TY - JOUR
T1 - Asymptotic Methods for Transaction Costs
AU - Mayerhofer, Eberhard
N1 - Publisher Copyright:
© 2024 by the author.
PY - 2024/4
Y1 - 2024/4
N2 - We propose a general approximation method for the determination of optimal trading strategies in markets with proportional transaction costs, with a polynomial approximation of the residual value function. The method is exemplified by several problems, from optimally tracking benchmarks and hedging the log contract to maximizing utility from terminal wealth. Strategies are also approximated by practically executable, discrete trades. We identify the necessary trade-off between the trading frequency and trade size to ensure satisfactory agreement with the theoretically optimal, continuous strategies of infinite activity.
AB - We propose a general approximation method for the determination of optimal trading strategies in markets with proportional transaction costs, with a polynomial approximation of the residual value function. The method is exemplified by several problems, from optimally tracking benchmarks and hedging the log contract to maximizing utility from terminal wealth. Strategies are also approximated by practically executable, discrete trades. We identify the necessary trade-off between the trading frequency and trade size to ensure satisfactory agreement with the theoretically optimal, continuous strategies of infinite activity.
KW - asymptotics
KW - portfolio choice
KW - reflected diffusions
KW - shadow prices
KW - transaction costs
UR - http://www.scopus.com/inward/record.url?scp=85191394961&partnerID=8YFLogxK
U2 - 10.3390/risks12040064
DO - 10.3390/risks12040064
M3 - Article
AN - SCOPUS:85191394961
SN - 2227-9091
VL - 12
JO - Risks
JF - Risks
IS - 4
M1 - 64
ER -