An analyst is studying housing prices over time in a certain region. They use a current map and so only consider neighborhoods that have survived without major incidents (like natural disasters, economic decline, etc.). They will probably underestimate the risk and overestimate the return of real estate investment in that region.
e.g. only paying a maximum amount if tragedy strikes
Frequency
Setting a threshold to which the policy only pays out after the threshold has been passed
Keeps the insurance company from being needled to death by administrative costs of frequent policy payouts
e.g. minor doctor appointments
Reinsurance
Policies that produce an option-like exposure, where one can pass risk above a fixed level of losses to the counterparty for a fixed premium (excess of loss). Other options are to share risks in more or less equal proportions.
Allows insurers take on risky (and potentially more profitable) policies by taking on an insurance policy themselves for the excess risk
airplanes, volatile manufacturing, etc.
Analysis
Fit one distribution to the smaller and more frequent attritional losses, and another disruption to the extreme losses, with the latter distribution often motivated by extreme value theory
This approach ignores the fact the each loss has an upper bound determined by the limits on the policy generating the loss. Also, since these extreme losses follow a very heavy tailed distribution, naïve estimators of the statistical properties of these losses are likely to be biased
Shadow Moments
Transform the data to a new domain that is unbounded, parameterizing EVT distributions in this domain, and then translating the implications of these models back to the original bounded domain
Cirillo, P., & Taleb, N. N. (2016). On the statistical properties and tail risk of violent conflicts. Physica A: Statistical Mechanics and Its Applications, 452, 29–45. https://doi.org/10.1016/j.physa.2016.01.050
Cirillo, P., & Taleb, N. N. (2020, June 1). Tail risk of contagious diseases. Nature Physics, Vol. 16, pp. 606–613. https://doi.org/10.1038/s41567-020-0921-x
Market Basket Analysis
Support: What percent of patients have disease 1 and disease 2?
Confidence: Of the people w/disease1, what percent also have disease 2?
Lift: How much more likely are you to have disease 2 if you already had disease 1 (and vice versa)