Actuarial students are taught from the start that probability and expectation are the foundation of their work. These concepts are central to calculating insurance premiums, valuing future cash flows, and assessing risks. They are based on the idea that the future can be described numerically and that outcomes can be predicted with sufficient information. Yet the world we live in is rarely that simple. The future often unfolds in unexpected ways, raising the question of whether our traditional mathematical tools are always enough to capture reality.

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In classical probability theory, several assumptions are made. It is believed that all possible outcomes can be identified, that each has a known probability, and that an expected value can be obtained by calculating a weighted average of these probabilities. This works well in structured environments such as rolling dice or playing cards, where the range of possible outcomes is fixed and easily measured. However, real-world situations rarely follow such clear boundaries. Events in the global economy, technology, or health can emerge suddenly, changing the conditions under which models were built.

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Major world events such as the COVID-19 pandemics or rapid technological advancements have shown how uncertain the future can be. In these cases, new possibilities continue to appear, while probabilities that once seemed valid quickly lose their relevance. This reflects the difference between probability and uncertainty. Probability assumes complete knowledge of the event space, whereas uncertainty acknowledges that not all possible outcomes can be foreseen and that the future may contain scenarios we have never imagined.

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To navigate this deeper level of uncertainty, it is helpful to think in terms of suppositions rather than strict expectations. A supposition can be seen as an informed assumption about the future that recognises the limits of current knowledge. This approach accepts that predictions are never absolute, but instead are reasoned estimates based on what is presently known. When applied in areas such as pricing, forecasting, or risk assessment, it encourages actuaries to remain flexible and humble, recognising that even the best models are approximations of reality.

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The way the human brain processes information provides a useful analogy. Rather than recording the world with complete precision, the brain creates mental maps based on relationships and patterns. It interprets experiences through context and connection rather than through perfect calculation. This way of thinking aligns with the idea of possibility rather than probability, where degrees of belief and potential outcomes are considered instead of fixed percentages. Such thinking can be more realistic when dealing with incomplete or changing information.

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For actuarial students and professionals alike, this perspective offers several important lessons. Every model represents only a simplified version of reality, so assumptions should always be questioned. Flexibility is essential; formulas must be adapted to new and uncertain situations rather than applied mechanically. Beyond mathematical skills, understanding human behaviour, psychology, and other disciplines can help actuaries approach uncertainty with creativity and insight. Most importantly, uncertainty should not be viewed as a flaw to eliminate, but as an inherent part of the world that can be explored through scenario analysis, stress testing, and sensitivity modelling.

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In conclusion, actuarial work has always revolved around managing risk and interpreting uncertainty. However, the modern world—with its rapid technological progress, climate challenges, and shifting economic conditions—demands more than numerical precision. By combining the clarity of expectations with the openness of suppositions, actuaries can build models that better reflect the complexity of reality. The aim is not to reject probability but to recognise its limits and approach the future with adaptability and curiosity. Uncertainty, rather than being something to fear, is what gives depth and meaning to the actuarial profession.

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Reference: https://www.theactuarymagazine.org/expectations-probability-and-uncertainty/