Before revision:  For this application, our model allows to conclude that, even in the least efficient scenario from the households point of view, i.e., when the insurance is provided by a monopoly, this mechanism improves significantly the living conditions of the riskiest households by ensuring them a sufficient consumption of energy  .
After revision:  For this application, our model allows to conclude that, even in the least efficient scenario from the households point of view, i.e., when the insurance is provided by a monopoly, this mechanism improves significantly the living conditions of the riskiest households by ensuring them a sufficient consumption of energy . The effectiveness of in-kind insurance is highlighted through a comparison with income insurance, but our results nevertheless underline the need to regulate such insurance market .