Dynamic Portfolio Optimization with Transaction Costs and State-Dependent Drift

Abstract

The problem of dynamic portfolio choice with transaction costs is often addressed by constructing a Markov Chain approximation of the continuous time price processes. Using this approximation, we present an efficient nu-$ The authors are grateful to the two anonymous reviewers and the editor, Professor Immanuel Bomze, for their helpful comments and advice. Preprint submitted to European Journal of Operational ResearchDecember 17, 2014 merical method to determine optimal portfolio strategies under time-and state-dependent drift and proportional transaction costs. This scenario arises when investors have behavioral biases or the actual drift is unknown and needs to be estimated. Our numerical method solves dynamic optimal portfolio problems with an exponential utility function for time-horizons of up to 40 years. It is applied to measure the value of information and the loss from transaction costs using the indifference principle.

Liquidity Risks, Transaction costs and Online Portfolio Selection

“…Both the methods show better backtesting results than their benchmarks with single-period prediction of t + 1. 2 Brown and Smith (2011), Palczewski et al (2015) used risk-averse utility functions instead of the mean-variance portfolio.…”

“…OPS directly optimises a portfolio in terms of the long-term investment without forecasting (Li and Hoi 2014), and it differs from the previous studies of prediction-based portfolio selection (Freitas et al 2009, Otranto 2010, Brown and Smith 2011, Ferreira and Santa-Clara 2011, Gârleanu and Pedersen 2013, DeMiguel et al 2014, Palczewski et al 2015, which i) forecasts the expected values or covariance matrix of stock returns 1 and ii) uses the mean-variance optimisation. 2 Therefore, OPS neither suffers from the difficulty of the prediction nor uses in-sample and out-of-sample tests.…”

Singular stochastic control model for algae growth management in dam downstream

“…Since x 0 (x) is decreasing in [0, ε] for small ε > 0 by Equations (41) and (43), and 0 ≥ x 0 (x) ≥ ε 0 (ε) > −∞, we have the centered square integrable martingale property…”

“…The singular control of the present SDE is slightly different from the conventional ones [3, Chapter 4.5 of 44] in that the singular control variable is multiplied by a power function of the state variable in the former. Related SDEs with a not usual but simpler singular control terms multiplied by state variables have been mathematically and numerically analysed [2,22,38,41,48]. A performance index to be maximized by the decision-maker, which is the manager of the dam, is presented under the assumptions that there exists a target value of the dam discharge and that the growth of algae is considered as not desirable.…”

Do portfolio investors need to consider the asymmetry of returns on the Russian stock market?

“…Other examples of closed-form solutions with exponential utility include (Çanakoğlu and Özekici, 2009), where the asset returns are independent, and (Bodnar et al, 2015), where the asset returns follow a vector autoregressive process of order one. Using exponential utility Palczewski et al (2015) study the influence of transaction costs on the optimal portfolio choice.…”