Optimal Long Term Investment Model with Memory


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.

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@inproceedings{Inoue2006OptimalLT, title={Optimal Long Term Investment Model with Memory}, author={Akihiko Inoue}, year={2006} }