Essays on risk exchanges within a collective

This thesis considers a group of investors who have joined their endowments and formed a collective. The collective is assumed to construct an internal (intra-group) market where its members can exchange assets (trade) under conditions that can be different to those that prevail outside of the collective. Two chapters of this thesis focus on the intra-group trades that are both financially fair and Pareto efficient. There are formulated conditions under which there exists a unique set of financially fair and Pareto efficient intra-group trades (redistribution). The results of these chapters were published in Journal of Mathematical Economics and in Insurance: Mathematics and Economics. The last chapter considers a collective in a setting where there are bid-ask spreads on an extra-group market and the collective is free to use its intra-group market. In this setting, we define an equilibrium similar to the competitive equilibria, and we investigate under which bid-ask spreads is the intra-group market superuous or, to the contrary, when the intra-group market can accommodate all equilibrium trades. The chapter also proposes a measure of tendency to trade internally” and offers a link with the term “group heterogeneity”.