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.
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© 2002 Springer Science+Business Media Dordrecht
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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
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DOI: https://doi.org/10.1007/978-1-4757-3613-7_13
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