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Multiplicative background risk

Author

Listed:
  • Franke, Günter
  • Schlesinger, Harris
  • Stapleton, Richard C.

Abstract

We consider random wealth of the multiplicative form xy, where x and y are statistically independent random variables. We assume that x is endogenous to the economic agent, but that y is an exogenous and uninsurable background risk. Our main focus is on how the randomness of y affects risk-taking behavior for decisions on the choice of x. We characterize conditions on preferences that lead to more cautious behavior. We also develop the concept of the affiliated utility function, which we define as the composition of the underlying utility function and the exponential function. This allows us to adapt several results for additive background risk to the multiplicative case.

Suggested Citation

  • Franke, Günter & Schlesinger, Harris & Stapleton, Richard C., 2002. "Multiplicative background risk," Discussion Papers, various Research Units FS IV 02-06, Social Science Research Center Berlin (WZB).
  • Handle: RePEc:zbw:wzbdiv:fsiv0206
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    References listed on IDEAS

    as
    1. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, pages 53-73.
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    More about this item

    Keywords

    background risk; standard risk aversion; affiliated utility function;

    JEL classification:

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

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