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Intertemporal asset pricing and the marginal utility of wealth

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  • Battauz, Anna
  • De Donno, Marzia
  • Ortu, Fulvio
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    Abstract

    Abstract We consider the general class of discrete-time, finite-horizon intertemporal asset pricing models in which preferences for consumption at the intermediate dates are allowed to be state-dependent, satiated, non-convex and discontinuous, and the information structure is not required to be generated by a Markov process of state variables. We supply a generalized definition of marginal utility of wealth based on the Fréchet differential of the value operator that maps time t wealth into maximum conditional remaining utility. We show that in this general case all state-price densities/stochastic discount factors are fully characterized by the marginal utility of wealth of optimizing agents even if their preferences for intermediate consumption are highly irregular. Our result requires only the strict monotonicity of preferences for terminal wealth and the existence of a portfolio with positive and bounded gross returns. We also relate our generalized notion of marginal utility of wealth to the equivalent martingale measures/risk-neutral probabilities commonly employed in derivative asset pricing theory. We supply an example in which our characterization holds while the standard representation of state-price densities in terms of marginal utilities of optimal consumption fails.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Mathematical Economics.

    Volume (Year): 47 (2011)
    Issue (Month): 2 (March)
    Pages: 227-244

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    Handle: RePEc:eee:mateco:v:47:y:2011:i:2:p:227-244

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    Web page: http://www.elsevier.com/locate/jmateco

    Related research

    Keywords: Arbitrage Viability Linear pricing rules Optimal portfolio-consumption problems Marginal utility of wealth;

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    1. Anna Battauz & Marzia De Donno & Fulvio Ortu, 2011. "Envelope theorems in Banach lattices," Working Papers, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University 396, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    2. Nizar Allouch & Cuong Le Van, 2008. "Walras and dividends equilibrium with possibly satiated consumers," Working Papers, Development and Policies Research Center (DEPOCEN), Vietnam 08, Development and Policies Research Center (DEPOCEN), Vietnam.
    3. John Y. Campbell & John H. Cochrane, 1994. "By force of habit: a consumption-based explanation of aggregate stock market behavior," Working Papers 94-17, Federal Reserve Bank of Philadelphia.
    4. Andrew B. Abel, 1990. "Asset Prices under Habit Formation and Catching up with the Joneses," NBER Working Papers 3279, National Bureau of Economic Research, Inc.
    5. David M Kreps & Evan L Porteus, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Levine's Working Paper Archive 625018000000000009, David K. Levine.
    6. Grossman, Sanford J & Laroque, Guy, 1990. "Asset Pricing and Optimal Portfolio Choice in the Presence of Illiquid Durable Consumption Goods," Econometrica, Econometric Society, Econometric Society, vol. 58(1), pages 25-51, January.
    7. Mark J Machina, 1982. ""Expected Utility" Analysis without the Independence Axiom," Levine's Working Paper Archive 7650, David K. Levine.
    8. Kreps, David M., 1981. "Arbitrage and equilibrium in economies with infinitely many commodities," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 8(1), pages 15-35, March.
    9. Sato, Norihisa, 2010. "Satiation and existence of competitive equilibrium," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 46(4), pages 534-551, July.
    10. Polemarchakis, H. M. & Siconolfi, P., 1993. "Competitive equilibria without free disposal or nonsatiation," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 22(1), pages 85-99.
    11. Grishchenko, Olesya V., 2010. "Internal vs. external habit formation: The relative importance for asset pricing," Journal of Economics and Business, Elsevier, Elsevier, vol. 62(3), pages 176-194, May.
    12. Allouch, Nizar & Le Van, Cuong, 2009. "Erratum to "Walras and dividends equilibrium with possibly satiated consumers"," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 45(3-4), pages 320-328, March.
    13. David A. Chapman, 1998. "Habit Formation and Aggregate Consumption," Econometrica, Econometric Society, Econometric Society, vol. 66(5), pages 1223-1230, September.
    14. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, Elsevier, vol. 20(3), pages 381-408, June.
    15. repec:hal:journl:halshs-00241543 is not listed on IDEAS
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