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

Abstract

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 consu mption and from the sentimental value of the forest that bears a risk of disaster. We consider a bivari ate utility function depending on consumption and sentimental value of forest. In this context, we an alyse insurance and/or self-insurance decisions. We show that, under fair premium, full insurance is op timal only if the cross derivative of the utility function equals zero. Under-insurance and over-insu rance may also be optimal depending on the sign of this cross derivative. We also show that, under a positive loading factor, optimal partial insuranc e 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 aversi on increases the level of insurance demand and self insurance 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 s elfinsurance may be substitutes, and if preferences ar e separable and exhibit decreasing absolute risk aversion, then insurance and self-insurance are alw ays considered as substitutes.