The paper studies an individual risk model where both a policy of per-claim insurance and a policy of reinsurance of aggregated losses are chosen by the insurer in order to maximize their expected utility. The problem is solved under additional constraints on the reinsurer's risk and the residual risk of the insured that should be met with probability one. We show that the only solution to the problem is the following: the optimal reinsurance is a modification of the stop loss reinsurance policy, so-called stop loss reinsurance with an upper limit; the optimal insurer's indemnity is a combination of the stop loss and the deductible policies. The results are illustrated by a numerical example for the case of exponential utility function.