A marginal indemnity function approach to optimal reinsurance under the Vajda condition

To manage the risk of insurance companies, a reinsurance transaction is among myriad management mechanisms top ranked choice. In this paper, we study design optimal contracts within measure minimization framework and subject to Vajda condition. The condition requires reinsurer take an increasing proportion loss when it increases therefore imposes constraints on indemnity function. distortion-risk-measure-based objective function very generic, allows for, for example, minimize risk-adjusted value insurer’s liability, heterogeneous beliefs regarding distribution by insurer reinsurer. Under mild condition, propose backward-forward optimization method that based marginal formulation. show applicability simplicity our strategy, provide three concrete examples with Value-at-Risk: one follows from imposing Pareto optimality, beliefs. We conclude paper empirical application Danish fire losses Value-at-Risk Tail Value-at-Risk.