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

In this paper, we propose to analyse the choice of risk management activity made by a non-industrial private forest owner who derives utility from consumption and from the sentimental value of the forest that bears a risk of disaster. We consider a bivariate utility function depending on consumption and sentimental value of forest. In this context, we analyse insurance and/or self-insurance decisions. We show that, under fair premium, full insurance is optimal only if the cross derivative of the utility function equals zero. Under-insurance and over-insurance may also be optimal depending on the sign of this cross derivative. We also show that, under a positive loading factor, optimal partial insurance is validated only if the cross derivative is positive; otherwise full insurance may be optimal even with a loading insurance. We also observe that risk aversion increases the level of insurance demand and selfinsurance activity, extending this standard result obtained with an univariate utility function to a bivariate utility function. Moreover, when the forest owner can simultaneously insure and invest in self-insurance activity, full insurance is never optimal if the cross derivative is positive. Finally, we prove that insurance and selfinsurance may be substitutes, and if preferences are separable and exhibit decreasing absolute risk aversion, then insurance and self-insurance are always considered as substitutes.