Utility Maximisation with a Time Lag in Trading
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.
KeywordsAsymptotic binomial tree optimisation portfolio choice time-lag
Unable to display preview. Download preview PDF.
- 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.Google Scholar
- Karatzas, I., and S. E. Shreve (1998). Methods ofMathematicalFinance. Springer, New York.Google Scholar
- Rogers, L. C. G. and O. Zane (1998). A simple model of liquidity effects. University of Bath preprint.Google Scholar
- Rogers, L. C. G. (1999). Why is the effect of proportional transactions costs O(82/3)? University of Bath preprint.Google Scholar
- Rogers, L. C. G. and D. Williams (2000). Diffusions, Markov Processes, and Martingales, Vol. 2. Cambridge University Press, Cambridge.Google Scholar
- Shreve, S. E. (1995). Liquidity premium for capital asset pricing with transaction costs. Mathematical Finance, IMA Volume 65,117–133, Springer, New York.Google Scholar