TY - JOUR
T1 - Almost Perfect Shadow Prices
AU - Mayerhofer, Eberhard
N1 - Publisher Copyright:
© 2024 by the author.
PY - 2024/2
Y1 - 2024/2
N2 - Shadow prices simplify the derivation of optimal trading strategies in markets with transaction costs by transferring optimization into a more tractable, frictionless market. This paper establishes that a naïve shadow price ansatz for maximizing long-term returns, given average volatility yields a strategy that is, for small bid–ask spreads, asymptotically optimal at the third order. Considering the second-order impact of transaction costs, such a strategy is essentially optimal. However, for risk aversion different from one, we devise alternative strategies that outperform the shadow market at the fourth order. Finally, it is shown that the risk-neutral objective rules out the existence of shadow prices.
AB - Shadow prices simplify the derivation of optimal trading strategies in markets with transaction costs by transferring optimization into a more tractable, frictionless market. This paper establishes that a naïve shadow price ansatz for maximizing long-term returns, given average volatility yields a strategy that is, for small bid–ask spreads, asymptotically optimal at the third order. Considering the second-order impact of transaction costs, such a strategy is essentially optimal. However, for risk aversion different from one, we devise alternative strategies that outperform the shadow market at the fourth order. Finally, it is shown that the risk-neutral objective rules out the existence of shadow prices.
KW - portfolio choice
KW - reflected diffusions
KW - shadow prices
KW - transaction costs
UR - http://www.scopus.com/inward/record.url?scp=85185923473&partnerID=8YFLogxK
U2 - 10.3390/jrfm17020070
DO - 10.3390/jrfm17020070
M3 - Article
AN - SCOPUS:85185923473
SN - 1911-8074
VL - 17
JO - Journal of Risk and Financial Management
JF - Journal of Risk and Financial Management
IS - 2
M1 - 70
ER -