24, 2020.
types of risk •
CAPM •
market charges for idiosyncratic risk •
winner's curse •
ambiguity aversion •
tranching capital •
fungible capital •
distortion functions •
scenario-loss domain •
expected losses with limited liability •
equal priority •
expected loss by line with equal priority •
natural allocation •
frictional costs of capital •
two-line example •
understanding conditional losses by line •
why negative margins? •
market structure implications •
four market actors •
how risks pool •
why is Florida homeowners written in monoline companies?
How to Allocate Capital if You Really Must
Major/Mildenhall, CAS Spring Meeting, May 13, 2020
why allocate capital? •
allocate cost of capital •
tranching capital •
fungible capital •
distortion functions •
scenario-loss domain •
expected losses with limited liability •
equal priority •
expected loss by line with equal priority •
natural allocation •
two-line example •
understanding conditional losses by line •
why negative margins?
Spectral Risk Measures and Applications in Insurance ERM
Major/Mildenhall, ASTIN Special Interest Webinar, March 25, 2020
why allocate capital? •
allocate cost of capital •
tranching capital •
distortion functions •
scenario-loss domain •
expected losses with limited liability •
equal priority •
expected loss by line with equal priority •
natural allocation •
four-line example