Optimal insurance contracts without the non-negativity constraint on indemnities revisited

In the literature on optimal indemnity schedules, indemnities are usually restricted to be non-negative. Gollier (1987) shows that this constraint might well bind: insured could get higher expected utility if insurance contracts would allow payments from the insured to the insurer at some losses. However, due to the insurers' cost function Gollier supposes, the optimal insurance contract he derives underestimates the relevance of the non-negativity constraint on indemnities. This paper extends Gollier's findings by allowing for negative indemnity payments for a broader class of insurers' cost functions.