Proportional and excess-of-loss reinsurance under investment gains

On the assumption that investment fund follows the logarithm-normal distribution, the paper derives the forms of proportional and excess-of-loss reinsurance contracts which make the convex combination of the insurer's rate of return v(1) and the reinsurer's rate of return v(2) exceeds R at the probability of f. In the whole paper, the premium takes the expectation principle. (C) 2010 Elsevier Inc. All rights reserved.