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This survey is an introduction to asymptotic methods for portfolio-choice problems with small transaction costs. We outline how to derive the corresponding dynamic programming equations and simplify them in the small-cost limit. This allows…

Portfolio Management · Quantitative Finance 2017-05-25 Johannes Muhle-Karbe , Max Reppen , H. Mete Soner

We consider a new approach to portfolio selection in presence of transaction costs which allows to map the problem into one without costs. The proposed approach connects all the quantities of interest to exit times and probabilities to…

Disordered Systems and Neural Networks · Physics 2008-12-10 R. Baviera

In this short note, we consider mean-variance optimized portfolios with transaction costs. We show that introducing quadratic transaction costs makes the optimization problem more difficult than using linear transaction costs. The reason…

Portfolio Management · Quantitative Finance 2020-01-07 Pierre Chen , Edmond Lezmi , Thierry Roncalli , Jiali Xu

The introduction of transaction costs into the theory of option pricing could lead not only to the change of return for options, but also to the change of the volatility. On the base of assumption of the portfolio analysis, a new equation…

General Physics · Physics 2007-05-23 Alexander Morozovsky

The effect of proportional transaction costs on systematically generated portfolios is studied empirically. The performance of several portfolios (the index tracking portfolio, the equally-weighted portfolio, the entropy-weighted portfolio,…

Portfolio Management · Quantitative Finance 2019-04-22 Johannes Ruf , Kangjianan Xie

This paper considers the finite horizon portfolio rebalancing problem in terms of mean-variance optimization, where decisions are made based on current information on asset returns and transaction costs. The study's novelty is that the…

Methodology · Statistics 2025-08-21 Qingliang Fan , Marcelo C. Medeiros , Hanming Yang , Songshan Yang

Transaction costs play a critical role in asset allocation and consumption strategies in portfolio management. We apply the methods of dynamic programming and singular perturbation expansion to derive the closed-form leading solutions to…

Portfolio Management · Quantitative Finance 2023-04-18 Yingting Miao , Qiang Zhang

We apply numerical dynamic programming techniques to solve discrete-time multi-asset dynamic portfolio optimization problems with proportional transaction costs and shorting/borrowing constraints. Examples include problems with multiple…

Portfolio Management · Quantitative Finance 2020-03-05 Yongyang Cai , Kenneth Judd , Rong Xu

In this paper, we provide a comprehensive review of recent advances in robust portfolio selection problems and their extensions, from both operational research and financial perspectives. A multi-dimensional classification of the models and…

Portfolio Management · Quantitative Finance 2022-01-13 Alireza Ghahtarani , Ahmed Saif , Alireza Ghasemi

This paper studies a finite-horizon portfolio selection problem with non-concave terminal utility and proportional transaction costs, in which the commonly used concavification principle for terminal value is no longer applicable. We…

Mathematical Finance · Quantitative Finance 2025-06-04 Shuaijie Qian , Chen Yang

The classical discrete time model of proportional transaction costs relies on the assumption that a feasible portfolio process has solvent increments at each step. We extend this setting in two directions, allowing for convex transaction…

Mathematical Finance · Quantitative Finance 2021-01-15 Emmanuel Lepinette , Ilya Molchanov

An investor with constant relative risk aversion and an infinite planning horizon trades a risky and a safe asset with constant investment opportunities, in the presence of small transaction costs and a binding exogenous portfolio…

Portfolio Management · Quantitative Finance 2013-01-09 Johannes Muhle-Karbe , Ren Liu

In this paper, we consider the problem of hedging Asian options in financial markets with transaction costs. For this, we use the asymptotic hedging approach. The main task of asymptotic hedging in financial markets with transaction costs…

Mathematical Finance · Quantitative Finance 2020-01-07 Serguei Pergamenchtchikov , Alena Shishkova

We employ perturbation analysis technique to study multi-asset portfolio optimisation with transaction cost. We allow for correlations in risky assets and obtain optimal trading methods for general utility functions. Our analytical results…

Portfolio Management · Quantitative Finance 2009-05-06 Siu Lung Law , Chiu Fan Lee , Sam Howison , Jeff N. Dewynne

We theoretically and empirically study portfolio optimization under transaction costs and establish a link between turnover penalization and covariance shrinkage with the penalization governed by transaction costs. We show how the ex ante…

Portfolio Management · Quantitative Finance 2020-03-26 Nikolaus Hautsch , Stefan Voigt

We study how trading costs are reflected in equilibrium returns. To this end, we develop a tractable continuous-time risk-sharing model, where heterogeneous mean-variance investors trade subject to a quadratic transaction cost. The…

Portfolio Management · Quantitative Finance 2018-04-06 Bruno Bouchard , Masaaki Fukasawa , Martin Herdegen , Johannes Muhle-Karbe

We consider the problem of option hedging in a market with proportional transaction costs. Since super-replication is very costly in such markets, we replace perfect hedging with an expected loss constraint. Asymptotic analysis for small…

Portfolio Management · Quantitative Finance 2014-09-12 Bruno Bouchard , Ludovic Moreau , Mete H. Soner

This survey reviews portfolio choice in settings where investment opportunities are stochastic due to, e.g., stochastic volatility or return predictability. It is explained how to heuristically compute candidate optimal portfolios using…

Portfolio Management · Quantitative Finance 2013-11-08 Ren Liu , Johannes Muhle-Karbe

We discuss the time evolution of quotation of stocks and commodities and show that they form an Ising chain. We show that transaction costs induce arbitrage risk that usually is neglected. The full analysis of the portfolio theory is…

Condensed Matter · Physics 2015-06-24 E. W. Piotrowski , J. Sladkowski

Online portfolio selection is a fundamental problem in computational finance, which has been extensively studied across several research communities, including finance, statistics, artificial intelligence, machine learning, and data mining,…

Computational Finance · Quantitative Finance 2013-05-21 Bin Li , Steven C. H. Hoi
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