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Consumption and asset prices and recursive preferences

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  • Mark Fisher
  • Christian Gilles
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    Abstract

    We analyze consumption and asset pricing with recursive preferences given by Kreps--Porteus stochastic differential utility (K--P SDU). We show that utility depends on two state variables: current consumption and a second variable (related to the wealth--consumption ratio) that captures all information about future opportunities. This representation of utility reduces the internal consistency condition for K--P SDU to a restriction on the second variable in terms of the dynamics of a forcing process (consumption, the state--price deflator, or the return on the market portfolio). Solving the model for (i) optimal consumption, (ii) the optimal portfolio, and (iii) asset prices in general equilibrium amounts to finding the process for the second variable that satisfies this restriction. We show that the wealth--consumption ratio is the value of an annuity when the numeraire is changed from units of the consumption good to units of the consumption process, and we characterize certain features of the solution in a non-Markovian setting. In a Markovian setting, we provide a solution method that is quite general and can be used to produce fast, accurate numerical solutions that converge to the Taylor expansion.

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    Bibliographic Info

    Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series Finance and Economics Discussion Series with number 1998-40.

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    Date of creation: 1998
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    Handle: RePEc:fip:fedgfe:1998-40

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    Related research

    Keywords: Consumption (Economics) ; Prices;

    This paper has been announced in the following NEP Reports:

    References

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    1. Duffie, Darrell & Skiadas, Costis, 1994. "Continuous-time security pricing : A utility gradient approach," Journal of Mathematical Economics, Elsevier, vol. 23(2), pages 107-131, March.
    2. R. Mehra & E. Prescott, 2010. "The equity premium: a puzzle," Levine's Working Paper Archive 1401, David K. Levine.
    3. Alberto Giovannini & Philippe Weil, 1989. "Risk Aversion and Intertemporal Substitution in the Capital Asset Pricing Model," NBER Working Papers 2824, National Bureau of Economic Research, Inc.
    4. Weil, Philippe, 1989. "The equity premium puzzle and the risk-free rate puzzle," Journal of Monetary Economics, Elsevier, vol. 24(3), pages 401-421, November.
    5. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
    6. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-94, March.
    7. repec:fth:harver:1421 is not listed on IDEAS
    8. Darrell Duffie & Rui Kan, 1996. "A Yield-Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406.
    9. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-36.
    10. L. C. G. Rogers, 1997. "The Potential Approach to the Term Structure of Interest Rates and Foreign Exchange Rates," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 157-176.
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