  We find the optimal indemnity to maximize the expected utility of terminal
wealth of a buyer of insurance whose preferences are modeled by an exponential
utility. The insurance premium is computed by a convex functional. We obtain a
necessary condition for the optimal indemnity; then, because the candidate
optimal indemnity is given implicitly, we use that necessary condition to
develop a numerical algorithm to compute it. We prove that the numerical
algorithm converges to a unique indemnity that, indeed, equals the optimal
policy. We also illustrate our results with numerical examples.
