Asymptotic analysis for optimal investment and consumption with transaction costs

Karel Janeček () and Steven Shreve ()

Finance and Stochastics, 2004, vol. 8, issue 2, 206 pages

Abstract: We consider an agent who invests in a stock and a money market and consumes in order to maximize the utility of consumption over an infinite planning horizon in the presence of a proportional transaction cost $\lambda > 0$ . The utility function is of the form U(c)=c 1-p /(1-p) for p > 0, $p\neq 1$ . We provide a heuristic and a rigorous derivation of the asymptotic expansion of the value function in powers of $\lambda^{1/3}$ , and we also obtain asymptotic results on the boundary of the “no-trade” region. Copyright Springer-Verlag Berlin/Heidelberg 2004

Keywords: Transaction costs; optimal control; asymptotic analysis; utility maximation (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/s00780-003-0113-4

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