The effectiveness of utility-maximization techniques for portfolio management relies on our ability to estimate correctly the parameters of the dynamics of the underlying financial assets. In the setting of complete or incomplete financial markets, we investigate whether small perturbations of the market coefficient processes lead to small changes in the agent's optimal behavior, as derived from the solution of the related utility-maximization problems. Specifically, we identify the topologies on the parameter process space and the solution space under which utility-maximization is a continuous operation, and we provide a counterexample showing that our results are best possible, in a certain sense. A novel result about the structure of the solution of the utility-maximization problem, where prices are modeled by continuous semimartingales, is established as an offshoot of the proof of our central theorem. Published by Elsevier B.V. MSC: 91B16; 91B28

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This paper provides an easily verifiable regularity condition under which the investor's utility maximizer depends continuously on the description of her preferences in a general incomplete financial setting. Specifically, we extend the setting of Jouini and Napp (2004) to include noise generated by a general continuous semi-martingale and to the case where the market price of risk process is allowed to be a general adapted process satisfying a mild integrability condition. This extension allows us to obtain positive results for both the mean-reversion model of Kim and Omberg (1996) and the stochastic volatility model of Heston (1993). Finally, we provide an example set in Samuelson's complete financial model illustrating that without imposing additional regularity, the continuity property of the investor's optimizer can fail.

In the setting of exponential investors and uncertainty governed by Brownian motions we first prove the existence of an incomplete equilibrium for a general class of models. We then introduce a tractable class of exponential-quadratic models and prove that the corresponding incomplete equilibrium is characterized by a coupled set of Riccati equations. Finally, we prove that these exponential-quadratic models can be used to approximate the incomplete models we studied in the first part.