Optimal reinsurance with concave ceded loss functions under VaR and CTE risk measures

► We study the optimal reinsurance problem under VaR and CTE optimization criteria. ► The ceded loss function is confined to the class of increasing concave functions. ► The quota-share reinsurance with a policy limit is optimal under VaR risk measure. ► The full reinsurance with a policy limit is optimal under CTE risk measure.