エピソード

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

    LOR16: The quantile function, the survival function and the PDF
    2025/04/19
    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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    14 分
  • LOR15: The cumulative distribution function of a random variable

    LOR15: The cumulative distribution function of a random variable
    2025/04/12
    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?

    Become a supporter of this podcast: https://www.spreaker.com/podcast/the-logic-of-risk--6469023/support.
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    14 分
  • LOR14: Sigma-algebras and probability spaces

    LOR14: Sigma-algebras and probability spaces
    2025/04/06
    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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    17 分
  • LOR13: Back to risk, introducing risk measures

    LOR13: Back to risk, introducing risk measures
    2025/03/29
    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?

    Become a supporter of this podcast: https://www.spreaker.com/podcast/the-logic-of-risk--6469023/support.
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    17 分
  • LOR12: Keynes, Jeffreys, Jaynes and finally Kolmogorov

    LOR12: Keynes, Jeffreys, Jaynes and finally Kolmogorov
    2025/03/22
    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?

    Become a supporter of this podcast: https://www.spreaker.com/podcast/the-logic-of-risk--6469023/support.
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    22 分
  • LOR11: Probability as logic, and the logic of probability.

    LOR11: Probability as logic, and the logic of probability.
    2025/03/15
    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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    17 分
  • LOR10: Fighting the hydra of frequentism, or why subjectivism is preferable

    LOR10: Fighting the hydra of frequentism, or why subjectivism is preferable
    2025/03/08
    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?

    Become a supporter of this podcast: https://www.spreaker.com/podcast/the-logic-of-risk--6469023/support.
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    15 分
  • LOR9: Probability does not exist, or the subjectivist approach

    LOR9: Probability does not exist, or the subjectivist approach
    2025/03/01
    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?

    Become a supporter of this podcast: https://www.spreaker.com/podcast/the-logic-of-risk--6469023/support.
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    19 分