Optimal Long-Term Investment Model with Memory

Optimal Long-Term Investment Model with Memory 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 parameters is also considered. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Optimal Long-Term Investment Model with Memory

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Publisher
Springer-Verlag
Copyright
Copyright © 2007 by Springer
Subject
Mathematics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Methods
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-006-0867-0
Publisher site
See Article on Publisher Site

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 parameters is also considered.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Jan 1, 2007

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