# Asymptotic analysis for optimal investment and consumption with transaction costs

## Author Info

Listed author(s):
• Karel Janeček

()

• Steven Shreve

()

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## 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

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File URL: http://hdl.handle.net/10.1007/s00780-003-0113-4

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## Bibliographic Info

Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 8 (2004)
Issue (Month): 2 (05)
Pages: 181-206

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 Handle: RePEc:spr:finsto:v:8:y:2004:i:2:p:181-206 DOI: 10.1007/s00780-003-0113-4 Contact details of provider: Web page: http://www.springer.com Order Information: Web: http://www.springer.com/mathematics/quantitative+finance/journal/780/PS2

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