A generalized stochastic differential utility

Ali Lazrak and Marie-Claire Quenez ()
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Ali Lazrak: Sauder - Sauder School of Business [British Columbia] - UBC - University of British Columbia [Canada]
Marie-Claire Quenez: LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées - UPEM - Université Paris-Est Marne-la-Vallée - BEZOUT - Fédération de Recherche Bézout - CNRS - Centre National de la Recherche Scientifique - UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12 - CNRS - Centre National de la Recherche Scientifique

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Abstract: This paper generalizes, in the setting of Brownian information, the Duffie-Epstein (1992) stochastic differential formulation of intertemporal recursive utility (SDU). We provide a utility functional of state-contingent consumption plans that exhibits a local dependency with respect to the utility intensity process (the integrand of the quadratic variation) and call it the generalized SDU. This mathematical generalization of the SDU permits, in fact, more flexibility in the separation between risk aversion and intertemporal substitution and allows to model asymmetry in risk aversion.We extensively use the backward stochastic differential equation theory to give sufficient conditions for comparative and absolute risk aversion behavior as well as aversion to specific directional risk. Additionally, we discuss whether our functional exhibits monotonicity to its information filtration argument. For purposes of illustration, we provide some applications to the consumption/portfolio strategy selection problem in a complete securities market.

Keywords: Brownian filtrations; backward stochastic differential equations; recursive utility; risk aversion; uncertainty resolution (search for similar items in EconPapers)
Date: 2003-02-03
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Citations: View citations in EconPapers (15)

Published in Mathematics of Operations Research, 2003, Vol.28, n°1, pp.154-180. ⟨10.1287/moor.28.1.154.14259⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00485718

DOI: 10.1287/moor.28.1.154.14259

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