# Asymptotic analysis for optimal investment and consumption with transaction costs

## Author

Listed:
• Karel Janeček

()

• Steven Shreve

()

## 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

## Suggested Citation

• Karel Janeček & Steven Shreve, 2004. "Asymptotic analysis for optimal investment and consumption with transaction costs," Finance and Stochastics, Springer, vol. 8(2), pages 181-206, May.
• Handle: RePEc:spr:finsto:v:8:y:2004:i:2:p:181-206
DOI: 10.1007/s00780-003-0113-4
as

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

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### Keywords

Transaction costs; optimal control; asymptotic analysis; utility maximation;

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