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Robust optimal control for a consumption-investment problem

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Abstract

We give an explicit PDE characterization for the solution of the problem of maximizing the utility of both terminal wealth and intertemporal consumption under model uncertainty. The underlying market model consists of a risky asset, whose volatility and long-term trend are driven by an external stochastic factor process. The robust utility functional is defined in terms of a HARA utility function with risk aversion parameter 0 < α < 1 and a dynamically consistent coherent risk measure, which allows for model uncertainty in the distributions of both the asset price dynamics and the factor process. Ourmethod combines recent results by Wittmüß (Robust optimization of consumption with random endowment, 2006) on the duality theory of robust optimization of consumption with a stochastic control approach to the dual problem of determining a ‘worst-case martingale measure’.

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Authors and Affiliations

  1. Department of Mathematics, TU Berlin, Strasse des 17. Juni 136, 10623, Berlin, Germany

    Alexander Schied

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  1. Alexander Schied
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Correspondence to Alexander Schied.

Additional information

A. Schied was supported by Deutsche Forschungsgemeinschaft through the SFB 649 “Economic Risk”.

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Schied, A. Robust optimal control for a consumption-investment problem. Math Meth Oper Res 67, 1–20 (2008). https://doi.org/10.1007/s00186-007-0172-y

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  • DOI: https://doi.org/10.1007/s00186-007-0172-y

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