Robust maximization of consumption with logarithmic utility

Daniel Hernández-Hernández and Alexander Schied

No 2007-030, SFB 649 Discussion Papers from Humboldt University Berlin, Collaborative Research Center 649: Economic Risk

Abstract: We anlyze 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 consisten 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.

Date: 2007
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