2007/06/04 by Kasper Larsen, Larsen, Kasper, Gordan Žitković +1 · 1 citation
Economics, Econometrics and Finance · #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Financial Markets and Investment Strategies #Optimization and Control (math.OC) #Portfolio Management (q-fin.PM) #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.0706.0474
openalex publication_date 2007/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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.