Nearly-optimal asset allocation in hybrid stock investment models

Nearly-optimal asset allocation in hybrid stock investment models

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Article ID: iaor200570
Country: Netherlands
Volume: 121
Issue: 2
Start Page Number: 419
End Page Number: 444
Publication Date: May 2004
Journal: Journal of Optimization Theory and Applications
Authors: ,
Keywords: allocation: resources, markov processes
Abstract:

This work develops a class of stock-investment models that are hybrid in nature and involve continuous dynamics and discrete-event interventions. In lieu of the usual geometric Brownian motion formulation, hybrid geometric Brownian motion models are proposed, in which both the expected return and the volatility depend on a finite-state Markov chain. Our objective is to find nearly-optimal asset allocation strategies so as to maximize the expected returns. The use of the Markov chain stems from the motivation of capturing the market trends as well as various economic factors. To incorporate these economic factors into the models, the underlying Markov chain inevitably has a large state space. To reduce the complexity, a hierarchical approach is suggested, which leads to singularly-perturbed switching diffusion processes. By aggregating the states of the Markov chains in each weakly irreducible class into a single state, limit switching diffusion processes are obtained. Using such asymptotic properties, nearly-optimal asset allocation policies are developed.

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