03_Notes_ExpectedUtility

# 03_Notes_ExpectedUtility - HANDOUT ON RISK AVERSION If you...

This preview shows pages 1–3. Sign up to view the full content.

HANDOUT ON RISK AVERSION If you have comment on these notes (mistakes, typos, “unclear” points, please send me an email) Rene Schwengber, June 15 , 2011 The goal for these notes is to complement your notes taken in class 1 . This is required reading material. 1. Portfolio choice problem We talked in class on the importance of the question: “How to best invest resources in a uncertain environment”, or, “How to optimally invest money for future consumption?”. The goal of this documente is to familiarize the student with the general problem for a consumer choosing financial assets. “Create affordable portfolio X from the set of available assets X in order to maximize the agent utility” in symbols: max X U ( X ) (1.1) subject to pX I X X (1.2) the first contraint is affordability (your portfolio costs less than your total wealth invested I ) , the second represent that you can choose only among available securities, i.e., your portfolio has to be created with available assets from start. In other words, this problem reads: Pick X in order to maximize U , however, you must pick X that is (1) affordable (2) and available to be bought. There are several concepts behind this problem. We need to understant the set X , presumably the agent has a preference, % over X , this preference can be represented by the utility function U (i.e, the function U maps X to a real number, and preserves the order of % ). We start it’s description bellow. First a review of some concepts from decision theory. Definition. Given a set of alternative choices, say C , and an ordering % over it 2 we say that a real valued function u : C → R represents the order % if for all pair of alternatives x, y in C we have: x % y if and only if u ( x ) u ( y ) . In words, the agent’s ranking % over the set C , is preserved by the function u . If he prefer x over y , then his utility associated with x is higher than his utility associated with y. 1 examples and other part of these notes can be found in chapter 3 of the book by Danthine, check the syllabus for the reference. For the part of choice you can read Theory of Value chapter 4, or you intermediate micro book. 2 an order is any binary relation R that satisfies (i) reflexivity, xRx (ii) transitivity xRy, yRz implies xRz and (iii) anti-symmetric if xRy and yRx then y = x . 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
4751 - Spring 2011 - June 15, 2011 Rene Schwenger Fact. If we have a preference % over C , that is represented by a function that maps C into the set real numbers, U : C → R , it must be true then that such preference is complete . That is, for any pair of elements X, Y in C , we must have X % Y or Y % X . This is the case, since associated to X we have a number U ( X ) which in turn is always T than the number U ( Y ) . As observed in class an investment decision scenario, the set of available choices is best described by a set of random variables.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern