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Efficient Consumption Set Under Recursive Utility and Unknown Beliefs

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  • Ali Lazrak
  • Fernando Zapatero

Abstract

In a context of complete financial markets where asset prices follow Ito's processes, we characterize the set of consumption processes which are optimal for a given stochastic differential utility (e.g. Duffie and Epstein (1992)) when beliefs are unknown. Necessary and sufficient conditions for the efficiency of a consumption process, consists of the existence of a solution to a quadratic backward stochastic differential equation and a martingale condition. We study the efficiency condition in the case of a class of homothetic stochastic differential utilities and derive some results for those particular cases. In a Markovian context, this efficiency condition becomes a partial differential equation.

Suggested Citation

  • Ali Lazrak & Fernando Zapatero, 2002. "Efficient Consumption Set Under Recursive Utility and Unknown Beliefs," Research Paper Series 85, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:85
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    File URL: http://www.qfrc.uts.edu.au/research/research_papers/rp85.pdf
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    References listed on IDEAS

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    Cited by:

    1. Firoozi, Fathali, 2006. "On the martingale property of economic and financial instruments," International Review of Economics & Finance, Elsevier, vol. 15(1), pages 87-96.
    2. Fabio Antonelli & Carlo Mancini, 2016. "Consumption optimization for recursive utility in a jump-diffusion model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 39(2), pages 293-310, November.
    3. Nobuhiro Nakamura, 2004. "Numerical Approach to Asset Pricing Models with Stochastic Differential Utility," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(3), pages 267-300, September.
    4. Stéphane Loisel, 2010. "Understanding, Modeling and Managing Longevity Risk: Key Issues and Main Challenges," Post-Print hal-00517902, HAL.

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