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Robust Maximization of Consumption with Logarithmic Utility

Daniel Hernández-Hernández and Alexander Schied

SFB 649 Discussion Papers from Humboldt University, Collaborative Research Center 649

Abstract: We analyze the stochastic control approach to the dynamic maximization of the robust utility of consumption and investment. The robust utility functionals are defined in terms of logarithmic utility and a dynamically consistent convex risk measure. The underlying market is modeled by a diffusion process whose coefficients are driven by an external stochastic factor process. Our main results give conditions on the minimal penalty function of the robust utility functional under which the value function of our problem can be identified with the unique classical solution of a quasilinear PDE within a class of functions satisfying certain growth conditions.

Keywords: Robust utility maximization; optimal consumption; stochastic factor model; stochastic control; convex risk measure; dynamic consistency; Hamilton-Jacobi-Bellman equation (search for similar items in EconPapers)
JEL-codes: D81 G11 (search for similar items in EconPapers)
Pages: 7
Date: 2007-05
New Economics Papers: this item is included in nep-dge and nep-upt
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Citations: View citations in EconPapers (2)

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Handle: RePEc:hum:wpaper:sfb649dp2007-030