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 parameters is also considered.
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Inoue, A., Nakano, Y. Optimal Long-Term Investment Model with Memory. Appl Math Optim 55, 93–122 (2007). https://doi.org/10.1007/s00245-006-0867-0
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DOI: https://doi.org/10.1007/s00245-006-0867-0