Maria de Lourdes Centeno
CEMAPRE, ISEG - Universidade Lisboa

In the first part of the seminar we are concerned with the optimal form of reinsurance when the cedent seeks to maximize the adjustment coefficient of the retained risk (related to the probability of ultimate ruin) - which we prove to be equivalent to maximizing the expected utility of wealth, with respect to an exponential utility with a certain coefficient of risk aversion. Assuming that the premium calculation principle is a convex functional we prove existence and uniqueness of solutions and provide a necessary optimality condition. These results are used to find the optimal reinsurance policy when the reinsurance loading is increasing with the variance. The optimal contract is described by a nonlinear function, of a similar form than in the aggregate case. In the second part of the talk we consider the case where the insurer restricts the reinsurance strategies to functions of the individual claims, which is the case for most nonproportional treaties placed in the market. The same kind of optimal arrangement is obtained. In the third part of the presentation we consider the case of an insurer holding a portfolio of k dependent risks. It is assumed that the number of claims of a risk may depend on the number of claims of the other risks of the portfolio. The type of the optimal arrangement for a given risk only depends on the premium of that particular risk.