Risk sharing with multiple indemnity environments

• Propose an insurance model with multiple risk environments. Solve Pareto optimal experience refunds, indemnity profiles, and premiums. Show that layer-type indemnities, within each environment, are optimal. Explore the effect on profiles by probabilities of to allocate sharing gains equally between buyer seller. Optimal arrangements have been substantially studied in literature, from aspects generalizing objective functions, incorporating more business constraints, investigating different optimality criteria. This paper proposes We study case where two agents endowed Value-at-Risk or Tail Value-at-Risk, when both risk-neutral but heterogeneous beliefs regarding underlying probability distribution. show optimal, which may be environment-specific. From optimality, we get premium can chosen a given interval, propose