# Asymptotic analysis for optimal investment and consumption with transaction costs

## Author Info

• 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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## 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

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## Related research

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

## References

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## Citations

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Cited by:
1. Ales Cerny & Stephan Denkl & Jan Kallsen, 2013. "Hedging in L\'evy models and the time step equivalent of jumps," Papers 1309.7833, arXiv.org.
2. Maxim Bichuch, 2011. "Asymptotic Analysis for Optimal Investment in Finite Time with Transaction Costs," Papers 1112.2749, arXiv.org.
3. Muthuraman, Kumar, 2007. "A computational scheme for optimal investment - consumption with proportional transaction costs," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1132-1159, April.
4. Dai, Min & Wang, Hefei & Yang, Zhou, 2012. "Leverage management in a bull–bear switching market," Journal of Economic Dynamics and Control, Elsevier, vol. 36(10), pages 1585-1599.
5. Johannes Muhle-Karbe & Ren Liu, 2012. "Portfolio Selection with Small Transaction Costs and Binding Portfolio Constraints," Papers 1205.4588, arXiv.org, revised Jan 2013.
6. Paolo Guasoni & Johannes Muhle-Karbe, 2012. "Portfolio Choice with Transaction Costs: a User's Guide," Papers 1207.7330, arXiv.org.
7. Jose V. Alcala & Arash Fahim, 2013. "Balancing small fixed and proportional transaction cost in trading strategies," Papers 1304.7562, arXiv.org.
8. Jin Hyuk Choi, 2013. "Asymptotic analysis for Merton's problem with transaction costs in power utility case," Papers 1309.3721, arXiv.org, revised Sep 2013.
9. Dylan Possama\"i & H. Mete Soner & Nizar Touzi, 2012. "Homogenization and asymptotics for small transaction costs: the multidimensional case," Papers 1212.6275, arXiv.org, revised Jan 2013.
10. Bruno Bouchard & Ludovic Moreau & Mete H. Soner, 2013. "Hedging under an expected loss constraint with small transaction costs," Papers 1309.4916, arXiv.org.
11. H. Mete Soner & Nizar Touzi, 2012. "Homogenization and asymptotics for small transaction costs," Papers 1202.6131, arXiv.org, revised Jun 2013.
12. Christoph K\"uhn & Johannes Muhle-Karbe, 2013. "Optimal Liquidity Provision in Limit Order Markets," Papers 1309.5235, arXiv.org.
13. Albert Altarovici & Johannes Muhle-Karbe & H. Mete Soner, 2013. "Asymptotics for Fixed Transaction Costs," Papers 1306.2802, arXiv.org, revised Oct 2013.
14. Casassus, Jaime & Ceballos, Diego & Higuera, Freddy, 2010. "Correlation structure between inflation and oil futures returns: An equilibrium approach," Resources Policy, Elsevier, vol. 35(4), pages 301-310, December.
15. Stefan Gerhold & Johannes Muhle-Karbe & Walter Schachermayer, 2010. "The dual optimizer for the growth-optimal portfolio under transaction costs," Papers 1005.5105, arXiv.org, revised Oct 2010.
16. Valeri Zakamouline, 2004. "A Unified Approach to Portfolio Optimization with Linear Transaction Costs," GE, Growth, Math methods 0404003, EconWPA, revised 21 Apr 2004.
17. Christian Bayer & Bezirgen Veliyev, 2012. "Utility Maximization in a Binomial Model with transaction costs: a Duality Approach Based on the Shadow Price Process," Papers 1209.5175, arXiv.org.
18. João Amaro de Matos & Nuno Silva, 2011. "Consuming durable goods when stock markets jump: a strategic asset allocation approach," GEMF Working Papers 2012-01, GEMF - Faculdade de Economia, Universidade de Coimbra.
19. Jan Kallsen & Johannes Muhle-Karbe, 2013. "The General Structure of Optimal Investment and Consumption with Small Transaction Costs," Papers 1303.3148, arXiv.org.

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