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Unformatted text preview: ACTL3004: Week 1 Financial Economics for Insurance and Superannuation: Week 1 Introduction, Utility Theory and Pricing Fundamentals ACTL3004: Week 1 Course Introduction About the lecturer Brian W.B. CHU I Graduated from Macquarie University with BCom (Act Std)/BApp Fin in 2005 and MCom (Act Std) by Thesis in 2008 I Currently a PhD candidate at UNSW I Former Associate Lecturer in Macquarie University (20062007) I 8 years of university teaching experience I Industry experience in corporate finance, executive remuneration consulting, workers compensation research and superannuation consulting I Lecturer of Part III Course 1 (Investments) and Course 5A (Finance) ACTL3004: Week 1 Course Introduction Motivation for Financial Economics I Aim to understand the financial markets, its behaviour and how financial instruments are priced I Recognise financial instruments as packaged cash flows of varying size and timing I Understand pricing involves discounting cash flows to present I Recognise discount rate depends on certain risks, and employ the right approach to quantify such risks I Appreciate investor behaviour both individually and collectively in order to adjust these discount rates ACTL3004: Week 1 Introduction to Utility Theory The Utility Axioms The Four Axioms Let w be wealth and let u ( w ) denote the utility function of wealth. This function will be used to denote or represent individual preferences. Axioms 1. Complete/Comparable: Can state for all alternative outcomes. ie.that A is preferred to B . ( A B ) or otherwise. 2. Transitive: If A B , and B C , then A C 3. Independent: If A B , and consider some D . The person is indifferent between a gamble that gives A wp p and D wp 1p B wp p and D wp 1p 4. Certainty Equivalent: Everything (gamble) has a price. An investor whose risk preferences are consistent with these four axioms will always make decisions according to the expected utility theorem. ACTL3004: Week 1 Introduction to Utility Theory Expected Utility Theorem Expected Utility Theorem Definition Suppose that an individual is subject to a random wealth W with den sity function f W ( ) . Then the expected utility of wealth is defined to be E [ u ( W )] = Z u ( w ) f W ( w ) dw , assuming, of course, that the wealth is a continuous random variable. In the case of discrete, the expected utility can be similarly defined. ACTL3004: Week 1 Introduction to Utility Theory Expected Utility Theorem Expected Utility Theorem Expected Utility Theorem Consider two random wealths W 1 and W 2 . An individuals preferences have an expected utility representation if there exists a function u so that W 1 is preferred to W 2 , that is we write it as W 1 < W 2 if and only if E [ u ( W 1 )] E [ u ( W 2 )] ....
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This note was uploaded on 08/07/2011 for the course ACTL 3004 at University of New South Wales.
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