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A general theory of risk apportionment

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  • Gollier, Christian

Abstract

Suppose that the conditional distributions of x˜ (resp. y˜) can be ranked according to the m-th (resp. n-th) risk order. Increasing their statistical concordance increases the (m,n) degree riskiness of (x˜,y˜), i.e., it reduces expected utility for all bivariate utility functions whose sign of the (m,n) cross-derivative is (−1)m+n+1. This means in particular that this increase in concordance of risks induces a m+n degree risk increase in x˜+y˜. On the basis of these general results, I provide different recursive methods to generate high degrees of univariate and bivariate risk increases. In the reverse-or-translate (resp. reverse-or-spread) univariate procedure, a m degree risk increase is either reversed or translated downward (resp. spread) with equal probabilities to generate a m+1 (resp. m+2) degree risk increase. These results are useful for example in asset pricing theory when the trend and the volatility of consumption growth are stochastic or statistically linked.

Suggested Citation

  • Gollier, Christian, 2021. "A general theory of risk apportionment," Journal of Economic Theory, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:jetheo:v:192:y:2021:i:c:s0022053121000065
    DOI: 10.1016/j.jet.2021.105189
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    Cited by:

    1. Wong, Kit Pong, 2021. "Comparative risk aversion with two risks," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    2. James K. Hammitt, 2023. "Downside risk aversion vs decreasing absolute risk aversion: an intuitive exposition," Theory and Decision, Springer, vol. 95(1), pages 1-10, July.
    3. Crainich, David & Eeckhoudt, Louis & Courtois, Olivier Le, 2020. "Intensity of preferences for bivariate risk apportionment," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 153-160.
    4. Paan Jindapon & Liqun Liu & William S. Neilson, 2021. "Comparative risk apportionment," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(1), pages 91-112, April.
    5. Christian Gollier, 2020. "If the Objective is Herd Immunity, on Whom Should it be Built?," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 76(4), pages 671-683, August.

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    Keywords

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    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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