Multiplicative background risk
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.
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- Yacine Ait-Sahalia & Andrew W. Lo, 2000.
"Nonparametric Risk Management and Implied Risk Aversion,"
NBER Working Papers
6130, National Bureau of Economic Research, Inc.
- Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51.
- Guiso, Luigi & Jappelli, Tullio & Terlizzese, Daniele, 1994.
"Income Risk, Borrowing Constraints and Portfolio Choice,"
CEPR Discussion Papers
888, C.E.P.R. Discussion Papers.
- Guiso, Luigi & Jappelli, Tullio & Terlizzese, Daniele, 1996. "Income Risk, Borrowing Constraints, and Portfolio Choice," American Economic Review, American Economic Association, vol. 86(1), pages 158-72, March.
- Doherty, Neil A & Schlesinger, Harris, 1983. "Optimal Insurance in Incomplete Markets," Journal of Political Economy, University of Chicago Press, vol. 91(6), pages 1045-54, December.
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