Optimal Robust Insurance with a Finite Uncertainty Set

Dr Junlei Hu from the Department of Mathematical Sciences will be discussing "Optimal Robust Insurance with a Finite Uncertainty Set" in this research seminar.

Decision-makers who usually face model/parameter risk may prefer to act prudently by identifying optimal contracts that are robust to such sources of uncertainty. We tackle this issue under a finite uncertainty set that contains a number of probability models that are candidates for the "true", but unknown model.

Various robust optimisation models are proposed, some of which are already known in the literature, and we show that all of them could be efficiently solved. The numerical experiments are run for various risk preference choices and it is found that for relatively large sample size, the decision-maker should focus on finding the best possible fit for the unknown probability model in order to achieve the most robust decision.

If only small samples are available, then the decision-maker should consider two robust optimisation models, namely the Weighted Average Model or Weighted Worst-case Model, rather than focusing on statistical tools aiming to estimate the probability model. Amongst those two, the better choice of the robust optimisation model depends on how much interest the decision-maker puts on the tail risk when defining its objective function.

These findings suggest that one should be very careful when robust optimal decisions are sought in the sense that the decision-maker should first understand the features of its objective function and the size of the available data, and then to decide whether robust optimisation or statistical inference is the best practical approach.