In this project we study an optimal reinsurance problem where the insurer’s risk-adjusted liability gets minimized. To better reflect the spirit of reinsurance, we impose exogenously Vajda condition on indemnity functions which requires the reinsurer to pay an increasing proportion of loss. To consider both robustness and tail risk, the insurer is assumed to apply Range-Value-at-Risk (RVaR) to evaluate its risk. Under the expected value premium principle, we derive the closed-form solution to our problem, which includes the results in Chi and Weng (2013) as special cases. Some comparative studies and sensitivity analysis are also carried out through numerical examples.