Optimal Insurance

Tangency on the diagonal

Loads and partial coverage

Deductibles and the load's fingerprint

When insurance fails

At fair odds with risk-averse v, what coverage does the consumer buy?

At gamma 0.35, full coverage costs 140 and yields (860, 860), utility 29.33, while uninsured utility is 29.84. What does the consumer do?

What is the economic logic of a deductible in optimal contracts?

Why do private markets struggle to insure hurricane or pandemic risk at fair odds?

At gamma 0.28, compute the premium for full coverage of the 400 loss, and write the number.

With v the square root, compute the uninsured expected utility, 0.75 root 1000 plus 0.25 root 600, rounded to two decimals, and write the number.

At the fair gamma of 0.25 with v the square root, full coverage yields (900, 900). What utility does the insured enjoy?

At gamma of 0.28, full coverage costs 112 and yields (888, 888), utility about 29.80. What does the consumer do?

A policy with a 100 deductible charges gamma 0.35 on the remaining 300 of coverage. What bundle does buying it produce?

Insurance data show most policies partial rather than full. What explains the pattern?

At gamma of 0.30, compute the premium for full coverage of the 400 loss, and write the number.

With a 100 deductible and 300 of coverage at gamma 0.35, compute the bad-state consumption, and write the number.