Risk management activities of a non-industrial privateforest owner with a bivariate utility function

We analyze the insurance and self-insurance choices of a private forest owner whoseutility is bivariate (consumption and forest amenity value). We show that under fairpremium, full insurance is optimal only if the cross derivative of the utility func-tion is equal to zero, whereas under unfair premium, optimal partial insurance isvalidated only if the cross derivative is positive. We also show that insurance andself-insurance may be substitutes, and if preferences are separable and the cost ofinsurance is not so high, then insurance and self-insurance are always considered assubstitutes. However, we find in an illustration with a non-separable bivariate utilityfunction, characterized by weights given to consumption and amenities, that insur-ance and self-insurance are complement. We obtain that the weight given to amenitiessubstantially affects optimal risk management activities for unfair insurance. Theseresults highlight the importance to represent the forest owner’s behavior through abivariate utility function.