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Title: Functionally generated portfolios in stochastic portfolio theory
Author: Xie, Kangjianan
ISNI:       0000 0004 8506 7545
Awarding Body: UCL (University College London)
Current Institution: University College London (University of London)
Date of Award: 2020
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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.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available