This thesis considers optimal intertemporal consumption and investment problems in which the transaction costs on purchases of the risky asset are infinite. Equivalently, the problems can be classified as (infinitely divisible) asset sale problems with the restriction that the asset cannot be (re)-purchased. We will first present the classical Merton [41] model which comprises an agent with constant relative risk aversion (CRRA) who wishes to maximise the expected utility of consumption over an infinite horizon. Further, we introduce the extension of the single-asset Merton model with proportional transaction costs by Davis and Norman [13]. After discussing two preliminary optimal consumption and asset sale problems, we consider the special case of the Davis and Norman model, in which the transaction costs on purchase are infinite. Effectively, the asset cannot be purchased but only be sold. We manage to provide a complete and thorough analysis of the problem with rigorous proofs by a new solution technique, which reduces the problem into a first crossing problem. Based on the new solution technique, we conduct the comparative statics to analyse the optimal strategies and the indifference price, especially their dependance on model parameters. Some surprising results are found and are further discussed. We then consider the optimal consumption and investment problem with multiple risky assets and with infinite transaction costs. We manage to make significant progress towards an analytical solution and completely characterise the different possible behaviours of the agent by understanding the existence and finiteness of a first crossing problem. The monotonicity of the indifference price in model parameters is proved and a comparative statics is conducted.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:647975 |
| Date | January 2014 |
| Creators | Zhu, Yedi |
| Publisher | University of Warwick |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://wrap.warwick.ac.uk/67811/ |
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