Robust Utility Maximization in a Stochastic Factor Model
AbstractWe give an explicit PDE characterization for the solution of a robust utility maximization problem in an incomplete market model, whose volatility, interest rate process, 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 negative risk aversion 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. Our method combines two recent advances in the theory of optimal investments: the general duality theory for robust utility maximization and the stochastic control approach to the dual problem of determining optimal martingale measures.
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Bibliographic InfoPaper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2006-007.
Length: 18 pages
Date of creation: Dec 2005
Date of revision: Aug 2006
optimal investment; model uncertainty; incomplete markets; stochastic volatility; coherent risk measures; optimal control; convex duality;
Find related papers by JEL classification:
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-02-12 (All new papers)
- NEP-FIN-2006-02-12 (Finance)
- NEP-UPT-2006-02-12 (Utility Models & Prospect Theory)
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