Representations of Uncertainty for Decision Modelling

On Monday 6 May 2024 Benjamin Narum will hold a trial lecture on a prescribed topic and defend his thesis for the PhD degree at NHH.

Decisions are rarely made under certainty about future events, and when uncertainty has considerable implications for decisions, this should change how we think about decision-making. In such settings, it is typically most effective to apply strategies that use options to enable the flexibility to deal with a variety of future outcomes.

Ultimately, Benjamin Narum aims to construct computational decision support models that find such effective strategies within complicated environments. Typical applications of such decision models include logistics, operations, finance, and engineering. Dealing with uncertainty can be challenging since it typically requires us to solve complicated integrals. By the nature of common applications, distributions can be high dimensional and attain other difficult characteristics.

The first part of the thesis explores effective integration techniques and aims to widen the scope of applications that can effectively be dealt with using decision support tools. The second part addresses operational risk management in aquaculture. This is a problem which requires strong modelling assumptions, effective computational techniques and which stretches the capabilities of effectively dealing with uncertainty.

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On Friday 26 April 2024 Thomas Lange will hold a trial lecture on a prescribed topic and defend his thesis for the PhD degree at NHH.

The first paper proposes an integration technique that exploits the structure of decision models. It explores the relation between decisions and their corresponding implications to construct highly parsimonious representations of uncertainty.

The second paper reviews techniques for gauging the performance of decisions with respect to uncertainty, using mathematical bounds to otherwise intractable integrals. The paper explores close relations between distribution approximation and function approximation, and techniques for dissecting intractable integrals into more manageable pieces. The authors also show that some intuitive approaches for approximating uncertainty can in fact lead to conservative bounds instead. Aquaculture farmers are exposed to considerable biological, operational and market risk, and must deal with complicated operational trade-offs.

This makes aquaculture well suited for quantitative decision modelling. A distributional forecasting model for biological risk is developed and reveals large exposure and great heterogeneity across sites. Furthermore, decision models show that site wide diversification and explicit consideration of uncertainty can be built into harvest plans to considerably improve their performance. Narum also finds that the overall risk exposure in the industry is large.