Федеральное государственное автономное образовательное учреждение высшего образования
«НАЦИОНАЛЬНЫЙ ИССЛЕДОВАТЕЛЬСКИЙ УНИВЕРСИТЕТ
«ВЫСШАЯ ШКОЛА ЭКОНОМИКИ»
Факультет экономических наук
КУРСОВАЯ РАБОТА
ФЕДОТЕНКОВ АЛЕКСЕЙ ИГОРЕВИЧ
по направлению подготовки Экономика
образовательная программа «Экономика»
Выполнил:
Студент группы БЭК1813
Федотенков Алексей Игоревич
Руководитель:
Долгих София Игоревна
Москва 2020
Introduction
Decision-making often takes place in our everyday life. We may make choices, that seem easy
and rational to us, but there is some complicity to it, that cannot be seen by a naked eye. Many of
those decisions are displays of a gain-loss opportunity, that can affect our future wealth.
How do we handle such a situation as a rational human being, that wants not only to conserve
their wealth but to multiply it?
That’s where different sciences come in handy.
Economics, mathematics, psychology, game-theory all of which are being bounded together by a
representative of one of them in order to find the most suitable way of dealing with risk.
These are the theories I’m about to cover in my article. But for this presentation we’ll cover only
two of them.
Expected Utility Theory
Some centuries ago mathematicians like Daniel Bernoulli was one of them.
His introduction of St. Petersburg paradox in 1738 is considered the beginnings of the expected
utility hypothesis. This hypothesis has proven 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.
His work was only the beginning of what’s now called general utility hypothesis. The main goal
of this hypothesis is to severely generalise already known varieties of classical and contemporary
theories. Theories that are mainly aimed at understanding utilities of decision-making under risk
and uncertainty.
To begin with, we shall meet those theories in person and try to distinguish them from one
another. At least by understanding circumstances they operate in.
As we already know Bernoulli’s expected utility is a true originator of this branch. It tries to
guess subject’s preferences with regard to choices, that have uncertain outcomes. Theory states,
that subjective value of a gamble is a moral expectation of this game by a gambler, where his
valuation may differ from the dollar value of the potential results. In easy terms, we may say,
that subject is usually misunderstands his potential gain because of how non-mathematical his
expectations are. There is a wonderful paradox, that helps to understand this theory.
It involves you flipping a coin until you get to heads. The number of flips it took you put as an
exponent to 2 is an amount you receive in dollars. In this example we can trace player’s moral
expectancy and compare it to the mathematical expectation of the game itself. As you can tell
there is no upper bound of potential gain in this paradox, even though with rising of the reward
it’s probability plummets. So, expected value of this paradox is infinite. It means, that wealthmaximising person should bet all money he has. But people never do so.
This is where Bernoulli’s solution come in handy. He states, that even though the gamble has
infinite expected value, it’s expected utility for a subject is finite. By this he hypothesised
diminishing marginal utility of increasingly larger amounts of money. As a conclusion he
proposed that a nonlinear function of utility of an outcome should be used instead of the
expected value of an outcome, accounting for risk aversion, where the risk premium is higher for
low-probability events than the difference between the payout level of a particular outcome and
its expected value. Bernoulli further proposed that it was not the goal of the gambler to maximize
his expected gain but to instead maximize the logarithm of his gain. There are many more
hypotheses, that ill cover in my work later.
Prospect Theory
For now, I’d like to explain only one more hypothesis, that was developed as an enhanced
version of bernoulli’s one.
The prospect theory, that was brought to us by Daniel Kahneman and Amos Tversky in 1979. To
clearly understand this work we should learn it’s axioms first, as they differ from it’s
predecessor.
Firstly, the subject is psychology of a gain-loss opportunity, we are no longer looking at only the
utility of a gain. Secondly, prospect theory takes into account reference points. For example,
today you have 1 million dollars and your friend has 9 of them. Tomorrow both of you have 5
million. According to Bernoulli, both of you will be happy equally, as you have same amounts of
money, not taking into account, that your friend lost 4 million and you got them. However,
prospect theory treats this situation differently. It considers your previous point, from which you
got here and tells us, that you will be the only one happy from these changes. What is more, it
tells us, that the amount of happiness you will get is around twice as smaller than the amount of
sadness your friend will feel, even though the changes in your wealth are equal. Thirdly, Amos
and Tversky tell us, that not every person in their model is rational, which makes this theory
even closer to reality. Finally, this hypothesis explains risk-seeking. To explain this very
difference, I have to cover some theoretical aspects first.
As I’ve already told you people make decisions based on the potential gain or losses relative to
their specific situation (the reference point) rather than in absolute terms. Faced with a risky
choice leading to gains, individuals are risk-averse, preferring solutions that lead to a lower
expected utility but with a higher certainty (concave value function). Faced with a risky choice
leading to losses, individuals are risk-seeking, preferring solutions that lead to a lower expected
utility as long as it has the potential to avoid losses (convex value function). These two
statements directly argue with the expected utility theory, that takes into account only choices
with maximum utility.
This was one of examples of hypothesis comparison I’ll be conducting in my work.
What is this work about?
My work will be analysing different utility theories. Theoretically at first and empirically after.
To carry out such analysis, I’ll have to make a comprehensive comparison, which should bring
out all pros and cons of each theory. Only after such a comparison we shall proceed to an
empirical analysis.
Goals of this work
To start with, I need strong determiners of each theory. That’s why I’ll distinguish them by their
main objectives. As you’ve heard from me earlier today, this aspects can differ dramatically. If
these theories study decision-making under different circumstances, than it is no wonder one
may omit some psychological aspect others don’t, we sure do have to take it into account as well.
For the next goal, I’ll try to swap objectives of these theories, where it is going to be possible, in
order to test their versatility. One of the most important part of my work is empirical testing.
After covering all the differences and similarities, we’ll test all the hypothesises empirically. The
results will be compared. And on top of them I’ll try to derive the most versatile and
comprehensible utility hypothesis to use under risk.
Why economists should be interested in this work?
Firstly, theories, that are being inspected have much common with game-theories. Secondly, my
article tries explaining everything, that has to do with decision-making and behaviour of an
average person. Finally, my comparison will explain, which phycological processes in making
decisions under risk stay hidden from every theory.
As for the novelty and usability of results im going to get…
One of the most complicated parts of my work is going to be the out of the native context
comparison. It should definitely bring some brand new results, because the last attempt to do
such a look fat these theories was done several decades from now. Surely, it must be difficult to
bring something new, when you’r writing your first article, thus my main goal will still be as it
follows: to systematically compile and compare all widely known hypotheses. The last, but not
the least important point in my work is empirical testing of theories on a tv-show data, which can
be used to trick the gamble afterwards.
Literature
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*Kahneman, Daniel; Tversky, Amos (1979). "Prospect Theory: An Analysis of Decision under
Risk" (PDF). Econometrica. 47 (2): 263–291.
Bernoulli, Daniel; Originally published in 1738; translated by Dr. Louise Sommer. (January
1954). "Exposition of a New Theory on the Measurement of Risk". Econometrica. The Econometric
Society. 22 (1): 22–36. doi:10.2307/1909829. JSTOR 1909829. Archived from the original on 2014-0316. Retrieved 2006-05-30.