Multivariate Utility Maximization with Proportional Transaction Costs
Owen, Mark; Campi, Luciano (2011), Multivariate Utility Maximization with Proportional Transaction Costs, Finance and Stochastics, 15, 3, p. 461-499. http://dx.doi.org/10.1007/s00780-010-0125-9
TypeArticle accepté pour publication ou publié
Journal nameFinance and Stochastics
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Abstract (EN)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.
Subjects / KeywordsDuality Theory; Lagrange Duality; Multivariate Utility Function; Asymptotic Satiability; Optimal Portfolio; Transaction Costs; Foreign Exchange Market
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