REF: 2021

Impact case study

Managing severe uncertainty


Professor Richard Bradley and Professor Roman Frigg have been influential in introducing new ways that AXA XL thinks about aspects of its decision-making under uncertainty. Their work is beginning to evolve the explicit consideration and treatment of uncertainty in different parts of the business, and we are currently assessing methods to implement some of their recommendations in our decision-making chains.

Manager – Science and Head of Science

AXA XL (insurance company)

Professor Richard Bradley

Research by

Professor Richard Bradley

Department of Philosophy, Logic and Scientific Method

Professor Roman Frigg

Research by

Professor Roman Frigg

Department of Philosophy, Logic and Scientific Method

LSE research has reshaped the way in which decisions under conditions of extreme uncertainty can be addressed in the insurance industry and financial sector.  

What was the problem? 

How do you price insurance premiums against natural hazards?  

Prevailing practice in the insurance industry is to design mathematical models to estimate the likelihood of natural catastrophes, such as hurricanes and earthquakes, and of the vulnerability of insured assets to them. This allows companies to determine their exposure to losses arising from such an event and use these projections to calculate insurance premiums and the capital holdings they require to keep the risk of ruin below the level required by national regulators.  

However, because of the sparsity of data concerning extreme events and the complexity of the underlying physical processes, these models are highly uncertain, and their projections are not fully trusted by insurance underwriters.  

The level of uncertainty in such models reflects broader questions of decision-making in the context of highly uncertain scenarios, including considering systematic risks in the financial sector and how to model climate change.  

What did we do? 

Professor Richard Bradley and Professor Roman Frigg have developed a body of work on scientific uncertainty and its implications for decision-making, which was brought together in the LSE project “Managing Severe Uncertainty” (2013 to 2016). This has yielded a method of confidence-sensitive decision-making that combines complementary strands of research: Bradley’s on decision-making under severe uncertainty and Frigg’s on uncertainty in environmental modelling.  

Bradley’s work draws on the emerging fields of imprecise probability and decision-making under ambiguity in which a set of probability measures for uncertain outcomes is combined with a decision rule that prescribes actions that are robust across each probability measure. The main challenge here is to specify the relevant set of probabilities. Bradley solves this problem by introducing a confidence grading of them, which is determined by the weight of scientific evidence supporting them. Decision-makers must then set the required level of confidence in these probabilities in view of what is at stake and how ambiguity-averse they are. They then adopt an action that is robust with respect to the smallest set of probability functions meeting this confidence level.  

Frigg’s work investigates the impacts of structural model error on the predictive ability of environmental models. He argues that the effect of errors in models for weather and climate systems is such that no statistical method will improve their projections. It is better instead to take the outputs of a range of different models into account in decision-making, each accompanied by a realistic assessment of uncertainties, even if there are theoretical relations between different models.  

These two strands come together in their joint work, with former PhD student Dr Joe Roussos, on uncertainty-sensitive decision algorithms in cases in which the relevant probabilities are the outputs of the models in a “model ensemble” – a collection of different and often conflicting models for the same target. They show that the standard practice of basing decisions on weighted averages can have detrimental consequences because decisions can be taken based on results that all models regard as overwhelmingly unlikely.  

Bradley, Frigg, and Roussos developed an alternative method of rational decision-making with model ensembles. Their “confidence approach” consists of: constructing a nested set of probability intervals based on model outputs; confidence-grading them based on the best available scientific evidence; evaluating the decision-maker’s stake in a certain decision; eliciting the decision-maker’s cautiousness; and finally making a decision based on the chosen interval using a decision rule for imprecise probabilities.  

This method, they demonstrated, can be used to price insurance policies against hurricane damage in a way that helps to determine fair and sustainable premiums while also complying with regulations.  

What happened? 

This innovative method of confidence-sensitive decision-making has reshaped the way in which decision-making in situations of extreme uncertainty are addressed in both the insurance industry and the financial sector.  

Since 2016, Bradley and Frigg have worked with the insurance company AXA XL, which provides insurance and risk management services for mid-sized to large companies. The insurer’s science unit, headed by Dr Tom Philp and Dr Mike Maran, asked Bradley and Frigg to investigate how underwriters might make better use of information yielded by AXA XL’s suite of models for risk management. In collaboration with Roussos, they derived a method for making decisions based on information contained in these models. Their recommendations have informed the practice of decision-making in several parts of AXA XL, most notably concerning natural catastrophes in the North Atlantic. Discussions continue to expand the scheme to other areas of the business. This new approach has allowed the insurer to include a realistic and substantiated risk premium in its contracts, thereby avoiding ad-hoc adjustments in pricing, protecting against under-selling policies, and ensuring that prices are equitable and grounded in a reasoned assessment of the relevant uncertainties. 

Following his work at AXA XL, Philp established a new private venture, Maximum Information, with Bradley and Frigg as science advisers, to provide transparent and reliable atmospheric catastrophe and climate change uncertainty analytics to a number of stakeholders, including to AXA XL. Maximum Information is the first company to include uncertainty and its attendant sensitivities in the modelling chain, integrating them in a comprehensive decision theory framework from the beginning.   

A second start-up, Syntherion KIG, is also influenced by Bradley and Frigg’s work. The Swiss risk management venture advises small and medium-sized banks on how to tackle their risk/return dilemma, by providing a software tool that optimises risk-return-ratios in real-time. Syntherion’s CEO, Christian Hoffmann, spent five months as an external visitor at LSE in 2012 (and has returned regularly), and Bradley and Frigg’s research has helped to shape his understanding of the limitations of traditional statistical modelling of risk and uncertainty management.  

Bradley and Frigg’s approach has also influenced work in the financial sector through advice provided to the Bank of England and the Sovereign Wealth Fund of Singapore by independent adviser Andrew Wong. After reading their work in 2014, Wong contacted Bradley and Frigg and they have provided him with confidential advice since then. This informs the advice he gives to both bodies, which focuses on risks around the global financial system. The Global Financial Crisis suggested that many of the risk models for complex derivatives were incomplete, and significantly underestimated potential losses. According to Wong, it is in this context that: 

It becomes clear how important it is that progress be made on the related questions of how best to think about models for complex phenomena, what are the limitations and constraints on such modelling efforts, how do we think about decision-making under uncertainty, and are there better ways to use models for real-world decision-making … I believe [Bradley and Frigg’s] work is important, theoretically and also in the translation of the work into the decision-making spheres in many fields, public and private.