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Dynamic optimal portfolio theory

Parnell, James E. (1997) Dynamic optimal portfolio theory. Master of Science thesis, Dublin City University.

In this thesis we consider a financial market model consisting of a bond with deterministic growth rate, and d risky assets, governed by Brownian motion with drift. We can shift money from one asset to the other without loss of capital. Optimal investment and consumption (spending) decisions are examined for different types of investors with various criteria for optimality. An investor’s level of satisfaction with any amount of wealth is measured by a utility function. The problem has been solved by Merton [4] and others for the small investor with no transaction costs. Here we suppose the investor is large, i.e., his strategy has an effect on the asset price evolution. The approach parallels th a t taken by Cvitanic and Karatzas [5] for constrained portfolios. The theorems therein are adjusted appropriately to account for the investor’s effect on prices instead of constraining the portfolios as Cvitanic and Karatzas do. As in Cvitanic and Karatzas [5], Karatzas et al.[6] and several others duality theory and martingale methods are introduced to prove the existence of the optimal portfolio which maximises the expected final utility. An algorithm is suggested to find this portfolio under certain market conditions.
Item Type:Thesis (Master of Science)
Date of Award:1997
Supervisor(s):Buffet, Emmanuelle
Uncontrolled Keywords:Brownian motion processes; Portfolio management Mathematical models; Duality theory (Mathematics); Martingales
DCU Faculties and Centres:DCU Faculties and Schools > Faculty of Science and Health > School of Mathematical Sciences
Use License:This item is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 3.0 License. View License
ID Code:19269
Deposited On:17 Sep 2013 13:15 by Celine Campbell . Last Modified 05 Dec 2023 15:12

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