Multi-period risk sharing under financial fairness

We work with a multi-period system where a finite number of agents need to share multiple monetary risks. We look for the solutions that are both Pareto efficient utility-wise and financially fair value-wise. A buffer enables the inter-temporal capital transfer. Expected utility is used to evaluate the utility, and a risk-neutral measure is essential for determining the risk sharing rules. It can be shown that in the model setting there always exists a unique risk sharing rule that is both Pareto efficient and financially fair. An iterative algorithm is introduced to calculate this rule numerically.