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Consumption and asset prices with homothetic recursive preferences

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  • Mark Fisher
  • Christian Gilles
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    Abstract

    When preferences are homothetic, utility can be expressed in terms of current consumption and a variable that captures all information about future opportunities. We use this observation to express the differential equation that characterizes utility as a restriction on the information variable in terms of the dynamics of consumption. We derive the supporting price system and returns process and thereby characterize optimal consumption and portfolio decisions. We provide a fast and accurate numerical solution method and illustrate its use with a number of Markovian models. In addition, we provide insight by changing the numeraire from units of consumption to units of the consumption process. In terms of the new units, the wealth-consumption ratio (which is closely related to the information variable) is the value of a coupon bond and the existence of an infinite-horizon solution depends on the positivity of the asymptotic forward rate.

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    File URL: http://www.frbatlanta.org//filelegacydocs/wp9917.pdf
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    Bibliographic Info

    Paper provided by Federal Reserve Bank of Atlanta in its series Working Paper with number 99-17.

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    Date of creation: 1999
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    Handle: RePEc:fip:fedawp:99-17

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    Keywords: Asset pricing ; Consumption (Economics) ; Interest rates ; Wealth;

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    References

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    1. R. Mehra & E. Prescott, 2010. "The equity premium: a puzzle," Levine's Working Paper Archive 1401, David K. Levine.
    2. Phillippe Weil, 1997. "The Equity Premium Puzzle and the Risk-Free Rate Puzzle," Levine's Working Paper Archive 1833, David K. Levine.
    3. Schroder, Mark & Skiadas, Costis, 1999. "Optimal Consumption and Portfolio Selection with Stochastic Differential Utility," Journal of Economic Theory, Elsevier, vol. 89(1), pages 68-126, November.
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    Cited by:
    1. George Chacko & Luis M. Viceira, 2005. "Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets," Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1369-1402.
    2. Benzoni, Luca & Collin-Dufresne, Pierre & Goldstein, Robert S., 2011. "Explaining asset pricing puzzles associated with the 1987 market crash," Journal of Financial Economics, Elsevier, vol. 101(3), pages 552-573, September.

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