# Expected Utility Theory and Risk Aversion

and Risk Aversion

Seminar Paper

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Contents

S.no.

Topic

Page No.

1.

Acknowledgment

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2.

Introduction

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3.

Is this theory Empirically true?

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4.

5.

How do different people with different levels of risk

aversion behave, under the EUT?

Major Criticism: Coherence of Large & Small Stake

gambles

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6.

Conclusion

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7.

References

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Acknowledgement

I would like to thank Mr. because without his constant guidance and support this paper would not have been possible. His timely feedback and valuable inputs kept me on the right path to complete this paper.

I would also like to take this opportunity to thank University who provided me with the required facilities and reading material which greatly helped in completing this paper.

I would also like to thank my family and friends who always pushed me and motivated me to work hard whenever I lost all hopes of completing this paper on time.

All in all, it was a wonderful and enriching experience completing this paper.

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2.

Introduction

Expected Utility Theory (EUT) states that the decision maker (DM) chooses between risky or uncertain prospects by comparing their expected utility values, i.e., the weighted sums obtained by adding the utility values of outcomes multiplied by their respective probabilities. In economics, game theory, and decision theory the expected utility hypothesis is a theory of utility in which “betting preferences” of people with regard to uncertain outcomes (gambles) are represented by a function of the payouts (whether in money or other goods), the probabilities of occurrence, risk aversion, and the different utility of the same payout to people with different assets or personal preferences. This theory has proved useful to explain some popular choices that seem to contradict the expected value criterion (which takes into account only the sizes of the payouts and the probabilities of occurrence), such as occur in the contexts of gambling and insurance. Daniel Bernoulli initiated this theory in 1738. Until the mid-twentieth century, the standard term for the expected utility was the moral expectation, contrasted with “mathematical expectation” for the expected value.

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Axioms of this theory

There are four axioms of the expected utility theory that define a rational decision maker. They are completeness, transitivity, independence and continuity. Completeness assumes that an individual has well defined preferences and can always decide between any two alternatives.

This means that the individual either prefers A to B, or is indifferent between A and B, or prefers B to A.

Transitivity assumes that, as an individual decides according to the completeness axiom, the

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individual also decides consistently.

This means that if A>B and B>C, then A>C will always be true. Independence also pertains to well-defined preferences and assumes that two gambles mixed with a third one maintain the same preference order as when the two are presented independently of the third one. The independence axiom is the most controversial one. The independence axiom means that, if A>B then there must exist a lottery C such that, (t)A + (1-t)C > (t)B + (1-t)C will also hold true. (Where, t is the probability of choosing the lottery.) Continuity assumes that when there are three lotteries (A, B and C) and the individual prefers A to B and B to C, then there should be a possible combination of A and C in which the individual is then indifferent between this mix and the lottery B.

Let A, B and C be lotteries with A>B and B>C then there exists a probability p such that B is equally good as (p)A + (1-p)C

If all these axioms are satisfied, then the individual is said to be rational and the preferences can be represented by a utility function, i.e. one can assign numbers (utilities) to each outcome of the lottery such that choosing the best...

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