Precautionary self-insurance-cum-protection

- Precautionary self-insurance-cum-protection is examined.
- Additive/multiplicative background risk is introduced.
- Monotone comparative statics and risk apportionment are used.
- Prudence is required for precautionary self-insurance-cum-protection.

Precautionary self-insurance-cum-protection (SICP) arises when an individual spends more on SICP when background risk is introduced. We develop a two-period model wherein additive/multiplicative background risk prevails in the second period. Using the theory of monotone comparative statics and risk apportionment, we derive necessary and sufficient conditions under which the individual spends more on SICP when the background risk deteriorates via higher-order stochastic dominance. Prudence is called for to create a precautionary motive that induces the individual to shift his wealth in a way to reduce the loss of expected utility caused by the addition of background risk, thereby giving rise to the precautionary SICP.