The Logic of Risk

In this episode we introduce moments, the bedrock of studying random variables and risk.
We begin with a concise overview, then zero in on simple (raw) moments, the foundation upon which central and standardized moments are built. You’ll learn how to compute an expected value (the first moment) and how to extend the same principles to higher-order simple moments.
Are you ready to take the risk?

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In this episode, we dive into the critical difference between extremes and outliers. As we will soon discover, understanding this distinction is vital for accurate modeling, especially when assessing (tail) risk.
We'll explore how both concepts relate to the range of possible values--the support--of a random variable and show you how to avoid common modeling pitfalls. 
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In this episode, building on the cumulative distribution function F (CDF) introduced in Episode 15, we define the quantile function Q, the survival function S, and the probability density function f (PDF). 
We then explore how each of these tools helps describe the behavior of a random variable.
Along the way, we also introduce Value-at-Risk (VaR), which becomes quite straightforward once you understand quantiles.
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In this episode, we continue laying the foundations of our mathematical treatment of risk. In particular, we introduce the cumulative distribution function, or CDF, as a tool for describing the probabilistic behavior of a random variable. We illustrate this with a simple example and discuss the basic characteristics of this interesting non-decreasing function, which will soon help us address very practical matters.
Are you ready to take the risk and follow Galileo's suggestion?

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In this episode, we answer the question we left hanging at the end of Episode 13: What is a sigma-algebra?
We will explore the properties of a sigma-algebra and explain why we want our event space to be one. Next, we will discuss probability spaces in a simple yet rigorous way, which will set the stage for understanding random variables and the mathematical treatment of risk measures.
Finally, we will discover why it can be inconvenient to swim naked.
Are you ready to wear a swimsuit?

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