Stability of utility-maximization in incomplete markets

[摘要] 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.

[发布日期] 2007-11-01

[效力级别]  Proceedings Paper

[关键词] appropriate topologies;continuous semimartingales;convex duality;market price of risk process;mathematical finance;utility-maximization;V-relative compactness;well-posedness