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Correlated risks, bivariate utility and optimal choices

Author

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  • Michel Denuit
  • Louis Eeckhoudt
  • Mario Menegatti

Abstract

In this paper, we consider a décision-maker facing a financial risk flanked by a background risk, possibly non-financial, such as health or environmental risk. A decision has to be made about the amount of an investment (in the financial dimension) resulting in a future benefit either in the same dimension (savings) or in the order dimension (environmental quality or health improvement). In the first case, we show that the optimal amount of savings decreases as the pair of risks increases in the bivariate increasing concave dominance rules of higher degrees which express the common preferences of all the decision-makers whose two-argument utility function possesses direct and cross derivatives fulfilling some specific requirements. Roughly speaking, the optimal amount of savings decreases as the two risks become "less positively correlated" or marginally improve in univariate stochastic dominance. In the second case, a similar conclusion on optimal investment is reached under alternative conditions on the derivatives of the utility function.
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Suggested Citation

  • Michel Denuit & Louis Eeckhoudt & Mario Menegatti, 2011. "Correlated risks, bivariate utility and optimal choices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(1), pages 39-54, January.
    • Handle: RePEc:spr:joecth:v:46:y:2011:i:1:p:39-54
    DOI: 10.1007/s00199-009-0500-y
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    More about this item

    Keywords

    Precautionary savings; Background risk; Bivariate higher order increasing concave stochastic dominance; Risks correlation; D81; E21;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

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