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Title: Hedging and pricing European-type claims on non-traded asset using utility maximization
Author: Jingyi, Liu
ISNI:       0000 0004 2674 3240
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2009
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In our thesis, we consider the problem facing a risk-averse agent who owns a traded asset and a non-traded asset simultaneously. The agent wishes to know how to price and hedge the claims on the non-traded asset. Under the assumption that agents always maximize their expected utility of terminal wealth, utility indifference pricing has been adopted for this problem. Our contributions are presented as a series of Thesis Results when addressed in the thesis. In Chapter 2, we discover that the restriction on the utility function for Zariphoupoulou's analytical solution of the non-traded asset problem is the requirement that the utility function belongs to one of two classes of generalized utility functions. When an analytical formula is not available, we require a more efficient numerical technique. In Chapter 3, we present two new finite difference approximation algorithms, one linear and one nonlinear. The convergence proof of the linear algorithm is established. The proof of the nonlinear algorithm is supported by a local convergence test and a numerical comparison with the analytical solution. In Chapters 4 and 5, we show that the principle of utility indifference pricing can be transformed into sound and practical solutions of two new financial economics problems. In Chapter 4, we focus on a treasury interest risk management problem. We arrive at a useful financial recommendation for a strategic fixed-floating interest rate mixture decision. In Chapter 5, we create a new financial agricultural derivative product. We use the sugar market as an example and apply the utility indifference pricing method to pricing and hedging this agriculture contingent claim. Since a geometric Brownian motion for the underlying asset process assumption is inconsistent with the statistical behavior of the sugar market, we develop a fourth-moment approximate utility indifference pricing model by using a statistics series expansion method.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available