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Utility Maximisation with a Time Lag in Trading

  • L. C. G. Rogers
  • E. J. Stapleton
Part of the Applied Optimization book series (APOP, volume 74)

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.

Keywords

Asymptotic binomial tree optimisation portfolio choice time-lag 

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Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • L. C. G. Rogers
    • 1
  • E. J. Stapleton
    • 2
  1. 1.Department of Mathematical SciencesUniversity of BathBathGreat Britain
  2. 2.Market RiskHalifax Group Treasury & Wholesale BankingLondonGreat Britain

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