Optimal long term investment model with memory

2005/06/30 by Akihiko Inoue, Inoue, Akihiko, Yumiharu Nakano +1
Economics, Econometrics and Finance · Mathematics · #60G10 (Primary) 62P05 #93E20 (Secondary) #FOS: Economics and business #FOS: Mathematics #MSC-class: 91B28 #Portfolio Management (q-fin.PM) #Probability (math.PR) #math.PR #msc:60G10 #msc:62P05 #msc:91B28 #msc:93E20 #q-fin.PM

paper · pdf · doi:10.48550/arxiv.math/0506621

25 pages, 3 figures. To appear in Applied Mathematics and Optimization

arxiv created 2006/05/05 · arxiv updated 2009/12/01

Abstract

We consider a financial market model driven by an Rⁿ-valued Gaussian process with stationary increments which is different from Brownian motion. This driving noise process consists of n independent components, and each component has memory described by two parameters. For this market model, we explicitly solve optimal investment problems. These include (i) Merton's portfolio optimization problem; (ii) the maximization of growth rate of expected utility of wealth over the infinite horizon; (iii) the maximization of the large deviation probability that the wealth grows at a higher rate than a given benchmark. The estimation of paremeters is also considered.

Related

• Optimal long-term investment in illiquid markets when prices have negative memory
• On optimal investment with processes of long or negative memory
• On long term investment optimality
• A Black--Scholes Model with Long Memory
• Binary market models with memory