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An understanding of these mathematical concepts develops a better understanding of finance and investing. So stay a while and you'll soon find the essential mathematic knowledge that all investors need! Read full introduction.
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Introduction to Markov Chains Part 1 |
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Written by Irvin Zhan
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Saturday, 26 November 2011 00:00 |
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A Digression: Markov Chains
Markov chains are simple, easy-to-learn mathematical models. It is used to predict non-evolving systems over time and is commonly used in the business world.
As useful as it seems, Markov chains cannot be learned without a basic knowledge of math matrices. Thus, this article and the next one will be broken down into two parts, the first explaining math matrices and the second explaining their application to Markov chains. If you are already familiar with mathematical matrices, click here to learn about Markov chains!
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A Mathematical Approach to Success |
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Written by Irvin Zhan
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Friday, 14 October 2011 02:00 |
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You are a student. You need money and fast. You have $1,000 cash on hand, and within 10 years, you want to place it on the investment of your lifetime. Open a recent newspaper and turn to the business section. Amidst the mess of worry and panic, you are bound to be met with a flurry of headlines on the next new big investment, companies that are expected to achieve great returns.
“BRLA has exceptional IPO; 237% projected growth - next Google?”
“Undiscovered investment gold mine, 23% expected returns, SIO”
“Anti-Lehman Brothers: High faith in OVI – 64% growth next year!”
So many opportunities! However, with the limited capital, you may only choose one of these companies within the 10-year span. Which opportunity will you take? When should you take it? How do you maximize the probability that you will pick the best possible investment? Impossible, you say! Indeed; in the way it’s described, an optimal strategy is not possible. With several assumptions however, mathematics provides us a way to be a savvy investor…
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Prisoner's Dilemma: Part 1 |
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Written by Irvin Zhan
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Saturday, 17 September 2011 00:00 |
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Two prisoners are locked up in separate cellblocks and accused of a crime. The police give each prisoner a chance to confess. If one confesses and the other keeps quiet, then the confessor will be set free and the other will face 20 years in prison. If both prisoners confess, then each will face 10 years in prison. If both players keep quiet, each will only face 5 years in jail. What will they do?
This is the prisoner’s dilemma, one of the most studied games in game theory. Above, we see a classic example of it with some arbitrary values. There are many versions of it, but we’ll start with a technical definition (P,Q,R,S are variables):
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Written by Irvin Zhan
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Sunday, 21 August 2011 00:00 |
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(This article is the third in a series introducing Game Theory. To start at the beginning, click Economics Squared on the right sidebar.)
In this article, we start with normal form games, games which are represented in matrix form. Let’s start by redefining what a game is.
A game must have
- a number of players
- set of strategies for each player
- outcomes that depend on their choice of strategies
- players preference of outcomes (rationality)
For now, we will focus mainly on games with 2 players.
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Utility and Game Matrices |
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Written by Irvin Zhan
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Monday, 08 August 2011 00:00 |
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(This article is the second in a series introducing Game Theory. To start at the beginning, click Economics Squared on the right sidebar.)
Utility
It is hard to dive into game theory without first mentioning a bit about utility and game matrices. Let's begin with the concept of utility. Ever hear the expression, "money isn't everything"? It is quite true. Money isn't everything... but utility is!
Utility is an abstract measure of worth. Though we usually think of worth in terms of money, utility measures worth more broadly. It takes into consideration all types of value, whether it be monetary, happiness, or something else.
Utility is best illustrated with an example. Suppose you buy an ice cream sundae and eat it. What types of outcomes may result? You might be down $3, yet be 500 calories "richer". On a hot day, the ice cream may have made you happier. Perhaps the first bite that marked the end of your diet, causing you to feel guilt.
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