Multivariate utility maximization with proportional transaction costs

Details Multivariate utility maximization with proportional transaction costs Multivariate utility maximization with proportional transaction costs

2008-11-24

arxiv.org/abs/0811.3889v2

Mathematics

Probability

Addition of two examples (Examples 3.2 and 3.13) and a few other, minor presentational improvements

Scientific paper

We present an optimal investment theorem for a currency exchange model with random and possibly discontinuous proportional transaction costs. The investor's preferences are represented by a multivariate utility function, allowing for simultaneous consumption of any prescribed selection of the currencies at a given terminal date. We prove the existence of an optimal portfolio process under the assumption of asymptotic satiability of the value function. Sufficient conditions for asymptotic satiability of the value function include reasonable asymptotic elasticity of the utility function, or a growth condition on its dual function. We show that the portfolio optimization problem can be reformulated in terms of maximization of a terminal liquidation utility function, and that both problems have a common optimizer.

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