Advanced Main Ideas Behind . . . Computational Methods Specific - PowerPoint PPT Presentation

Why Economics and . . . Important Aspects of . . . Traditional (Basic) . . . Need to Go Beyond . . . Advanced Main Ideas Behind . . . Computational Methods Specific Topics . . . Topics Related to . . . in Economics and Finance Algorithms How People Actually . . . Home Page (A Pre-View of the Fall 2018 Class) Title Page ◭◭ ◮◮ Vladik Kreinovich Department of Computer Science ◭ ◮ University of Texas at El Paso El Paso, TX 79968, USA Page 1 of 28 vladik@utep.edu Go Back http://www.cs.utep.edu/vladik Full Screen Close Quit

Why Economics and . . . Important Aspects of . . . 1. Why Economics and Finance Are Important: Traditional (Basic) . . . High-Level Perspective Need to Go Beyond . . . • The ultimate goal of science and engineering is to make Main Ideas Behind . . . the world a better place. Specific Topics . . . Topics Related to . . . • Numerous innovations do make our lives better: Algorithms – cell phones and emails make it easier to communi- How People Actually . . . cate, Home Page – commercial websites make buying easier. Title Page • However, in many cases, innovations come with nega- ◭◭ ◮◮ tive side effects: e.g., ◭ ◮ – fracking makes energy cheaper but can lead to pol- Page 2 of 28 lution, – self-driving cars will probably make travel safer, Go Back but they may increase unemployment. Full Screen • How to take into account everyone’s interests? Close Quit

Why Economics and . . . Important Aspects of . . . 2. High-Level Perspective (cont-d) Traditional (Basic) . . . • Modern economics and finance techniques enable us to Need to Go Beyond . . . formulate such questions in precise numerical terms. Main Ideas Behind . . . Specific Topics . . . • After this, we need to design and apply computational Topics Related to . . . techniques to solve these problems. Algorithms • In this class, we will learn the basic computational How People Actually . . . ideas and techniques used in solving these problems. Home Page • Of course, we will only learn the basics. Title Page • To really become a quant , it is necessary to learn many ◭◭ ◮◮ technical details and tricks. ◭ ◮ • It is not possible to cover all this in one semester. Page 3 of 28 • However, what we will do is cover most basic ideas Go Back behind these tricks. Full Screen Close Quit

Why Economics and . . . Important Aspects of . . . 3. Why Economics and Finance Are Important: Traditional (Basic) . . . Pragmatic Perspective Need to Go Beyond . . . • In the real world, every business needs to ne profitable. Main Ideas Behind . . . Specific Topics . . . • The need to take economic and financial aspects into Topics Related to . . . account influences decisions about software: Algorithms – when we release it, How People Actually . . . – how much we test it, Home Page – how much efforts we can afford to spend on opti- Title Page mizing it. ◭◭ ◮◮ • It is not realistic to expect that every employee under- ◭ ◮ stand all the related economic and financial details. Page 4 of 28 • However, having a basic understanding definitely helps one to become a more productive employee. Go Back Full Screen • It also improves the chances of moving up the ladder, to leadership positions. Close Quit

Why Economics and . . . Important Aspects of . . . 4. Pragmatic Perspective: What We Plan to Do Traditional (Basic) . . . In This Class Need to Go Beyond . . . • Again, this class is not a substitute for real economics Main Ideas Behind . . . and business classes. Specific Topics . . . Topics Related to . . . • Basic knowledge from this class will help better under- Algorithms stand how companies function. How People Actually . . . Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 5 of 28 Go Back Full Screen Close Quit

Why Economics and . . . Important Aspects of . . . 5. Important Aspects of Decision Making in Eco- Traditional (Basic) . . . nomics and Finance Need to Go Beyond . . . • One of our main objectives is to come up with strate- Main Ideas Behind . . . gies for group decision making. Specific Topics . . . Topics Related to . . . • We need strategies that take into account interest of al Algorithms the people involved. How People Actually . . . • In order to make these decisions, we need to have a Home Page good understanding of individual people’s preferences. Title Page • Once we learn people’s preferences, we can help people ◭◭ ◮◮ make decisions which best reflect these preferences. ◭ ◮ • It is also important to take into account that: Page 6 of 28 – when people actually make decisions, – they often do not use complex optimization algo- Go Back rithms, Full Screen – they use their intuition which often leads only to Close sub-optimal decisions. Quit

Why Economics and . . . Important Aspects of . . . 6. Decision Making in Economics and Finance Traditional (Basic) . . . (cont-d) Need to Go Beyond . . . • It is therefore important to learn: Main Ideas Behind . . . Specific Topics . . . – not only how people should make decisions, Topics Related to . . . – but also how they actually make decisions. Algorithms • Whatever decisions we make, these decisions affect the How People Actually . . . future; therefore: Home Page – to make appropriate decisions, Title Page – we must make reasonable predictions about the fu- ◭◭ ◮◮ ture state of economics. ◭ ◮ • When we decide which company to work for, we predict Page 7 of 28 which company will survive in the long run. Go Back • When we invest money for retirement, we predict which Full Screen stock will remain valuable. Close Quit

Why Economics and . . . Important Aspects of . . . 7. Decision Making in Economics and Finance Traditional (Basic) . . . (cont-d) Need to Go Beyond . . . • To predict future values of corresponding quantities, Main Ideas Behind . . . we can use: Specific Topics . . . Topics Related to . . . – past values of this quantity and/or Algorithms – current (and past) values of related quantities. How People Actually . . . • These are all the problems that we will deal with in Home Page this class: Title Page – prediction, ◭◭ ◮◮ – individual decision making, and ◭ ◮ – group decision making. Page 8 of 28 Go Back Full Screen Close Quit

Why Economics and . . . Important Aspects of . . . 8. Traditional (Basic) Approach to Prediction and Traditional (Basic) . . . Decision Making Need to Go Beyond . . . • The simplest predictions models are linear models Main Ideas Behind . . . Specific Topics . . . n � y ≈ a 0 + a i · x i . Topics Related to . . . i =1 Algorithms How People Actually . . . • In these models, we estimate: Home Page – the predicted value y as Title Page – a linear combination of the past and current values ◭◭ ◮◮ x i of one or several quantities. ◭ ◮ • The coefficients of this linear combination must be de- Page 9 of 28 termined based on the available data � n , y ( k ) � Go Back x ( k ) 1 , . . . , x ( k ) . Full Screen Close Quit

Why Economics and . . . Important Aspects of . . . 9. Traditional Approach (cont-d) Traditional (Basic) . . . • The standard way of finding these coefficients is by Need to Go Beyond . . . minimizing the mean squared error Main Ideas Behind . . . Specific Topics . . . �� 2 K � � n a i · x ( k ) � � y ( k ) − Topics Related to . . . a 0 + . i Algorithms i =1 k =1 How People Actually . . . • This Least Squares method will be the first thing we Home Page study in this class. Title Page • Once we can predict the values of different quantities, ◭◭ ◮◮ the next step is: ◭ ◮ – to make a decision Page 10 of 28 – that would maximize the corresponding objective function. Go Back Full Screen Close Quit

Why Economics and . . . Important Aspects of . . . 10. Traditional (Basic) Approach to Prediction Traditional (Basic) . . . and Decision Making Need to Go Beyond . . . • The simplest objective functions are quadratic Main Ideas Behind . . . Specific Topics . . . m m m � � � J ( v 1 , . . . , v m ) = j 0 + j i · v i + j ik · v i · v k . Topics Related to . . . i =1 i =1 j = k Algorithms How People Actually . . . • So, we will study how to optimize quadratic functions. Home Page • Our first example will be on how to best invest money. Title Page • It is based on the 1950s portfolio optimization work of ◭◭ ◮◮ the Nobelist Harry Markowitz. ◭ ◮ • We will also discuss how Markowitz theory helps: Page 11 of 28 – decrease medicines’ side effects and Go Back – speed up machine learning. Full Screen Close Quit

Why Economics and . . . Important Aspects of . . . 11. Need to Go Beyond Traditional Techniques Traditional (Basic) . . . • Traditional techniques assume: Need to Go Beyond . . . Main Ideas Behind . . . – that the dependencies are linear, Specific Topics . . . – that we have full information about all the data, Topics Related to . . . and Algorithms – that the optimization function is quadratic. How People Actually . . . Home Page • All these assumptions are simplifying: in real life, Title Page – dependencies are often non-linear, ◭◭ ◮◮ – we usually have only partial information, and – objective functions are more complex. ◭ ◮ Page 12 of 28 • To deal with real-life situations, we need to use ad- vanced computational techniques. Go Back • This is what we will study in this class. Full Screen Close Quit