The Logic of Risk

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.
Are you ready to take the risk?

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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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In this episode, we come back to the definition of risk and start discussing how we can measure it. That is why we need to introduce risk measures. But that requires us to be more formal and speak about the sample space and the event space in a more mathematical way.
Ready to discover the power set?
We are paving the way to introduce the probability space, a pivotal concept for us.
Ready to take the risk?

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In this episode, we conclude our overview of the various schools of thought on probability.
We begin by examining the logicist perspectives of Keynes, Jeffreys, and Jaynes before transitioning to Kolmogorov's axiomatic definition.
We will briefly review the three basic axioms of probability and explain why the axiomatic approach is not a definition in the traditional sense, but rather a framework that transcends the objectivist–subjectivist debate.
Are you ready to take the risk?

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This episode introduces logicism, examining how modern logic informs our understanding of probability. Can logicism be considered as a bridge between probabilistic objectivism and subjectivism? 
What did Wittgenstein think about probability?
Is probability the new logic of science?


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In this episode, we delve into subjective probability by drawing on Bruno de Finetti’s ideas. We show how viewing probability as a fair bet may lead to coherent estimates. We discuss how de Finetti challenges the circular and limiting nature of the classical and frequentist definitions, arguing that personal judgment, informed by data, experts, and even intuition, is key.
We also covers advanced ideas like Jeffrey's radical probabilism, ultimately emphasizing the need for continuous learning and humility in decision-making. 
Are you ready to take the risk?

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We introduce the subjectivist perspective on probability, featuring thinkers like Bruno de Finetti, Frank Ramsey, and Leonard Savage, who argue that probability is not an objective entity but rather something we invent to manage uncertainty arising from our limited knowledge.
De Finetti’s “betting” approach interprets probability as the price one would pay for a chance to win a fixed payoff, showing how different beliefs produce different numerical values.
From Laplace’s demon to everyday life, the notion of chance emerges because our knowledge is partial, compelling us to create probability and risk rather than discover them as objective realities. 
Are you ready to take the (subjective) risk?

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In this episode of The Logic of Risk, we continue our discussion on the propensity interpretation of probability. We start by showing how Popper thought propensity could cope with the peculiar uncertainty of quantum mechanics, as well as with the problem of one-shot events, which frequentism could not handle.
We then briefly touch Gillies' view, and introduce the reference class problem we will encounter often in our future conversations.
Ready to take the risk?

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In this episode, we move beyond the classical and frequentist definitions of probability to explore the propensity interpretation.
We examine how Peirce and Popper viewed probability as an objective tendency of random phenomena.
While this approach offers an interesting perspective, and it can be useful in fields like quantum mechanics, it also raises challenges, especially when dealing with single events. 
We also discuss historical bias and its impact on risk management and financial decision-making.

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In this episode, we delve deeper into the frequentist definition of probability, showing how probabilities emerge from limiting relative frequencies. We discuss why this approach can be useful for mass random phenomena but falls short for single or rare events—especially in risk management contexts involving heavy-tailed risks. Through examples, we highlight the dangers of relying solely on historical data and underscore the need for more robust tools to capture the true nature of randomness.

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Welcome to the fifth episode of The Logic of Risk. After introducing the classical definition, we begin a review of the main schools of thought in probability. We’ll see that some are objectivist and others are subjectivist, plus a few that position themselves somewhere in between. Among the objectivist schools, we’ll introduce the most commonly used (and abused) one: the frequentist school.
Are you ready to take the risk?

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In this episode, we provide an introduction to probability by exploring the classical definition, a concept rooted in the Renaissance and often used for pedagogical purposes. While historically significant, it has limitations in real-life applications.
We'll also delve into key concepts in probability theory, including the sample space, event space, mutually exclusive events, and independence.
Are you ready to take the risk?

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After defining risk as the possibility of harm in Episode 1 and exploring the harm profile in Episode 2, we now turn our attention to the concept of possibility. To that end, we introduce probability as a way to assess possibility. This episode serves as an essential introduction to the various schools of thought on probability, which we will cover in the next episodes.

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In this episode, we dive into the concept of harm, a fundamental component of risk—how can we understand, measure, and even rank it? We will break down its key dimensions and talk about a possible hierarchy.
Starting today, you’ll find some bonus materials waiting for you at www.thelogicofrisk.com. For Episode 2, there’s a picture ready for you to check out. Don’t miss it!

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Welcome to Episode 1 of The Logic of Risk.
In this introductory segment, we will begin by defining “risk” and uncovering why it’s far more nuanced than most people typically think.
Are you ready to take the risk?

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