2016/08/02 by Huy N. Chau, Chau, Huy N., Miklós Rásonyi +2
Economics, Econometrics and Finance · #60G22 #93E20 #Capital Investment and Risk Analysis #FOS: Economics and business #Financial Markets and Investment Strategies #Mathematical Finance (q-fin.MF) #Stochastic processes and financial applications #msc:60G22 #msc:93E20 #q-fin.MF
paper · pdf · doi:10.48550/arxiv.1608.00768
21 pages
openalex publication_date 2016/08/02 · arxiv created 2017/03/27 · arxiv updated 2017/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of utility maximization for investors with power utility functions. Building on the earlier work Larsen et al. (2016), we prove that the value of the problem is a Frechet-differentiable function of the drift of the price process, provided that this drift lies in a suitable Banach space. We then study optimal investment problems with non-Markovian driving processes. In such models there is no hope to get a formula for the achievable maximal utility. Applying results of the first part of the paper we provide first order expansions for certain problems involving fractional Brownian motion either in the drift or in the volatility. We also point out how asymptotic results can be derived for models with strong mean reversion.