Insurance Economics and Principles of Insurance
This domain tests why insurance exists and how markets and contracts behave: risk aversion and willingness to pay, the principle of indemnity, moral hazard, adverse selection and market equilibrium, and the economics behind compulsory cover such as Iranian motor third-party liability.
Core rules
- Risk-averse agents have concave utility; the maximum premium equals the certainty equivalent. The risk premium is the excess over the expected loss and grows with variance and absolute risk aversion −u''/u'.
- The principle of indemnity caps recovery at the actual loss; subrogation and insurable interest support it and reduce moral hazard.
- Moral hazard is unobservable behaviour after contracting (deductibles, co-insurance and monitoring mitigate it); adverse selection is unobservable risk type before contracting (screening, underwriting, compulsory pooling).
- Rothschild-Stiglitz: with two risk types, a separating equilibrium may feature partial cover for low risks, and pooling may unravel.
- Insurability requires measurable, fortuitous, independent losses with calculable frequency and affordable premiums.
Worked example
Wealth 100, loss 40 with probability 0.1, utility ln(w), fair premium 4. Expected utility without cover: 0.9 ln100 + 0.1 ln60 = 4.5541. With full cover at premium P, ln(100 − P) = 4.5541 gives 100 − P = 95.02, so P = 4.98. The maximum premium exceeds the expected loss by about 0.98 - the risk premium.
Traps
- Reporting the risk premium as the expected loss, or vice versa.
- Assuming a deductible is always optimal; it depends on loading and risk aversion.
- Confusing moral hazard with adverse selection.
- Ignoring how wealth affects the willingness to pay for the same risk.
- Treating compulsory pooling as solving moral hazard.