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 ). All Pareto optimal risk profiles are obtained by pooling each other’s risk and, then, reallocate (see e.g. Gerber and Pafumi (1998)). 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.