The General Structure of Optimal Investment and Consumption with Small Transaction Costs

41 Pages Posted: 9 Apr 2013 Last revised: 16 May 2015

See all articles by Jan Kallsen

Jan Kallsen

Munich University of Technology

Johannes Muhle-Karbe

Carnegie Mellon University - Department of Mathematical Sciences

Multiple version iconThere are 2 versions of this paper

Date Written: May 15, 2015

Abstract

We investigate the general structure of optimal investment and consumption with small proportional transaction costs. For a safe asset and a risky asset with general continuous dynamics, traded with random and time-varying but small transaction costs, we derive simple formal asymptotics for the optimal policy and welfare. These reveal the roles of the investors' preferences as well as the market and cost dynamics, and also lead to a fully dynamic model for the implied trading volume. In frictionless models that can be solved in closed form, explicit formulas for the leading-order corrections due to small transaction costs are obtained.

Keywords: transaction costs, optimal investment and consumption, trading volume, asymptotics

JEL Classification: G11, G12

Suggested Citation

Kallsen, Jan and Muhle-Karbe, Johannes, The General Structure of Optimal Investment and Consumption with Small Transaction Costs (May 15, 2015). Swiss Finance Institute Research Paper No. 13-15. Available at SSRN: https://ssrn.com/abstract=2246785 or http://dx.doi.org/10.2139/ssrn.2246785

Jan Kallsen

Munich University of Technology ( email )

Arcisstrasse 21
Munich, 80333
Germany

Johannes Muhle-Karbe (Contact Author)

Carnegie Mellon University - Department of Mathematical Sciences ( email )

Pittsburgh, PA 15213-3890
United States

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