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Optimal long term investment model with memory

Akihiko Inoue·Yumiharu Nakano
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Abstract

We consider a financial market model driven by an R^n-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.

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Akihiko Inoue, Yumiharu Nakano. 2006-05-05. Optimal long term investment model with memory. https://arxiv.org/abs/math/0506621

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