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Volume 10/Number 2, Winter 2006/07 Research Papers The influence of correlation on multi-asset
portfolio optimization with transaction costs Colin Atkinson
Pongsathorn Ingpochai Mathematics Department, Imperial College of Science, Technology and Medicine, 180 Queens Gate, London SW7 2AZ, UK
In this paper, we consider the optimal portfolio selection and consumption rule of an investor who faces proportional transaction costs when trading multiple risky assets. As the portfolio under consideration consists of multiple risky assets, which makes the numerical methods formidable, we apply perturbation analyses. We also allow the risky assets to have correlation between their price processes. The objective is to transform the singular stochastic control problem which arises from the transaction costs to a free boundary and partial differential equations problem. Once the problem has been formulated, we establish the transaction boundaries that define the no transaction region and dictate the optimal investment strategy. We provide numerical results for two and three correlated risky assets portfolios. A general procedure for solving N risky assets portfolios is described.
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