Insurance Deductibles, explained.
An insurance deductible is the portion of an eligible loss retained by the policyholder before the specified cover pays.
Why it happens
Initial wealth one hundred faces a quarter probability of losing forty. Premium equals expected indemnity times one plus a loading; two-state expected wealth and a log-utility certainty equivalent are computed separately.
An insurance deductible is the portion of an eligible loss retained by the policyholder before the specified cover pays.
Read the result
Expected final wealth and the log-utility certainty equivalent are different evaluations of the same two-state outcomes.
A worked example
Compare fair insurance with retaining the entire loss
Set premium loading zero and deductible forty to inspect uninsured wealth one hundred or sixty.
Reduce deductible to zero, yielding a fair premium ten and wealth ninety in either state.
Compare unchanged expected wealth ninety with the changed certainty equivalent under the stated risk-averse utility benchmark.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
Initial wealth one hundred faces a quarter probability of losing forty. Premium equals expected indemnity times one plus a loading; two-state expected wealth and a log-utility certainty equivalent are computed separately.
Where this idea is useful
A practical use
Distinguish a reduction in expected cost from a reduction in financial variability.
A common misconception
“Equal expected wealth means every risk preference must be indifferent.”
A risk-averse utility function can value reduced variability even when average wealth is unchanged; different preferences or costs change the comparison.
What this explanation leaves out
- Loss probability, payment enforcement and log utility are supplied assumptions. Exclusions, limits, changing behaviour and real contracts are omitted; no personal insurance recommendation is made.
Is log utility a measurement of my insurance preferences?
No. It is a supplied benchmark, with no personal calibration, real contract analysis or recommendation.
Are you optimising expected money, a utility criterion or a constraint on a possible loss?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.