The Logic of Risk

LOR18: Introducing (simple) moments

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 found

LOR17: Extremes and Outliers

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 modeli

LOR16: The quantile function, the survival function and the PDF

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 pr

LOR15: The cumulative distribution function of a random variable

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

LOR14: Sigma-algebras and probability spaces

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 w

LOR13: Back to risk, introducing risk measures

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 t

LOR12: Keynes, Jeffreys, Jaynes and finally Kolmogorov

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 Jayne

LOR11: Probability as logic, and the logic of probability.

This episode introduces logicism, examining how modern logic informs our understanding of probability. Can logicism be considered as a bridge between probabilistic object

LOR10: Fighting the hydra of frequentism, or why subjectivism is preferable

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

LOR9: Probability does not exist, or the subjectivist approach

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

LOR8: Propensity in play, from quantum mechanics to one-shot events

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

LOR7: Probability as propensity

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

LOR6: Frequentism, its pros and its cons

In this episode, we delve deeper into the frequentist definition of probability, showing how probabilities emerge from limiting relative frequencies. We discuss why this

LOR5: Moving toward Frequentism

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

LOR4: The classical definition of probability

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 purpo

LOR3: The possibility of harm, or an intro to probability

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

LOR2: Harm as a component of risk

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

LOR1: What is risk?

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 typic