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

  • Marielle BrunetteEmail author
  • Stéphane Couture
Research Article


We analyze the insurance and self-insurance choices of a private forest owner whose utility is bivariate (consumption and forest amenity value). We show that under fair premium, full insurance is optimal only if the cross derivative of the utility function is equal to zero, whereas under unfair premium, optimal partial insurance is validated only if the cross derivative is positive. We also show that insurance and self-insurance may be substitutes, and if preferences are separable and the cost of insurance is not so high, then insurance and self-insurance are always considered as substitutes. However, we find in an illustration with a non-separable bivariate utility function, characterized by weights given to consumption and amenities, that insurance and self-insurance are complement. We obtain that the weight given to amenities substantially affects optimal risk management activities for unfair insurance. These results highlight the importance to represent the forest owner’s behavior through a bivariate utility function.


Bivariate utility Cross derivative Forest management Insurance Risk Self-insurance 



This paper has been presented at the “Journées de Microéconomie Appliquée” (Clermont-Ferrand, June 2014) and at the International Conference on Economic and Financial Risks (Niort, June 2014). We are grateful to Jean-Louis Combes and Henri Loubergé for their valuable comments and to the participants of these two conferences for interesting discussions. The UMR BETA is supported by a grant from the French National Research Agency (ANR) as part of the “Investissements d’Avenir” program (ANR-11-LABX-0002-01), ARBRE Lab of Excellence.

Funding information

This work was supported by the project FORWIND (ANR-12-AGRO-0007).


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Copyright information

© L’Institut National de la Recherche Agronomique (INRA) 2018

Authors and Affiliations

  1. 1.BETAUniversité de Lorraine, Université de Strasbourg, AgroParisTech, CNRS, INRANancyFrance
  2. 2.MIATUniversité de Toulouse, INRACastanet-TolosanFrance

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