Homogenization and asymptotics for small transaction costs: the multidimensional case
In the context of the multi-dimensional infinite horizon optimal consumption-investment problem with proportional transaction costs, we provide the first order expansion in small transact costs. Similar to the one-dimensional derivation in our accompanying paper , the asymptotic expansion is expressed in terms of a singular ergodic control problem, and our arguments are based on the theory of viscosity solutions, and the techniques of homogenization which leads to a system of corrector equations. In contrast with the one-dimensional case, no explicit solution of the first corrector equation is available anymore. Finally, we provide some numerical results which illustrate the structure of the first order optimal controls.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Stefan Gerhold & Johannes Muhle-Karbe & Walter Schachermayer, 2010. "Asymptotics and Duality for the Davis and Norman Problem," Papers 1010.0627, arXiv.org, revised Aug 2011.
- C. Atkinson & S. Mokkhavesa, 2004. "Multi-asset portfolio optimization with transaction cost," Applied Mathematical Finance, Taylor & Francis Journals, vol. 11(2), pages 95-123.
- Dumas, Bernard & Luciano, Elisa, 1991. " An Exact Solution to a Dynamic Portfolio Choice Problem under Transactions Costs," Journal of Finance, American Finance Association, vol. 46(2), pages 577-95, June.
- Constantinides, George M, 1986. "Capital Market Equilibrium with Transaction Costs," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 842-62, August.
- Kumar Muthuraman & Sunil Kumar, 2006. "Multidimensional Portfolio Optimization With Proportional Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 301-335.
- Magill, Michael J. P. & Constantinides, George M., 1976. "Portfolio selection with transactions costs," Journal of Economic Theory, Elsevier, vol. 13(2), pages 245-263, October.
- 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, 05.
- Halil Mete Soner & Guy Barles, 1998. "Option pricing with transaction costs and a nonlinear Black-Scholes equation," Finance and Stochastics, Springer, vol. 2(4), pages 369-397.
- H. Mete Soner & Nizar Touzi, 2012. "Homogenization and asymptotics for small transaction costs," Papers 1202.6131, arXiv.org, revised Jun 2013.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1212.6275. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators)
If references are entirely missing, you can add them using this form.