I enjoyed the help and support from numerous friends and faculty members during whilst writing this thesis. My greatest debt however, goes to my supervisor, Professor Tony Dooley, who initiated me to the fantastic field of Malliavin calculus. With his incredible breadth and depth of knowledge and intuition, he guided me to structure and clarify my thought and suggested valuable insightful comments. This thesis would not have been possible to write without his help and support. I am also indebted to express my sincere thankfulness to the honours coordinators, Dr Ian Doust and Dr Brian Jefferies, who were very kind and supportive to us during the year. Dr Ben Goldys also deserves a special mention, for the recommendation of a number of useful references, and I very much enjoyed the casual discussions I had with him. Finally, I would like to thank everyone in the School of Mathematics, and the Department of Actuarial Studies for providing me with such a wonderful four years at UNSW
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