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Multiplicative background risk

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  • 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, WZB Berlin Social Science Center.
  • Handle: RePEc:zbw:wzbdiv:fsiv0206
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    References listed on IDEAS

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    6. Jackwerth, Jens Carsten, 2000. "Recovering Risk Aversion from Option Prices and Realized Returns," Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 433-451.
    7. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
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    Cited by:

    1. Lionel, ARTIGE, 2004. "Optimal Saving with Additive and Multiplicative Background Risk," LIDAM Discussion Papers IRES 2004030, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    2. Guenter Franke & Harris Schlesinger & Richard C. Stapleton, 2013. "Risk-Taking-Neutral Background Risk," CESifo Working Paper Series 4070, CESifo.

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    More about this item

    Keywords

    background risk; standard risk aversion; affiliated utility function;
    All these keywords.

    JEL classification:

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

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