From the three actions Tom Brown is undertaking, which is categorised as a pure risk?

Pure risk involves situations where the only possible outcomes are loss or no loss, with no potential for gain. The action of going horse riding without a helmet introduces the risk of injury (a loss) or avoiding injury (no loss). There is no opportunity for a positive outcome or gain resulting from the decision not to wear a helmet. This scenario perfectly fits the definition of a pure risk, which typically involves accidental, unforeseen events that are often insurable. The other scenarios involve the possibility of gain, classifying them as speculative risks.

A. Buying lottery tickets is a speculative risk. It is undertaken voluntarily with the hope of a gain (winning the prize), while also accepting the possibility of a loss (the cost of the tickets).
B. This is a speculative risk based on a financial decision. The action is taken to mitigate a larger future loss, which is a relative gain, but it also carries the risk of an opportunity loss if prices rise.

1. Vaughan, E. J., & Vaughan, T. (2013). Fundamentals of Risk and Insurance (11th ed.). John Wiley & Sons. In Chapter 1, "The Problem of Risk," the text distinguishes between pure risk (only outcomes are loss or no loss) and speculative risk (outcomes can be loss, no loss, or gain). Horse riding without a helmet is a classic example of exposure to pure risk.

2. Hopkin, P. (2018). Fundamentals of risk management: understanding, evaluating and implementing effective risk management (5th ed.). Kogan Page Publishers. Chapter 1, "Introduction to risk management," classifies risks and describes pure risks as those associated with "damage to property, liability and injury to persons," which aligns with the helmet scenario.

3. University of Wisconsin-Madison, School of Business. (n.d.). Actuarial Science, Risk Management, and Insurance 300: Principles of Risk Management Course Materials. Such foundational courses consistently define pure risk as having only downside potential (loss or no change), contrasting it with speculative risk (e.g., investments, gambling) which has upside potential.

4. ISO 31000:2018, Risk management — Guidelines. Clause 3.1 defines risk as the "effect of uncertainty on objectives." It notes that an effect can be a "deviation from the expected (positive, negative or both)." Pure risk represents the subset of this definition where the deviation can only be negative or neutral.