Abstract
This is a study of the effect of a delay in execution of trades on the solution to the classical Merton-Samuelson problem of optimal investment for an agent with CRRA utility. Such a delay is a ubiquitous feature of markets, more pronounced the less the liquidity of the market. The first problem considered is set in continuous time, where the single risky asset is a log-Lévy process and the investor is only allowed to change his portfolio at times which are multiples of some positive h; it is shown that the effect is at worst O(h). The discrete-time analogue is then analysed, where an agent is only allowed to change his portfolio one period h in advance. An expansion in powers of h is developed for the delay effect, and this is confirmed by numerical calculations: the asymptotics derived prove to be very good.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Benninga, S., and Protopapadakis, A. (1988). The equilibrium pricing of exchange rates and assets when trade takes time.Journal oflnternationalMoney and Finance, 7, 129–149.
Constantinides, G. M. (1986). Capital market equilibrium with transactions costs. Journal of Political Economy, 94, 842–862.
Davis, M. H. A., and A. Norman (1990). Portfolio selection with transactions costs. Mathematics of Operations Research, 15, 676–713.
Ehrlich, I. and W. A. Hamlen, Jr. (1995). Optimal portfolio and consumption decisions in a stochastic environment with precommitment. Journal of Economic Dynamics and Control, 19, 457–480.
Karatzas, I., and S. E. Shreve (1998). Methods ofMathematicalFinance. Springer, New York.
Merton, R.C. (1969). Lifetime portfolio selection under uncertainty: The continuous-time case. Review of Economics and Statistics, 51, 247–257.
Rogers, L. C. G. (2001). The relaxed investor and parameter uncertainty. Finance and Stochastics 5, 131–154.
Rogers, L. C. G. and O. Zane (1998). A simple model of liquidity effects. University of Bath preprint.
Rogers, L. C. G. (1999). Why is the effect of proportional transactions costs O(82/3)? University of Bath preprint.
Rogers, L. C. G. and D. Williams (2000). Diffusions, Markov Processes, and Martingales, Vol. 2. Cambridge University Press, Cambridge.
Samuelson, P. A. (1969). Lifetime portfolio selection by dynamic stochastic programming. Review of Economics and Statistics, 51, 239–246.
Shreve, S. E. (1995). Liquidity premium for capital asset pricing with transaction costs. Mathematical Finance, IMA Volume 65,117–133, Springer, New York.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Rogers, L.C.G., Stapleton, E.J. (2002). Utility Maximisation with a Time Lag in Trading. In: Kontoghiorghes, E.J., Rustem, B., Siokos, S. (eds) Computational Methods in Decision-Making, Economics and Finance. Applied Optimization, vol 74. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3613-7_13
Download citation
DOI: https://doi.org/10.1007/978-1-4757-3613-7_13
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-5230-1
Online ISBN: 978-1-4757-3613-7
eBook Packages: Springer Book Archive