TY - JOUR

T1 - Short Communication

T2 - A Note on Utility Maximization with Proportional Transaction Costs and Stability of Optimal Portfolios

AU - Bayraktar, Erhan

AU - Czichowsky, Christoph

AU - Dolinskyi, Leonid

AU - Dolinsky, Yan

N1 - Publisher Copyright:
© 2021 Erhan Bayraktar, Yan Dolinsky.

PY - 2021

Y1 - 2021

N2 - The aim of this short note is to establish a limit theorem for the optimal trading strategies in the setup of the utility maximization problem with proportional transaction costs. This limit theorem resolves the open question from [E. Bayraktar, L. Dolinskyi, and Y. Dolinsky, Finance Stoch., 24 (2020), pp. 1013-1034]. The main idea of our proof is to establish a uniqueness result for the optimal strategy. The proof of the uniqueness is heavily based on the dual approach which was developed recently in [Ch. Czichowsky and W. Schachermayer, Ann. Appl. Probab., 26 (2016), pp. 1888- 1941; Ch. Czichowsky, W. Schachermayer, and J. Yang, Math. Finance, 27 (2017), pp. 623-658; Ch. Czichowsky et al., Finance Stoch., 22 (2018), pp. 161-180].

AB - The aim of this short note is to establish a limit theorem for the optimal trading strategies in the setup of the utility maximization problem with proportional transaction costs. This limit theorem resolves the open question from [E. Bayraktar, L. Dolinskyi, and Y. Dolinsky, Finance Stoch., 24 (2020), pp. 1013-1034]. The main idea of our proof is to establish a uniqueness result for the optimal strategy. The proof of the uniqueness is heavily based on the dual approach which was developed recently in [Ch. Czichowsky and W. Schachermayer, Ann. Appl. Probab., 26 (2016), pp. 1888- 1941; Ch. Czichowsky, W. Schachermayer, and J. Yang, Math. Finance, 27 (2017), pp. 623-658; Ch. Czichowsky et al., Finance Stoch., 22 (2018), pp. 161-180].

KW - proportional transaction costs

KW - shadow price process

KW - utility maximization

UR - http://www.scopus.com/inward/record.url?scp=85128874465&partnerID=8YFLogxK

U2 - 10.1137/21M1431382

DO - 10.1137/21M1431382

M3 - Article

AN - SCOPUS:85128874465

SN - 1945-497X

VL - 12

JO - SIAM Journal on Financial Mathematics

JF - SIAM Journal on Financial Mathematics

IS - 4

ER -