Risk-layering and Optimal Insurance Uptake under Ambiguity: With an application to farmers exposed to drought risk in Austria

Many risks we face today will very likely not stay the same over time. For example, it is expected that climate change will alter future risks of natural disaster events considerably and, as a consequence, current risk management and governance strategies may not be effective anymore. Large ambiguities arise if future climate change impacts should be taken into account for analyzing risk management options today. Risk insurance, while albeit only one of many risk management actions possible, plays an important role in current societies for dealing with extremes. A natural starting point for our analysis is therefore the question of how ambiguity may be incorporated in a world with changing risks. To shed light on this question, we study how ambiguity can affect the uptake of insurance and risk mitigation within a risk-layer approach where each layer is quantified using distortion risk measures that should reflect the risk aversion of a decisionmaker toward extreme losses. Importantly, we obtain a closed-form solution for such a problem statement which allows an efficient numerical implementation. We apply this model to a case study of drought risk for Austrian farmers and address the question how ambiguity will affect the risk layers of different types of farmers and how subsidies may help to deal with current and future risks. We found that especially for small-scale farmers the consequences of increasing risk and model ambiguity are pronounced and subsidies are especially needed in this case to cover the high-risk layer.