In this master thesis, we study two Stackelberg games between a reinsurance company and an insurance company. In both games, each party maximizes its expected utility of terminal wealth. However, the reinsurer is the leader and the insurer is the follower, i.e., the reinsurer knows for each of its actions the rational response of the insurer, which can be seen as an advantage. In academic literature, such games are mainly modeled on the whole level of aggregated claims and the reinsurance strategy is adjusted dynamically. However, in practice the reinsurance strategy is adjusted at discrete time points and is related to a specific product or product line. Therefore, our first Stackelberg game is an example from the existing literature. In the second Stackelberg game, we consider an innovative reinsurance-insurance problem in a more realistic scenario, where the reinsurance is part of the design of a single life insurance product with a capital guarantee and the reinsurance is only traded at the product settlement date without further adjustments during the investment period. Moreover, we model the situation when the reinsurance is not written directly on the insurer’s portfolio but on a benchmark portfolio, which is highly correlated to it. We derive solutions to the optimization problem in semi-closed form by combining and generalizing non-standard portfolio optimization techniques. In the numerical studies, we find that in the Stackelberg equilibrium the reinsurer chooses the maximal reinsurance premium at which the insurer is buying the full amount of reinsurance. We also examine the sensitivity of the Stackelberg equilibrium with respect to changes in the market and product parameters.     «

In this master thesis, we study two Stackelberg games between a reinsurance company and an insurance company. In both games, each party maximizes its expected utility of terminal wealth. However, the reinsurer is the leader and the insurer is the follower, i.e., the reinsurer knows for each of its actions the rational response of the insurer, which can be seen as an advantage. In academic literature, such games are mainly modeled on the whole level of aggregated claims and the reinsurance strate...     »