Systemic Optimal Risk Transfer Equilibrium

Abstract

We propose a novel concept of a Systemic Optimal Risk Transfer Equilibrium (SORTE), which is inspired by the Bühlmann's classical notion of an Equilibrium Risk Exchange. We provide sufficient general assumptions that guarantee existence, uniqueness, and Pareto optimality of such a SORTE. In both the Bühlmann and the SORTE definition, each agent is behaving rationally by maximizing his/her expected utility given a budget constraint. The two approaches differ by the budget constraints. In Bühlmann's definition the vector that assigns the budget constraint is given a priori. On the contrary, in the SORTE approach, the vector that assigns the budget constraint is endogenously determined by solving a systemic utility maximization. SORTE gives priority to the systemic aspects of the problem, in order to optimize the overall systemic performance, rather than to individual rationality.

Multivariate Systemic Optimal Risk Transfer Equilibrium

“…for a given set of feasible allocations B ⊆ L 0 (Ω, F , P; R N ). We refer to [5] for a detailed discussion regarding such set B, as well as for examples for it. We just stress here the fact that the (possibly X−dependent) set B is meant to model agents' attitude or constraints in the risk exchange procedure at terminal time.…”

“…A Systemic Optimal Risk Transfer Equilibrium, denoted with SORTE, was introduced and analyzed in [5]. The SORTE concept was inspired by Bühlmann's notion of a Risk Transfer Equilibrium in insurance-reinsurance markets.…”

“…On the contrary, in the SORTE, such a vector is endogenously determined by solving a systemic utility maximization problem. As remarked in [5], "SORTE gives priority to the systemic aspects of the problem, in order to optimize the overall systemic performance, rather than to individual rationality". We refer to [5] for a more detailed motivation underlying the concept of a SORTE, as well as for the study of its existence, uniqueness and Pareto optimality.…”

“…As remarked in [5], "SORTE gives priority to the systemic aspects of the problem, in order to optimize the overall systemic performance, rather than to individual rationality". We refer to [5] for a more detailed motivation underlying the concept of a SORTE, as well as for the study of its existence, uniqueness and Pareto optimality. In Section 1.1 we will only very briefly recall its definition in order to compare it with the results of the present paper.…”

“…The capital allocation and risk sharing equilibrium that we consider in this new work, similarly to the one introduced in [5], can be applied to many contexts, such as: equilibrium among financial institutions, agents, or countries; insurance and reinsurance markets; capital allocation among business units of a single firm; wealth allocation among investors.…”