Two types of optimality criteria are commonly used when studying optimal reinsurance in the literature: maximizing the expected utility (EU) and minimizing risks. These criteria give different optimal policies. In practice, insurance companies are likely to consider both criteria when negotiating reinsurance policies. One approach is to maximize EU under some risk constraints, as was done in Bernard and Tian (2010). An alternative approach was in fact proposed in Borch (1960), which assumed that the admissible reinsurance policies in maximizing EU should be such that the reduction in variance of losses through the reinsurance transaction is maximized. In this paper, following Borch (1960), we first identify the set of reinsurance policies that minimize the total risks, measured by distortion risk measures, shared by the two parties, then we take this set of policies as admissible and determine the Pareto optimal policies that maximize the EU of the two parties