Without insurance

With insurance

Period 1

U ( c 1 * + a 0 ( r 0 i 0 ) )

U ( c 1 * + a 0 ( r 0 i 0 ) B )

Period 2

E U ( c 2 * + a 1 ( r 1 i 1 ) )

E U ( c 2 * + a 1 ( r 1 i 1 ) + z )

AS

U ( c 1 * + a 0 ( r 0 i 0 ) ) + δ E U ( c 2 * + a 1 ( r 1 i 1 ) )

U ( c 1 * + a 0 ( r 0 i 0 ) B ) + δ E U ( c 2 * + a 1 ( r 1 i 1 ) + z )