Reinsurance and portfolio optimisation under model uncertainty

Reinsurance and portfolio decisions are challenging under conditions of model uncertainty and non-convex risk measures. This thesis develops robust and tractable frameworks by explicitly accounting for dependence ambiguity, distributional uncertainty, and non-convexity in objective functions. First, for worst-case reinsurance for multiple lines of business with fixed marginal distributions and unknown dependence structure, Value-at-Risk (VaR) and Range Value-at-Risk (RVaR) are used to evaluate the risk in finding forms of optimal ceded loss function. For the VaR-based model with only two risks, the limited stop-loss reinsurance treaty is optimal for each line of business. Second, this thesis adapts Homotopy Optimisation with Perturbations and Ensembles (HOPE) to multi-line, non-convex reinsurance, achieving high-quality solutions far faster than conventional grid search on VaR-based problems, thereby closing the theory-practice gap. Third, the analysis presented in this thesis derives distributionally robust bounds for broad distortion risk metrics under some uncertainty sets, which are characterised by moment constraint, probability constraint via Wasserstein ball, or unimodality constraint, thereby identifying worst-case distributions. The numerical results for the application in portfolio optimisation are also derived to show the power of the theory