**Class time:** MW 3-4:20 pm, Room CCSB 1.0202

**Instructor:** Vladik
Kreinovich, email vladik@utep.edu, office CCSB 3.0404, office
phone (915) 747-6951

- The instructor's office hours are: Mondays 8:30-9 am and 1-2 pm, Wednesdays 10:30-12 pm and 5:30-6:30 pm, or by appointment.
- If you want to come during the scheduled office hours, there is no need to schedule an appointment.
- If you cannot come during the instructor's
scheduled office hours, please schedule an appointment in the
following way:
- use the instructor's appointments page http://www.cs.utep.edu/vladik/appointments.html to find the time when the instructor is not busy (i.e., when he has no other appointments), and
- send him an email, to vladik@utep.edu, indicating the day and time that you would like to meet.

**Prerequisite:**

- for graduate students: no special pre-requisites; graduate level standing is sufficient
- for undergraduate students: ideally, Statistics and Linear Algebra, but this is not required, we will recall the needed material anyway.

**Main objectives:** to learn advanced computational techniques
used in solving economic and financial problems -- from the
computational viewpoint, of course.

**Why economics and finance are important: high-level
perspective.** The ultimate goal of science and engineering is
to make the world a better place. Numerous innovations do make our
lives better:

- cell phones and emails make it easier to communicate,
- commercial websites make buying easier.

- fracking makes energy cheaper but can lead to pollution,
- self-driving cars will probably make travel safer, but they may increase unemployment.

**What we will do in the class in this regard.** In this class,
we will learn the basic computational ideas and techniques used in
solving the corresponding problems.

Of course, we will only learn the basics. To really become a
*quant* (a specialist in computational economics and
finance), it is necessary to learn many technical details and
tricks -- and it is not possible to cover all this in a
one-semester course. However, what we will do is cover most basic
ideas behind these tricks.

**Why economics and finance are important: pragmatic
perspective.** In the real world, every business needs to ne
profitable. The need to take economic and financial aspects into
account influences how much effort we spend on a software: when we
release it, how much we test it, how much efforts we can afford to
spend on optimizing it.

It is not realistic to expect that every employee understand all the related economic and financial details, but having a basic understanding definitely helps one to become a more productive employee -- and improves the chances of moving up the ladder, to leadership positions.

**What we will do in the class in this regard.** Again, this
class is not a substitute for real economics and business classes.
However, some basic knowledge acquired in this class will
hopefully help you better understand how companies function.

**Important aspects of decision making in economics and
finance.** As we have mentioned earlier, one of our main
objectives is to come up with strategies for group decision
making, strategies that take into account interest of al the
people involved.

In order to make these decisions, we need to have a good
understanding of individual people's preferences and interests.
Once we learn people's preferences, we can come up with algorithms
that help people make decisions which best reflect these
preferences. It is also important to take into account that when
people actually make decisions, they often do not use complex
optimization algorithms, they use their intuition which often
leads only to sub-optimal decisions. It is therefore important to
learn not only how people *should* make decisions, but also
how they *actually* make decisions.

Whatever decisions we make, these decisions affect the future. Therefore, to make appropriate decisions, we must make reasonable predictions about the future state of economics.

- When we decide which company to work for, we are trying to predict which company is more probable to survive in the long run.
- When we invest money for retirement, we are trying to predict which companies' stocks is more probable to remain valuable.

These are all the problems that we will deal with in this class:

- prediction,
- individual decision making, and
- group decision making.

**Traditional (basic) approach to prediction and decision
making.** The simplest predictions models are linear models,
when the predicted value is estimated as a linear combination of
the past and current values of one or several quantities. The
coefficients of this linear combination must be determined based
on the available data. The standard way of finding these
coefficients is by minimizing the mean squared error. This
*Least Squares* method will be the first thing we study in
this class.

Once we can predict the values of different quantities, the next step is to make a decision that would maximize the corresponding objective function. The simplest objective functions are quadratic, so we will study how to optimize quadratic functions. Our first example will be on how to best invest money -- based on the 1950s portfolio optimization work of the Nobelist Harry Markowitz.

We will also discuss how Markowitz theory helps decrease medicines' side effects and speed up machine learning.

**Need to go beyond traditional techniques.** Traditional
techniques assume:

- that the dependencies are linear,
- that we have full information about all the data, and
- that the optimization function is quadratic.

- dependencies are often non-linear,
- we usually have only partial information, and
- objective functions are more complex.

To deal with real-life situations, we need to use advanced computational techniques. This is what we will study in this class.

In dealing with such complex problems,

- it is important not just to come up with an optimal solution;
- it is also
important to have reasonably
*simple*solutions, solution which can be easily used in the real company, and - in view of
the uncertainty, it is important to have
*robust*solutions, solutions which work not just for some specific values of the corresponding coefficients, but also under possible deviations from these values.

**Main ideas behind the advanced economic and financial
techniques.** Sometimes, to select a proper model or a proper
algorithm, it is important to compare similar situations -- and/or
similar representations of the same situation. For example, in
physics, many fundamental equations can be derived from the
natural requirement that the corresponding formulas not change if
we simply change the measuring unit (e.g., from minutes to
seconds). This *symmetry* approach is productive not only in
physics, we will see that it is also productive in economics and
finance.

Symmetry ideas can help to find the models if we already know the objective function. When we do not yet have a clear expression for the objective function, symmetry ideas can help to find such an expression.

In some cases, it helps to consider three or more different
situations and to require *consistency*. A good example of
such consistency is *additivity*: when several countries form
a strong alliance -- like European Union (EU) -- then, e.g., the
formulas for trade with EU should lead to similar results whether
we consider EU as a single economic entity or as several different
countries.

It also often helps to compare economic and financial situations
with situations from other areas. For example, there are many
similarities between physical and economic processes, so many,
there there is a whole direction in economics, known as
*econophysics*. Its latest ideas are to borrow ideas and
techniques from quantum physics; this is known as *quantum
econometrics*.

In the class, we will show how these ideas help us solve the problems related to prediction and decision making in economics and finance.

**Specific topics covered in this class: general idea.** Let us
list specific topics covered in this class. Of course, this list
is approximate. We may not have enough time to cover all of this,
in which case we will follow the wise advise of one of my Russian
colleagues: "It is better not to have time for everything than not
to understand anything" ("Luchshe nichego ne uspet' chem nichego
ne poniat'.")

In all these topics, the emphasis will be on the main ideas, but we will also write some code -- usually, for simplified situations and simplified techniques.

**Specific topics covered in this class: prediction.** How
prediction works?

- we need to select a prediction model; such models usually comes with parameters that need to be determined from the data;
- based on the data, we need to find the values of these parameters which fit the data the best; for that, we need to describe fitness in precise terms, and then come up with efficient algorithms for finding the best-fit parameters.

**Topics related to selecting a model:**

- why linear models;
- which non-linear models should we choose: symmetry-motivated approach;
- first application: gravity model of trade;
- second application: how to predict production;
- state-of-the-art: main ideas behind quantum econometrics.

**Topics related to selecting a probability distribution:**

- symmetry-motivated distribution functions and their symmetry-motivated combinations;
- important case study: heavy-tailed Student distributions; see also;
- another case study: Matern covariance model;
- skew normal distributions;
- distributions of extreme values;
*copulas*;- symmetry-motivated objective functions: from Laplace indeterminacy principle to maximum entropy techniques and generalized entropy.

**Algorithms.** Depending on what information we have about the
corresponding probability distributions, we need different
algorithms:

- if we know the distribution -- or the family
containing the actual distribution -- then we should use
*maximum likelihood*; - different techniques should be used if if for some error components, we only know upper bounds -- this case is called interval uncertainty;
- if we have no information about the
probabilities, we should use
*robust methods*like l^{p}-techniques or empirical likelihood methods; in general, robust predictive econometrics leads to more accurate predictions.

For symmetry-motivated non-linear models, the corresponding symmetries help simplify the algorithms.

**Specific topics covered in this class: ideal individual
decision making.** We will start with a brief overview of the
traditional decision making theory, theory centered around the
notion of utility. We will then show how symmetries
help find the dependence of utility on several parameters.

We will then analyze how to make decisions under (interval)
uncertainty. The main idea is Nobelist Leo Hurwicz's
*optimism-pessimism criterion*. As an example, we will show
how Markowitz's portfolio
selection problem needs to be modified when we have no
information about correlations.

**Specific topics covered in this class: how people actually make
decisions.** According to the traditional decision theory,
ideally, people should:

- take into account all available information,
- make adequate estimates of the corresponding probabilities, and
- select the alternative for which the expected utility is the largest.

In practice, due to the limited ability of human information processing, we:

- take only some information into account,
- use approximate estimates of probabilities, and
- instead of always selecting the best alternative, often select close-to-optimal ones with some probability.

In this class, we will consider, explain, and analyze three example of such behavior:

- peak-end rule when people only take into account the peak and the end experiences; this rule is related to Dow Peak-and-Trough Theory of stock market behavior;
- probability-related empirical weights discovered by Nobelish Daniel Kahneman, and
- Nobelist Daniel McFadden's description of probabilistic choice.

**Specific topics covered in this class: group decision
making.** We start with the traditional approach to group
decision making: Nash's
bargaining solution. To illustrate this idea, we will use two
examples:

- gauging the state of a country's economy; for this, the formula coming from Nash's bargaining solution is more adequate than the usual Gross Domestic Product (GDP) -- since this formula takes inequality into account;
- the bankruptcy problem; in this example, we will follow the work of Nobelist Robert Aumann.

**What we do not cover at all.** Conflict situations and
related *game-theoretic* techniques are a whole separate
topic, requiring a special class.

**Main Source:** there are may books on computational methods
in economics and finance, but they are either too heavy on
economics, or too heavy on mathematics. Instead, we will use
handouts.

**Projects:** An important part of the class is a project.
There are three possible types of projects:

- An ideal class project is if you do something related to the class which is useful for your future thesis or dissertation. Please check with your advisor about it, maybe he or she wants you to read and report on some economics-related paper, maybe you need to do some economics-related research, whatever your advisor recommends will be a very good project for this class, just let the class instructor know what exactly you plan to do.
- If you have not yet selected an advisor, but you already know what research area you want to work in, come talks to the class instructor, we will try to find some appropriate topic -- and if you have any proposals already, great.
- If you do not have a research topic or you have a one but your advisor cannot find anything economics-related that will be helpful for your future thesis or dissertation, come talk to the instructor too.
- Maybe you like economics and want to start doing a related project, then come and talk to the instructor, we will try to find something that will be of interest to you.

- reviewing and reporting on a related paper, or
- doing some independent research (not research as in high school, but research as in graduate school, i.e., trying to come up with something new), or
- programming something economics-related.

**Exams:** There will be three tests:

- on Monday September 10,
- on Wednesday, October 17, and
- on Monday, November 19,

**Grades:**
Each topic means home assignments (mainly on the sheets of paper,
but some on the real computer). Some of them may be graded.
Maximum number of points:

- first test: 10
- second test: 10
- third test: 15
- home assignments: 10
- final exam: 35
- project: 20

A good project can help but it cannot completely cover possible deficiencies of knowledge as shown on the test and on the homeworks. In general, up to 80 points come from tests and home assignments. So:

- to get an A, you must gain, on all the tests and home assignments, at least 90% of the possible amount of points (i.e., at least 72), and also at least 90 points overall;
- to get a B, you must gain, on all the tests and home assignments, at least 80% of the possible amount of points (i.e., at least 64), and also at least 80 points overall;
- to get a C, you must gain, on all the tests and home assignments, at least 70% of the possible amount of points (i.e., at least 56), and also at least 70 points overall.

**Standards of Conduct:** You are expected to conduct
yourself in a professional and courteous manner, as prescribed
by the UTEP
Standards of Conduct.

Graded work, e.g., homework and tests, is to be completed independently and should be unmistakably your own work (or, in the case of group work, your team's work), although you may discuss your project with other students in a general way. You may not represent as your own work material that is transcribed or copied from another person, book, or any other source, e.g., a web page.

Academic dishonesty includes but is not limited to cheating, plagiarism and collusion.

- Cheating may involve copying from or providing information to another student, possessing unauthorized materials during a test, or falsifying data (for example program outputs) in laboratory reports.
- Plagiarism occurs when someone represents the work or ideas of another person as his/her own.
- Collusion involves collaborating with another person to commit an academically dishonest act.

**Disabilities:** If you feel you may have a disability that
requires accommodation, contact the The Center for Accommodations
and Support Services (CASS) at 747-5148, go to Room 106 E. Union,
or e-mail to cass@utep.edu. For
additional information, please visit the CASS website.