Bargaining for over-the-counter risk redistributions

In this paper, we use a non-cooperative and cooperative approach for bargaining for risk reallocations. We discuss the strategic interaction between two firms, who trade risk over-the-counter in a one-period model. As a key example, we consider macro longevityrisk. The reason is that there is an incomplete market for this risk. Then, for the non-cooperative bargaining approach, we show that it is likely to end up in a situation similar as the Prisoner’s dilemma. Then, all Nash equilibria are of no interest for the firms. Theonly way to avoid this, is to restrict the strategy space a priori. Then, firms can agree on a fair joint strategy. In this way, an interesting Nash equilibrium may exist. So, cooperative behavior is required. Therefore, we discuss also a cooperative bargaining model. This is perfectly in line with the approach of Nash (1950b [19]). All Pareto optimal risk profiles are obtained by pooling each other’s risk and, then, reallocate (see e.g. Gerber and Pafumi (1998[7])). Them, we parameterize the Pareto set and we briefly discuss two well-known solution concepts of cooperative bargaining. Implicit formulas of posterior risk profiles corresponding to these concepts are obtained via a one-dimensional parameter. Throughout this paper, we provide some simple, numerical examples.