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Functionally generated portfolios in stochastic portfolio theory

Xie, Kangjianan; (2020) Functionally generated portfolios in stochastic portfolio theory. Doctoral thesis (Ph.D), UCL (University College London). Green open access

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Abstract

In this dissertation, we focus on constructing trading strategies through the method of functional generation. Such a construction is of great importance in Stochastic Portfolio Theory established by Robert Fernholz. This method is simplified by Karatzas and Ruf (Finance and Stochastics 21.3:753-787, 2017), where they also propose another method called additive functional generation. Inspired by their work, we first investigate the dependence of functional generation on an extra finite-variation process. A mollification argument and Komlós theorem yield a general class of potential arbitrage strategies. Secondly, we extend the analysis by incorporating transaction costs proportional to the trading volume. The performance of several portfolios in the presence of dividends and transaction costs is examined under different configurations. Next, we analyse the so-called leakage effect used to measure the loss in portfolio wealth due to renewing the portfolio constituents. Moreover, we further explore the method of additive functional generation by considering the conjugate of a portfolio generating function. The connection between functional generation and optimal transport is also studied. An extended abstract can be found before the first chapter of this dissertation.

Type: Thesis (Doctoral)
Qualification: Ph.D
Title: Functionally generated portfolios in stochastic portfolio theory
Event: UCL
Open access status: An open access version is available from UCL Discovery
Language: English
Additional information: Copyright © The Author 2020. Original content in this thesis is licensed under the terms of the Creative Commons Attribution 4.0 International (CC BY 4.0) Licence (https://creativecommons.org/licenses/by/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10091489
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