Vali Asimit
City St George's, University of London
Room: M3 3127
High-Dimensional Risk Sharing
Two agents with mean-variance preferences share p risks according to a proportional rule. We seek to reduce the estimation error, measured by the mean squared error (MSE), of Pareto-optimal rules. Plug-in estimators can be severely affected by estimation error, particularly when p is large relative to the sample size n. We quantify this error exactly and show how linear shrinkage can reduce it. With variance preferences, the optimal rule is estimation-free, but each agent’s optimal risk share is proportional to the aggregate variance. Assuming only finite fourth moments, we derive the oracle-optimal shrinkage intensity that minimises the MSE of the estimated aggregate variance. With mean-variance preferences, both the optimal rule and the optimal risk shares are affected by estimation error. Under multivariate normality, we derive the exact finite-sample MSEs of the plug-in rule and the plug-in estimator of the overall optimal risk, allowing the sample mean, the sample precision matrix, or both to be shrunk. We also derive the corresponding oracle-optimal shrinkage intensities. We then construct fully data-driven estimators of these oracle-optimal intensities and study their asymptotic properties in the high-dimensional regime, where both n and p are large. Illustrative examples demonstrate the theoretical results.