News article: Why horizon matters more than you think in decision making

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Why horizon matters more than you think in decision making

November 2025

Research

Read the full preprint here:

Horizon in decision making

Across finance, energy, insurance, and public policy, we evaluate risks that unfold over seconds, minutes, years, or decades. Yet the tools we often deploy carry an implicit, and sometimes hidden, time horizon. Using the wrong horizon to assess a position—pricing a short-dated exposure with a long-horizon tool, or vice versa—creates a distinct source of model error: horizon risk.

In a fist paper, the authors focus on a simple but powerful idea: risk is not just about how much could go wrong, but also how far in the future is your risk expected. They introduce h-longevity to quantify the “penalty” of using a risk measure with the wrong time horizon. The result is a framework that helps practitioners detect and correct for horizon mismatch.

Here is the intuition. Imagine you want to evaluate a position that will resolve in forty years, but you use a measure designed for three seconds. The paper formalizes how much extra risk you’re implicitly adding by stretching the horizon. That extra bit is captured by an adjustment term—call it a surcharge—that is always nonnegative and becomes exactly zero if and only if you match horizons. In other words: if you use the right clock, there’s no surcharge; choose the wrong one, and the surcharge tells you how much you are off.

Under the hood, the story involves fully-dynamic risk measures—tools that explicitly track two times: the first is when you are evaluating the risk, and the second is the horizon of the exposure (when the uncertainty resolves). This two-time perspective may sound technical, but it captures something very practical: decision-makers often evaluate and compare today risks that live on a different timescale. With a fully-dynamic approach, you can cleanly separate and compare them making it possible to pinpoint horizon risk and compute the corresponding surcharge.

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The authors propose different methods for constructing fully dynamic risk using backward stochastic differential equations (BSDEs) as tool. In many cases h-longevity is characterized explicitly. They consider measures generated by one BSDE or families of BSDEs, showing what properties the risk measures fulfill in the different cases. Also, they investigate the cases of measures generated by Volterra type BSDEs and family of those. While Volterra type equations intrinsically embed the effects of memory in the risk evaluation, it is also recognized that explicit solutions are often difficult to obtain.

The paper also clarifies how horizon risk fits with other foundational properties of risk evaluation. A common assumption in classic models is normalization: a “zero position” has zero risk. That’s useful in finance, but it may be unrealistic in settings like climate, environment, or health, where “doing nothing” might still be risky.

Another property identified in this work is restriction, which says that if you evaluate a short-horizon exposure using a longer-horizon tool, and then “restrict” back to the short horizon, you should get the same answer as if you had used the short-horizon tool from the start. When restriction holds universally, horizon risk is invisible—there is no penalty for mismatch. But in real-world, restriction does not hold, and that is precisely where h-longevity becomes essential: it diagnoses and quantifies the mismatch rather than sweeping it under the rug.

Time-consistency—the idea that today’s and tomorrow’s risk assessments should not contradict each other—is also re-examined through the horizon lens. There are different definitions of time-consistency possible, and each has different meaning and applications. In finance, time-consistency leads to correct pricing over time, minimizing adjustments (indirectly reducing transaction costs), and keeping arbitrage opportunities under control when using risk measures for pricing as, e.g., in risk indifference pricing.

Taken together, the contribution of this work is both conceptual and practical.

Conceptually, it names and formalizes a pervasive source of distortion—horizon risk—and offers h-longevity as a clean, nonnegative surcharge that disappears when you get the horizon right. Practically, it gives modelers and decision-makers conditions to ensure their tools behave sensibly.

The bottom line is straightforward: before debating whether a position is risky, make sure you’re measuring it on the right timeline. With a fully-dynamic, horizon-aware view, you can keep your risk yardstick honest, your decisions better calibrated, and your stakeholders better served.

The paper is written by Giulia di Nunno (UiO) and Emanuela Rosazza Gianin (University Milano Bicocca) is published in SIAM Journal on Financial Mathematics.

Two other follow-up papers are coming soon: horizon risk will be analyzed by the same authors together with interest rate uncertainty for a comprehensive risk evaluation, and new methods of Deep Operator BSDEs for computations, this work by Pere Diaz Lozano (UiO).

Check out the full paper for details:

Horizon in decision making

This popular science blog article was written with the help of GPT UiO, a service developed to use OpenAI's GPT models within UiO's privacy requirements. Image generated by Gemini.